@article{dadashova_smith_haider_2024, title={Local Identifiability Analysis, Parameter Subset Selection and Verification for a Minimal Brain PBPK Model}, volume={86}, ISSN={["1522-9602"]}, url={https://doi.org/10.1007/s11538-023-01234-4}, DOI={10.1007/s11538-023-01234-4}, number={2}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Dadashova, Kamala and Smith, Ralph C. and Haider, Mansoor A.}, year={2024}, month={Feb} }
 @article{nguyen_jameson_baldwin_nardini_smith_haugh_flores_2024, title={Quantifying collective motion patterns in mesenchymal cell populations using topological data analysis and agent-based modeling}, volume={370}, ISSN={["1879-3134"]}, DOI={10.1016/j.mbs.2024.109158}, journal={MATHEMATICAL BIOSCIENCES}, author={Nguyen, Kyle C. and Jameson, Carter D. and Baldwin, Scott A. and Nardini, John T. and Smith, Ralph C. and Haugh, Jason M. and Flores, Kevin B.}, year={2024}, month={Apr} }
 @article{smith_2023, title={Controller Design for Distributed Parameter Systems}, volume={43}, ISSN={["1941-000X"]}, url={https://doi.org/10.1109/MCS.2022.3216693}, DOI={10.1109/MCS.2022.3216693}, abstractNote={by KIRSTEN A. MORRIS}, number={1}, journal={IEEE CONTROL SYSTEMS MAGAZINE}, author={Smith, Ralph C. C.}, year={2023}, month={Feb}, pages={98–100} }
 @article{rostkowski_meurisse_thornton_smith_panesi_2022, title={Effects of problem complexity reduction on parameter sensitivity and classification in charring ablator scenarios}, volume={124}, ISSN={["1626-3219"]}, DOI={10.1016/j.ast.2022.107522}, abstractNote={We investigate here effects of adaptations like dimension reduction, omission of parameter correlation, and grid refinement on parameter influence over material temperature response and total recession. The task is accomplished by applying Morris screening and method of Sobol' sensitivity studies applied to a range of 3-D, 1-D, and 1-D TC1-driver cases for the MSL entry through the Martian atmosphere, where the material response of the MSL heat shield is simulated with NASA's PATO toolbox. Results of the investigation show that lower-dimensional approaches can, in some cases, be utilized for initial parameter screening prior to execution of a fully-detailed simulation, but in general, obtained sensitivities differ. Moreover, coarse computational grids do not impose significantly distinct input-output mechanics and can be utilized for accurate screening and quantitative sensitivity analysis exercises even with non-negligible residual values. The investigation also discusses the implications of an unknown correlation structure on parameter sensitivities while finding little evidence of significant correlation effects on parameter classification given input uncertainty bounds defined in this work.}, journal={AEROSPACE SCIENCE AND TECHNOLOGY}, author={Rostkowski, Przemyslaw and Meurisse, Jeremie B. E. and Thornton, John M. and Smith, Ralph C. and Panesi, Marco}, year={2022}, month={May} }
 @article{michaud_schmidt_smith_mattingly_2021, title={A hierarchical Bayesian model for background variation in radiation source localization}, volume={1002}, ISSN={["1872-9576"]}, DOI={10.1016/j.nima.2021.165288}, abstractNote={In this paper, we apply a new model to account for varying background radiation in radiological source localization. We present a hierarchical Bayesian model that simultaneously infers background and source location parameters without requiring separate estimation of the background radiation at each detector location. We employ a simplified photon transport model to reduce the computational expense of Bayesian model calibration. We demonstrate the model accuracy by localizing a cesium-137 source in a simulated city block, and we analyze experimental field measurements with varying background. In both cases, the model provides sufficient fidelity that we can locate the source while simultaneously estimating background radiation.}, journal={NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT}, author={Michaud, Isaac J. and Schmidt, Kathleen and Smith, Ralph C. and Mattingly, John}, year={2021}, month={Jun} }
 @article{miles_pash_smith_oates_2021, title={Bayesian inference and uncertainty propagation using efficient fractional-order viscoelastic models for dielectric elastomers}, volume={32}, ISSN={["1530-8138"]}, url={https://doi.org/10.1177/1045389X20969847}, DOI={10.1177/1045389X20969847}, abstractNote={ Dielectric elastomers are employed for a wide variety of adaptive structures. Many of these soft elastomers exhibit significant rate-dependencies in their response. Accurately quantifying this viscoelastic behavior is non-trivial and in many cases a nonlinear modeling framework is required. Fractional-order operators have been applied to modeling viscoelastic behavior for many years, and recent research has shown fractional-order methods to be effective for nonlinear frameworks. This implementation can become computationally expensive to achieve an accurate approximation of the fractional-order derivative. Accurate estimation of the elastomer’s viscoelastic behavior to quantify parameter uncertainty motivates the use of Markov Chain Monte Carlo (MCMC) methods. Since MCMC is a sampling based method, requiring many model evaluations, efficient estimation of the fractional derivative operator is crucial. In this paper, we demonstrate the effectiveness of using quadrature techniques to approximate the Riemann–Liouville definition for fractional derivatives in the context of estimating the uncertainty of a nonlinear viscoelastic model. We also demonstrate the use of parameter subset selection techniques to isolate parameters that are identifiable in the sense that they are uniquely determined by measured data. For those identifiable parameters, we employ Bayesian inference to compute posterior distributions for parameters. Finally, we propagate parameter uncertainties through the models to compute prediction intervals for quantities of interest. }, number={4}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, publisher={SAGE Publications}, author={Miles, Paul R. and Pash, Graham T. and Smith, Ralph C. and Oates, William S.}, year={2021}, month={Mar}, pages={486–496} }
 @article{pearce_nellenbach_smith_brown_haider_2021, title={Modeling and Parameter Subset Selection for Fibrin Polymerization Kinetics with Applications to Wound Healing}, volume={83}, ISSN={["1522-9602"]}, url={https://doi.org/10.1007/s11538-021-00876-6}, DOI={10.1007/s11538-021-00876-6}, abstractNote={During the hemostatic phase of wound healing, vascular injury leads to endothelial cell damage, initiation of a coagulation cascade involving platelets, and formation of a fibrin-rich clot. As this cascade culminates, activation of the protease thrombin occurs and soluble fibrinogen is converted into an insoluble polymerized fibrin network. Fibrin polymerization is critical for bleeding cessation and subsequent stages of wound healing. We develop a cooperative enzyme kinetics model for in vitro fibrin matrix polymerization capturing dynamic interactions among fibrinogen, thrombin, fibrin, and intermediate complexes. A tailored parameter subset selection technique is also developed to evaluate parameter identifiability for a representative data curve for fibrin accumulation in a short-duration in vitro polymerization experiment. Our approach is based on systematic analysis of eigenvalues and eigenvectors of the classical information matrix for simulations of accumulating fibrin matrix via optimization based on a least squares objective function. Results demonstrate robustness of our approach in that a significant reduction in objective function cost is achieved relative to a more ad hoc curve-fitting procedure. Capabilities of this approach to integrate non-overlapping subsets of the data to enhance the evaluation of parameter identifiability are also demonstrated. Unidentifiable reaction rate parameters are screened to determine whether individual reactions can be eliminated from the overall system while preserving the low objective cost. These findings demonstrate the high degree of information within a single fibrin accumulation curve, and a tailored model and parameter subset selection approach for improving optimization and reducing model complexity in the context of polymerization experiments.}, number={5}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Pearce, Katherine J. and Nellenbach, Kimberly and Smith, Ralph C. and Brown, Ashley C. and Haider, Mansoor A.}, year={2021}, month={May} }
 @article{miles_cook_angers_swenson_kiedrowski_mattingly_smith_2021, title={Radiation Source Localization Using Surrogate Models Constructed from 3-D Monte Carlo Transport Physics Simulations}, volume={207}, ISSN={["1943-7471"]}, DOI={10.1080/00295450.2020.1738796}, abstractNote={Abstract Recent research has focused on the development of surrogate models for radiation source localization in a simulated urban domain. We employ the Monte Carlo N-Particle (MCNP) code to provide high-fidelity simulations of radiation transport within an urban domain. The model is constructed to employ a source location ( ) as input and return the estimated count rate for a set of specified detector locations. Because MCNP simulations are computationally expensive, we develop efficient and accurate surrogate models of the detector responses. We construct surrogate models using Gaussian processes and neural networks that we train and verify using the MCNP simulations. The trained surrogate models provide an efficient framework for Bayesian inference and experimental design. We employ Delayed Rejection Adaptive Metropolis (DRAM), a Markov Chain Monte Carlo algorithm, to infer the location and intensity of an unknown source. The DRAM results yield a posterior probability distribution for the source’s location conditioned on the observed detector count rates. The posterior distribution exhibits regions of high and low probability within the simulated environment identifying potential source locations. In this manner, we can quantify the source location to within at least one of these regions of high probability in the considered cases. Employing these methods, we are able to reduce the space of potential source locations by at least 60%.}, number={1}, journal={NUCLEAR TECHNOLOGY}, author={Miles, Paul R. and Cook, Jared A. and Angers, Zoey V. and Swenson, Christopher J. and Kiedrowski, Brian C. and Mattingly, John and Smith, Ralph C.}, year={2021}, month={Jan}, pages={37–53} }
 @article{hollis_smith_wilson_2021, title={SURROGATE BASED MUTUAL INFORMATION APPROXIMATION AND OPTIMIZATION FOR URBAN SOURCE LOCALIZATION}, volume={11}, ISSN={["2152-5099"]}, url={http://dx.doi.org/10.1615/int.j.uncertaintyquantification.2021034400}, DOI={10.1615/Int.J.UncertaintyQuantification.2021034400}, abstractNote={The ability to efficiently and accurately localize potentially threatening nuclear radiation sources in urban environments is of critical importance to national security. Techniques to infer the location and intensity of a source using data from a configuration of radiation detectors, and the effectiveness of the source localization depends critically on how the detectors are configured. In this paper, we introduce a framework that uses surrogate models to efficiently compare and optimize different detector configurations. We compare our technique to others and demonstrate its effectiveness for selecting optimal detector configurations in the context of urban source localization.}, number={5}, journal={INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION}, publisher={Begell House}, author={Hollis, Andrew N. and Smith, Ralph C. and Wilson, Alyson G.}, year={2021}, pages={39–55} }
 @article{gao_miles_smith_oates_2021, title={The maximum entropy method for data fusion and uncertainty quantification in multifunctional materials and structures}, volume={10}, ISSN={["1530-8138"]}, url={https://doi.org/10.1177/1045389X211048220}, DOI={10.1177/1045389X211048220}, abstractNote={ The quantification of uncertainty in intelligent material systems and structures requires methods to objectively compare complex models to measurements, where the majority of cases include multiple model outputs and quantities of interests given multiphysics coupling. This creates questions about constructing appropriate measures of uncertainty during fusion of data and comparisons between data and models. Novel materials with complex or poorly understood coupling can benefit from advanced statistical analysis to judge models in light of multiphysics data. Here, we apply the Maximum Entropy (ME) method to more complicated ferroelectric single crystals containing domain structures and soft electrostrictive membranes under both mechanical and electrical loading. Multiple quantities of interest are considered, which requires fusing heterogeneous information together when quantifying the uncertainty of lower fidelity models. We find that parameters, which were initially unidentifiable using a single quantity of interest, become identifiable using multiple quantities of interest. We also show that posterior densities may broaden or narrow when multiple data sets are fused together. This is likely due to conflict or agreement, respectively, between the different quantities of interest and the multiple model outputs. Such information is important to advance our predictions of intelligent materials and structures from multi-model inputs and heterogeneous data. }, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, publisher={SAGE Publications}, author={Gao, Wei and Miles, Paul R. and Smith, Ralph C. and Oates, William S.}, year={2021}, month={Oct} }
 @article{peerless_kwansa_hawkins_smith_yingling_2021, title={Uncertainty Quantification and Sensitivity Analysis of Partial Charges on Macroscopic Solvent Properties in Molecular Dynamics Simulations with a Machine Learning Model}, volume={61}, ISSN={["1549-960X"]}, url={https://doi.org/10.1021/acs.jcim.0c01204}, DOI={10.1021/acs.jcim.0c01204}, abstractNote={The molecular dynamics (MD) simulation technique is among the most broadly used computational methods to investigate atomistic phenomena in a variety of chemical and biological systems. One of the most common (and most uncertain) parametrization steps in MD simulations of soft materials is the assignment of partial charges to atoms. Here, we apply uncertainty quantification and sensitivity analysis calculations to assess the uncertainty associated with partial charge assignment in the context of MD simulations of an organic solvent. Our results indicate that the effect of partial charge variance on bulk properties, such as solubility parameters, diffusivity, dipole moment, and density, measured from MD simulations is significant; however, measured properties are observed to be less sensitive to partial charges of less accessible (or buried) atoms. Diffusivity, for example, exhibits a global sensitivity of up to 22 × 10-5 cm2/s per electron charge on some acetonitrile atoms. We then demonstrate that machine learning techniques, such as Gaussian process regression (GPR), can be effective and rapid tools for uncertainty quantification of MD simulations. We show that the formulation and application of an efficient GPR surrogate model for the prediction of responses effectively reduces the computational time of additional sample points from hours to milliseconds. This study provides a much-needed context for the effect that partial charge uncertainty has on MD-derived material properties to illustrate the benefit of considering partial charges as distributions rather than point-values. To aid in this treatment, this work then demonstrates methods for rapid characterization of resulting sensitivity in MD simulations.}, number={4}, journal={JOURNAL OF CHEMICAL INFORMATION AND MODELING}, publisher={American Chemical Society (ACS)}, author={Peerless, James S. and Kwansa, Albert L. and Hawkins, Branden S. and Smith, Ralph C. and Yingling, Yaroslava G.}, year={2021}, month={Apr}, pages={1745–1761} }
 @article{alexanderian_gremaud_smith_2020, title={Variance-based sensitivity analysis for time-dependent processes}, volume={196}, ISSN={["1879-0836"]}, DOI={10.1016/j.ress.2019.106722}, abstractNote={The global sensitivity analysis of time-dependent processes requires history-aware approaches. We develop for that purpose a variance-based method that leverages the correlation structure of the problems under study and employs surrogate models to accelerate the computations. The errors resulting from fixing unimportant uncertain parameters to their nominal values are analyzed through a priori estimates. We illustrate our approach on a harmonic oscillator example and on a nonlinear dynamic cholera model.}, journal={RELIABILITY ENGINEERING & SYSTEM SAFETY}, author={Alexanderian, Alen and Gremaud, Pierre A. and Smith, Ralph C.}, year={2020}, month={Apr} }
 @article{gordon_gilkey_smith_michaud_williams_mousseau_hooper_jones_2019, title={A Mutual Information-Based Experimental Design Framework to Use High-Fidelity Nuclear Reactor Codes to Calibrate Low-Fidelity Codes}, volume={205}, ISSN={["1943-7471"]}, DOI={10.1080/00295450.2019.1590073}, abstractNote={Abstract Simulation-based nuclear reactor design requires highly efficient codes that quantify the requisite physics while having the efficiency required for optimization-based design and uncertainty quantification. To achieve the required accuracy and predictive capabilities, phenomenological parameters, often employed in closure relations or to quantify unmodeled or unresolved physics, must be calibrated for considered reactor conditions and designs. When available, experimental data with quantified observation errors are ideally employed for calibration. However, for many thermal-hydraulic, fuel, and Chalk River Unidentified Deposits modeling regimes, experimental data are prohibitively expensive or impossible to collect. For such cases, we demonstrate the use of a mutual information–based experimental design framework to employ validated high-fidelity codes to calibrate parameters in low-fidelity design codes. We demonstrate the use of the high-fidelity computational fluid dynamics package STAR-CCM+ to calibrate the turbulent mixing coefficient β in COBRA-TF (CTF). This includes the construction and verification of a surrogate for CTF, which permits the computationally intensive experimental design and Bayesian calibration steps. We also demonstrate Bayesian inference of parameter distributions for the Dittus-Boelter relation and propagation of these uncertainties through CTF to improve uncertainty bounds for computed maximum fuel temperatures.}, number={12}, journal={NUCLEAR TECHNOLOGY}, author={Gordon, Natalie and Gilkey, Lindsay and Smith, Ralph C. and Michaud, Isaac and Williams, Brian and Mousseau, Vincent and Hooper, Russell and Jones, Chris}, year={2019}, month={Dec}, pages={1685–1696} }
 @article{leon_miles_smith_oates_2019, title={Active subspace analysis and uncertainty quantification for a polydomain ferroelectric phase-field model}, volume={30}, ISSN={["1530-8138"]}, DOI={10.1177/1045389X19853636}, abstractNote={ We perform parameter subset selection and uncertainty analysis for phase-field models that are applied to the ferroelectric material lead titanate. A motivating objective is to determine which parameters are influential in the sense that their uncertainties directly affect the uncertainty in the model response, and fix noninfluential parameters at nominal values for subsequent uncertainty propagation. We employ Bayesian inference to quantify the uncertainties of gradient exchange parameters governing 180° and 90° tetragonal phase domain wall energies. The uncertainties of influential parameters determined by parameter subset selection are then propagated through the models to obtain credible intervals when estimating energy densities quantifying polarization and strain across domain walls. The results illustrate various properties of Landau and electromechanical coupling parameters and their influence on domain wall interactions. We employ energy statistics, which quantify distances between statistical observations, to compare credible intervals constructed using a complete set of parameters against an influential subset of parameters. These intervals are obtained from the uncertainty propagation of the model input parameters on the domain wall energy densities. The investigation provides critical insight into the development of parameter subset selection, uncertainty quantification, and propagation methodologies for material modeling domain wall structure evolution, informed by density functional theory simulations. }, number={14}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Leon, Lider S. and Miles, Paul R. and Smith, Ralph C. and Oates, William S.}, year={2019}, month={Aug}, pages={2027–2051} }
 @article{cook_smith_hite_stefanescu_mattingly_2019, title={Application and Evaluation of Surrogate Models for Radiation Source Search}, volume={12}, ISSN={["1999-4893"]}, DOI={10.3390/a12120269}, abstractNote={Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuous derivatives preclude the use of gradient-based optimization or data assimilation algorithms. We consider the problem of inferring the 2D location and intensity of a radiation source in an urban environment using a ray-tracing model based on Boltzmann transport theory. Whereas the code implementing this model is relatively efficient, extension to 3D Monte Carlo transport simulations precludes subsequent Bayesian inference to infer source locations, which typically requires thousands to millions of simulations. Additionally, the resulting likelihood exhibits discontinuous derivatives due to the presence of buildings. To address these issues, we discuss the construction of surrogate models for optimization, Bayesian inference, and uncertainty propagation. Specifically, we consider surrogate models based on Legendre polynomials, multivariate adaptive regression splines, radial basis functions, Gaussian processes, and neural networks. We detail strategies for computing training points and discuss the merits and deficits of each method.}, number={12}, journal={ALGORITHMS}, author={Cook, Jared A. and Smith, Ralph C. and Hite, Jason M. and Stefanescu, Razvan and Mattingly, John}, year={2019}, month={Dec} }
 @article{cleaves_alexanderian_guy_smith_yu_2019, title={DERIVATIVE-BASED GLOBAL SENSITIVITY ANALYSIS FOR MODELS WITH HIGH-DIMENSIONAL INPUTS AND FUNCTIONAL OUTPUTS}, volume={41}, ISSN={["1095-7197"]}, DOI={10.1137/19M1243518}, abstractNote={We present a framework for derivative-based global sensitivity analysis (GSA) for models with high-dimensional input parameters and functional outputs. We combine ideas from derivative-based GSA, random field representation via Karhunen--Lo\`{e}ve expansions, and adjoint-based gradient computation to provide a scalable computational framework for computing the proposed derivative-based GSA measures. We illustrate the strategy for a nonlinear ODE model of cholera epidemics and for elliptic PDEs with application examples from geosciences and biotransport.}, number={6}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Cleaves, Helen L. and Alexanderian, Alen and Guy, Hayley and Smith, Ralph C. and Yu, Meilin}, year={2019}, pages={A3524–A3551} }
 @article{miles_pash_smith_oates_2019, title={Global Sensitivity Analysis of Fractional-Order Viscoelasticity Models}, volume={10968}, ISSN={["1996-756X"]}, DOI={10.1117/12.2514160}, abstractNote={In this paper, we investigate hyperelastic and viscoelastic model parameters using Global Sensitivity Analysis (GSA). These models are used to characterize the physical response of many soft-elastomers, which are used in a wide variety of smart material applications. Recent research has shown the effectiveness of using fractionalorder calculus operators in modeling the viscoelastic response. The GSA is performed using parameter subset selection (PSS), which quantifies the relative parameter contributions to the linear and nonlinear, fractionalorder viscoelastic models. Calibration has been performed to quantify the model parameter uncertainty; however, this analysis has led to questions regarding parameter sensitivity and whether or not the parameters can be uniquely identified given the available data. By performing GSA we can determine which parameters are most influential in the model, and fix non-influential parameters at a nominal value. The model calibration can then be performed to quantify the uncertainty of the influential parameters.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS XIII}, author={Miles, Paul R. and Pash, Graham T. and Smith, Ralph C. and Oates, William S.}, year={2019} }
 @article{coleman_lewis_smith_williams_morris_khuwaileh_2019, title={Gradient-Free Construction of Active Subspaces for Dimension Reduction in Complex Models with Applications to Neutronics}, volume={7}, ISSN={["2166-2525"]}, DOI={10.1137/16M1075119}, abstractNote={Recent developments in the field of reduced-order modeling---and, in particular, active subspace construction---have made it possible to efficiently approximate complex models by constructing low-o...}, number={1}, journal={SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION}, author={Coleman, Kayla D. and Lewis, Allison and Smith, Ralph C. and Williams, Brian and Morris, Max and Khuwaileh, Bassam}, year={2019}, pages={117–142} }
 @article{alexanderian_reese_smith_yu_2019, title={Model Input and Output Dimension Reduction Using Karhunen-Loeve Expansions With Application to Biotransport}, volume={5}, ISSN={["2332-9025"]}, DOI={10.1115/1.4044317}, abstractNote={Abstract}, number={4}, journal={ASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS PART B-MECHANICAL ENGINEERING}, author={Alexanderian, Alen and Reese, William and Smith, Ralph C. and Yu, Meilin}, year={2019}, month={Dec} }
 @article{olsen_ottesen_smith_olufsen_2019, title={Parameter subset selection techniques for problems in mathematical biology}, volume={113}, ISSN={["1432-0770"]}, DOI={10.1007/s00422-018-0784-8}, abstractNote={Patient-specific models for diagnostics and treatment planning require reliable parameter estimation and model predictions. Mathematical models of physiological systems are often formulated as systems of nonlinear ordinary differential equations with many parameters and few options for measuring all state variables. Consequently, it can be difficult to determine which parameters can reliably be estimated from available data. This investigation highlights pitfalls associated with practical parameter identifiability and subset selection. The latter refer to the process associated with selecting a subset of parameters that can be identified uniquely by parameter estimation protocols. The methods will be demonstrated using five examples of increasing complexity, as well as with patient-specific model predicting arterial blood pressure. This study demonstrates that methods based on local sensitivities are preferable in terms of computational cost and model fit when good initial parameter values are available, but that global methods should be considered when initial parameter value is not known or poorly understood. For global sensitivity analysis, Morris screening provides results in terms of parameter sensitivity ranking at a much lower computational cost.}, number={1-2}, journal={BIOLOGICAL CYBERNETICS}, author={Olsen, Christian Haargaard and Ottesen, Johnny T. and Smith, Ralph C. and Olufsen, Mette S.}, year={2019}, month={Apr}, pages={121–138} }
 @article{bravo_smith_2019, title={Parameter-dependent Surrogate Model Development for PZT Bimorph Actuators Employed for Micro-air Vehicles}, volume={10968}, ISSN={["1996-756X"]}, DOI={10.1117/12.2514246}, abstractNote={In the paper, we discuss the use of the homogenized energy model (HEM) to develop a dynamic mode decomposition surrogate model for a PZT bimorph actuator used for micro-air vehicles including Robobee. The HEM quantifies the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in highly dynamic operating regimes. Due to the computation complexity of the HEM, we must develop a surrogate model. The surrogate model must be parameter- and control-dependent to be able to perform inverse problems or uncertainty quantification in different driving regimes. In the literature, DMD can be adapted to address different control inputs. We will discuss using interpolation over the parameters to adapt the DMD to include parameter dependence. Finally, we will discuss the results and limitations of the new surrogate model.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS XIII}, author={Bravo, Nikolas and Smith, Ralph C.}, year={2019} }
 @article{schmidt_smith_hite_mattingly_azmy_rajan_goldhahn_2019, title={Sequential optimal positioning of mobile sensors using mutual information}, volume={12}, ISSN={["1932-1872"]}, DOI={10.1002/sam.11431}, abstractNote={Abstract}, number={6}, journal={STATISTICAL ANALYSIS AND DATA MINING}, author={Schmidt, Kathleen and Smith, Ralph C. and Hite, Jason and Mattingly, John and Azmy, Yousry and Rajan, Deepak and Goldhahn, Ryan}, year={2019}, month={Dec}, pages={465–478} }
 @article{stefanescu_hite_cook_smith_mattingly_2019, title={Surrogate-Based Robust Design for a Non-Smooth Radiation Source Detection Problem}, volume={12}, ISSN={["1999-4893"]}, DOI={10.3390/a12060113}, abstractNote={In this paper, we develop and numerically illustrate a robust sensor network design to optimally detect a radiation source in an urban environment. This problem exhibits several challenges: penalty functionals are non-smooth due to the presence of buildings, radiation transport models are often computationally expensive, sensor locations are not limited to a discrete number of points, and source intensity and location responses, based on a fixed number of sensors, are not unique. We consider a radiation source located in a prototypical 250 m × 180 m urban setting. To address the non-smooth properties of the model and computationally expensive simulation codes, we employ a verified surrogate model based on radial basis functions. Using this surrogate, we formulate and solve a robust design problem that is optimal in an average sense for detecting source location and intensity with minimized uncertainty.}, number={6}, journal={ALGORITHMS}, author={Stefanescu, Razvan and Hite, Jason and Cook, Jared and Smith, Ralph C. and Mattingly, John}, year={2019}, month={Jun} }
 @article{jones_broughton_iamsasri_fancher_wilson_reich_smith_2019, title={The use of Bayesian inference in the characterization of materials and thin films}, volume={75}, ISSN={["2053-2733"]}, DOI={10.1107/S0108767319097940}, journal={ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES}, author={Jones, Jacob L. and Broughton, Rachel and Iamsasri, Thanakorn and Fancher, Chris M. and Wilson, Alyson G. and Reich, Brian and Smith, Ralph C.}, year={2019}, pages={A211–A211} }
 @article{liu_dinh_smith_sun_2019, title={Uncertainty quantification of two-phase flow and boiling heat transfer simulations through a data-driven modular Bayesian approach}, volume={138}, ISSN={["1879-2189"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85064892196&partnerID=MN8TOARS}, DOI={10.1016/j.ijheatmasstransfer.2019.04.075}, abstractNote={In this paper, we present an approach to inversely quantify the uncertainty of MCFD simulations through a data-driven modular Bayesian inference. Both the model parameter uncertainty and the model form uncertainty are evaluated in the proposed approach. Considering the high-dimensionality of parameter space related to the solver, we performed a sensitivity analysis to reduce the input parameter dimension for the Bayesian inference. Based on the reduced parameter dimension, surrogate models based on Gaussian Process (GP) and Principal Component Analysis (PCA) are constructed to reduce the computational cost in the Bayesian inference. Two case studies based on the proposed approach are performed, focusing on two-phase flow dynamics and on wall boiling heat transfer, respectively. In case study I, we are able to construct a GP-based surrogate model based on 8 principal components to represent the total 208 MCFD solver outputs. Moreover, both cases show that the proposed approach is able to quantify and reduce the parameter uncertainties with the support of experimental measurements. The posterior uncertainties of investigated parameters have 50%-90% narrowed uncertainty ranges compared to their prior uncertainties. Furthermore, a forward uncertainty propagation of the MCFD solver with the obtained uncertainties shows that the agreement between the solver predictions and experimental measurements are significantly improved.}, journal={INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER}, author={Liu, Yang and Dinh, Nam T. and Smith, Ralph C. and Sun, Xiaodong}, year={2019}, month={Aug}, pages={1096–1116} }
 @article{holodnak_ipsen_smith_2018, title={A PROBABILISTIC SUBSPACE BOUND WITH APPLICATION TO ACTIVE SUBSPACES}, volume={39}, ISSN={["1095-7162"]}, url={https://doi.org/10.1137/17M1141503}, DOI={10.1137/17M1141503}, abstractNote={Given a real symmetric positive semi-definite matrix E, and an approximation S that is a sum of n independent matrix-valued random variables, we present bounds on the relative error in S due to randomization. The bounds do not depend on the matrix dimensions but only on the numerical rank (intrinsic dimension) of E. Our approach resembles the low-rank approximation of kernel matrices from random features, but our accuracy measures are more stringent. 
In the context of parameter selection based on active subspaces, where S is computed via Monte Carlo sampling, we present a bound on the number of samples so that with high probability the angle between the dominant subspaces of E and S is less than a user-specified tolerance. This is a substantial improvement over existing work, as it is a non-asymptotic and fully explicit bound on the sampling amount n, and it allows the user to tune the success probability. It also suggests that Monte Carlo sampling can be efficient in the presence of many parameters, as long as the underlying function f is sufficiently smooth.}, number={3}, journal={SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Holodnak, John T. and Ipsen, Ilse C. F. and Smith, Ralph C.}, year={2018}, pages={1208–1220} }
 @article{leon_smith_miles_oates_2018, title={Active Subspace Uncertainty Quantification for a Polydomain Ferroelectric Phase-Field Model}, volume={10596}, ISSN={["1996-756X"]}, DOI={10.1117/12.2297207}, abstractNote={Quantum-informed ferroelectric phase field models capable of predicting material behavior, are necessary for facilitating the development and production of many adaptive structures and intelligent systems. Uncertainty is present in these models, given the quantum scale at which calculations take place. A necessary analysis is to determine how the uncertainty in the response can be attributed to the uncertainty in the model inputs or parameters. A second analysis is to identify active subspaces within the original parameter space, which quantify directions in which the model response varies most dominantly, thus reducing sampling effort and computational cost. In this investigation, we identify an active subspace for a poly-domain ferroelectric phase-field model. Using the active variables as our independent variables, we then construct a surrogate model and perform Bayesian inference. Once we quantify the uncertainties in the active variables, we obtain uncertainties for the original parameters via an inverse mapping. The analysis provides insight into how active subspace methodologies can be used to reduce computational power needed to perform Bayesian inference on model parameters informed by experimental or simulated data.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES XII}, author={Leon, Lider S. and Smith, Ralph C. and Miles, Paul and Oates, William S.}, year={2018} }
 @article{leon_smith_oates_miles_2018, title={Analysis of a multi-axial quantum-informed ferroelectric continuum model: Part 2—sensitivity analysis}, volume={29}, ISSN={1045-389X 1530-8138}, url={http://dx.doi.org/10.1177/1045389x18781024}, DOI={10.1177/1045389x18781024}, abstractNote={ We illustrate the use of global sensitivity analysis, and a parameter subset selection algorithm based on local sensitivity analysis, to quantify the relative influence of parameters in polarization and electrostrictive energy relations for a quantum-informed, single-domain, ferroelectric material model. A motivating objective is to determine which parameters are identifiable or influential in the sense that they are uniquely determined by density functional theory–generated data. Noninfluential parameters will be fixed at nominal values for subsequent Bayesian inference, uncertainty propagation, and material design since variations in these parameters are minimally reflected in responses. Whereas global sensitivity analysis is typically based on the assumption of mutually independent, uniformly distributed parameters, we demonstrate that inherent parameter correlations must be accommodated to achieve correct interpretations of parameter influence. For the considered energy functionals, we demonstrate that all of the parameters are influential and will be informed by density functional theory–simulated data. }, number={13}, journal={Journal of Intelligent Material Systems and Structures}, publisher={SAGE Publications}, author={Leon, Lider and Smith, Ralph C and Oates, William S and Miles, Paul}, year={2018}, month={Jul}, pages={2840–2860} }
 @article{brayfindley_smith_mattingly_brigantic_2018, title={Automated Defect Detection in Spent Nuclear Fuel Using Combined Cerenkov Radiation and Gamma Emission Tomography Data}, volume={204}, ISSN={0029-5450 1943-7471}, url={http://dx.doi.org/10.1080/00295450.2018.1490123}, DOI={10.1080/00295450.2018.1490123}, abstractNote={Abstract Spent fuel monitoring and characterization has been central to safeguards and nuclear facility monitoring for many years. The Digital Cerenkov Viewing Device (DCVD) has been used since the 1980s as a method of defect detection in spent fuel. In recent years, the accounting for large quantities of spent fuel before storage has renewed interest in this relatively quick and inexpensive method. This has an impact not only in safeguards, but also for nuclear power facilities, as accounting can be a long, arduous, and costly process. Additionally, the DCVD demonstrates limited accuracy in more complex cases such as substitution of a fuel rod with steel or a partial defect detection. A second method, gamma emission tomography (GET) has been explored as an improved defect detection method, but is much more expensive and invasive than DCVD. The present investigation identifies deficiencies in both methods and proposes a combination of data gathered from each method to address these deficiencies for improved spent fuel characterization. Initial results are promising, showing 97% detection of a single missing fuel rod when the data types are combined, versus approximately 50% and 70%, respectively, for DCVD and GET data on their own. These classification results are obtained with algorithms derived from facial recognition and applied to this problem, yielding unique accuracy in near real time while also maintaining the information barrier between output and measurement desired in safeguards.}, number={3}, journal={Nuclear Technology}, publisher={Informa UK Limited}, author={Brayfindley, Eva and Smith, Ralph C. and Mattingly, John and Brigantic, Robert}, year={2018}, month={Aug}, pages={343–353} }
 @inbook{paterson_reich_smith_wilson_jones_2018, title={Bayesian Approaches to Uncertainty Quantification and Structure Refinement from X-Ray Diffraction}, ISBN={9783319994642 9783319994659}, ISSN={0933-033X 2196-2812}, url={http://dx.doi.org/10.1007/978-3-319-99465-9_4}, DOI={10.1007/978-3-319-99465-9_4}, abstractNote={This chapter introduces classical frequentist and Bayesian inference applied to analyzing diffraction profiles, and the methods are compared and contrasted. The methods are applied to both the modelling of single diffraction profiles and the full profile refinement of crystallographic structures. In the Bayesian method, Markov chain Monte Carlo algorithms are used to sample the distribution of model parameters, allowing for the construction of posterior probability distributions, which provide both parameter estimates and quantifiable uncertainties. We present the application of this method to single peak fitting in lead zirconate titanate, and the crystal structure refinement of a National Institute of Standards and Technology silicon standard reference material.}, booktitle={Materials Discovery and Design}, publisher={Springer International Publishing}, author={Paterson, Alisa R. and Reich, Brian J. and Smith, Ralph C. and Wilson, Alyson G. and Jones, Jacob L.}, year={2018}, pages={81–102} }
 @article{lagergren_reeder_hamilton_smith_flores_2018, title={Forecasting and Uncertainty Quantification Using a Hybrid of Mechanistic and Non-mechanistic Models for an Age-Structured Population Model}, volume={80}, ISSN={0092-8240 1522-9602}, url={http://dx.doi.org/10.1007/s11538-018-0421-7}, DOI={10.1007/s11538-018-0421-7}, abstractNote={In this paper, we present a new method for the prediction and uncertainty quantification of data-driven multivariate systems. Traditionally, either mechanistic or non-mechanistic modeling methodologies have been used for prediction; however, it is uncommon for the two to be incorporated together. We compare the forecast accuracy of mechanistic modeling, using Bayesian inference, a non-mechanistic modeling approach based on state space reconstruction, and a novel hybrid methodology composed of the two for an age-structured population data set. The data come from cannibalistic flour beetles, in which it is observed that the adults preying on the eggs and pupae result in non-equilibrium population dynamics. Uncertainty quantification methods for the hybrid models are outlined and illustrated for these data. We perform an analysis of the results from Bayesian inference for the mechanistic model and hybrid models to suggest reasons why hybrid modeling methodology may enable more accurate forecasts of multivariate systems than traditional approaches.}, number={6}, journal={Bulletin of Mathematical Biology}, publisher={Springer Nature}, author={Lagergren, John and Reeder, Amanda and Hamilton, Franz and Smith, Ralph C. and Flores, Kevin B.}, year={2018}, month={Apr}, pages={1578–1595} }
 @article{bravo_smith_crews_2018, title={Uncertainty Quantification for PZT Bimorph Actuators}, volume={10596}, ISSN={["1996-756X"]}, DOI={10.1117/12.2297148}, abstractNote={In this paper, we discuss the development of a high fidelity model for a PZT bimorph actuator used for micro-air vehicles, which includes the Robobee. We developed a high-fidelity model for the actuator using the homogenized energy model (HEM) framework, which quantifies the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. We then discussed an inverse problem on the model. We included local and global sensitivity analysis of the parameters in the high-fidelity model. Finally, we will discuss the results of Bayesian inference and uncertainty quantification on the HEM.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES XII}, author={Bravo, Nikolas and Smith, Ralph C. and Crews, John}, year={2018} }
 @article{haque_kindrat_zhang_mikheev_kim_liu_chung_kuian_massad_smith_2018, title={Uncertainty-enabled design of electromagnetic reflectors with integrated shape control}, volume={10596}, ISSN={["1996-756X"]}, DOI={10.1117/12.2300396}, abstractNote={We implemented a computationally efficient model for a corner-supported, thin, rectangular, orthotropic polyvinylidene fluoride (PVDF) laminate membrane, actuated by a two-dimensional array of segmented electrodes. The laminate can be used as shape-controlled electromagnetic reflector and the model estimates the reflector’s shape given an array of control voltages. In this paper, we describe a model to determine the shape of the laminate for a given distribution of control voltages. Then, we investigate the surface shape error and its sensitivity to the model parameters. Subsequently, we analyze the simulated deflection of the actuated bimorph using a Zernike polynomial decomposition. Finally, we provide a probabilistic description of reflector performance using statistical methods to quantify uncertainty. We make design recommendations for nominal parameter values and their tolerances based on optimization under uncertainty using multiple methods.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES XII}, author={Haque, Samiul and Kindrat, Laszlo P. and Zhang, Li and Mikheev, Vikenty and Kim, Daewa and Liu, Sijing and Chung, Jooyeon and Kuian, Mykhailo and Massad, Jordan E. and Smith, Ralph C.}, year={2018} }
 @article{iamsasri_guerrier_esteves_fancher_wilson_smith_paisley_johnson-wilke_ihlefeld_bassiri-gharb_et al._2017, title={A Bayesian approach to modeling diffraction profiles and application to ferroelectric materials}, volume={50}, ISSN={1600-5767}, url={http://dx.doi.org/10.1107/S1600576716020057}, DOI={10.1107/S1600576716020057}, abstractNote={A new statistical approach for modeling diffraction profiles is introduced, using Bayesian inference and a Markov chain Monte Carlo (MCMC) algorithm. This method is demonstrated by modeling the degenerate reflections during application of an electric field to two different ferroelectric materials: thin-film lead zirconate titanate (PZT) of composition PbZr0.3Ti0.7O3 and a bulk commercial PZT polycrystalline ferroelectric. The new method offers a unique uncertainty quantification of the model parameters that can be readily propagated into new calculated parameters.}, number={1}, journal={Journal of Applied Crystallography}, publisher={International Union of Crystallography (IUCr)}, author={Iamsasri, Thanakorn and Guerrier, Jonathon and Esteves, Giovanni and Fancher, Chris M. and Wilson, Alyson G. and Smith, Ralph C. and Paisley, Elizabeth A. and Johnson-Wilke, Raegan and Ihlefeld, Jon F. and Bassiri-Gharb, Nazanin and et al.}, year={2017}, month={Feb}, pages={211–220} }
 @article{mcmahan_williams_smith_malaya_2017, title={A Linear Regression Framework for the Verification of Bayesian Model Calibration Algorithms}, volume={2}, ISSN={2377-2158}, url={http://dx.doi.org/10.1115/1.4037705}, DOI={10.1115/1.4037705}, abstractNote={We describe a framework for the verification of Bayesian model calibration routines. The framework is based on linear regression and can be configured to verify calibration to data with a range of observation error characteristics. The framework is designed for efficient implementation and is suitable for verifying code intended for large-scale problems. We propose an approach for using the framework to verify Markov chain Monte Carlo (MCMC) software by combining it with a nonparametric test for distribution equality based on the energy statistic. Our matlab-based reference implementation of the framework is shown to correctly distinguish between output obtained from correctly and incorrectly implemented MCMC routines. Since correctness of output from an MCMC software depends on choosing settings appropriate for the problem-of-interest, our framework can potentially be used for verifying such settings.}, number={2}, journal={Journal of Verification, Validation and Uncertainty Quantification}, publisher={ASME International}, author={McMahan, Jerry A., Jr. and Williams, Brian J. and Smith, Ralph C. and Malaya, Nicholas}, year={2017}, month={Sep}, pages={021006} }
 @inproceedings{gao_oates_smith_2017, title={A maximum entropy approach for uncertainty quantification and analysis of multifunctional materials}, DOI={10.1115/smasis2017-3919}, abstractNote={The Maximum Entropy (ME) method is shown to provide a new approach for quantifying model uncertainty in the presence of complex, heterogeneous data. This is important in model validation of a variety of multifunctional constitutive relations. For example, multifunctional materials contain field-coupled material parameters that should be self-consistent regardless of the measurement. A classical example is piezoelectricity which may be quantified from charge induced by stress or strain induced by an electric field. The proposed tools provide new statistical information to address measurement discrepancies, guide model development, and catalyze materials discovery for data fusion problems. The error between the model outputs and heterogeneous data is quantified and used to formulate a second moment constraint within the entropy functional. This leads to an augmented likelihood function that weights each individual set of data by its respective variance and covariance between each data set. As a first step, the method is evaluated on a piezoelectric ceramic to illustrate how the covariance matrix influences piezoelectric parameter estimation from heterogeneous electric displacement and strain data.}, booktitle={Proceedings of the asme conference on smart materials adaptive}, author={Gao, W. and Oates, W. S. and Smith, Ralph}, year={2017} }
 @inproceedings{oates_smith_2017, title={A multi-axial electromechanically-coupled homogenized energy model for ferroelectric materials}, DOI={10.1115/smasis2017-3848}, abstractNote={In this paper, we discuss the development and implementation of a 3-D electromechanically coupled homogenized energy model (HEM) for ferroelectric materials. A stochastic-based methodology is introduced and applied to problems involving large scale switching of ferroelectric and ferroelastic materials. Switching criteria for polarization variants are developed using density distributions in three dimensions to accommodate both electrical and mechanical loading and their coupled response. The theory accommodates non-proportional loading and major/minor loop hysteresis. Such formulations are known to accelerate computations for real-time control of nonlinear and hysteretic actuators. The proposed formulation maintains superior computational efficiency in the three dimensional case through the application of density formulations that are based on internal distributions of stress and electric field to produce a distribution of polarization switching events over a range of applied fields and stresses.}, booktitle={Proceedings of the asme conference on smart materials adaptive}, author={Oates, W. S. and Smith, Ralph}, year={2017} }
 @article{wentworth_smith_williams_2017, title={Bayesian model calibration and uncertainty quantification for an HIV model using adaptive Metropolis algorithms}, volume={26}, ISSN={1741-5977 1741-5985}, url={http://dx.doi.org/10.1080/17415977.2017.1312365}, DOI={10.1080/17415977.2017.1312365}, abstractNote={In this paper, we discuss Bayesian model calibration and use adaptive Metropolis algorithms to construct densities for input parameters in a previously developed HIV model. To quantify the uncertainty in the parameters, we employ two MCMC algorithms: Delayed Rejection Adaptive Metropolis (DRAM) and Differential Evolution Adaptive Metropolis (DREAM). The densities obtained using these methods are compared to those obtained through direct evaluation of Bayes formula. We also employ uncertainties in input parameters and observation errors to construct prediction intervals for a model response. We verify the accuracy of the Metropolis algorithms by comparing chains, densities and correlations obtained using DRAM, DREAM and direct numerical evaluation of Bayes’ formula. We also perform similar analysis for credible and prediction intervals for responses.}, number={2}, journal={Inverse Problems in Science and Engineering}, publisher={Informa UK Limited}, author={Wentworth, Mami T. and Smith, Ralph C. and Williams, Brian}, year={2017}, month={Apr}, pages={233–256} }
 @article{smith_zwart_2017, title={CPDE special section}, volume={44}, ISSN={["1367-5788"]}, DOI={10.1016/j.arcontrol.2017.09.007}, abstractNote={The world surrounding us has become increasingly technological. Nowadays, the influence of automation is perceived in each aspect of everyday life. If automation makes some aspects of life easier, faster and safer, empirical data also suggests that it could have negative performance and safety consequences regarding human operators, a set of difficulties called the “out-of-the-loop” (OOTL) performance problem. However, after decades of research, this phenomenon remains difficult to grasp and counter. In this paper, we propose a neuroergonomics approach to treat this phenomenon. We first describe how automation impacts human operators. Then, we present the current knowledge relative to this OOTL phenomenon. Finally, we describe how recent insights in neurosciences can help characterize, quantify and compensate this phenomenon.}, journal={ANNUAL REVIEWS IN CONTROL}, author={Smith, Ralph C. and Zwart, Hans}, year={2017}, pages={183–183} }
 @inproceedings{bravo_smith_crews_2017, title={Data-driven model development and feedback control design for PZT bimorph actuators}, DOI={10.1115/smasis2017-3847}, abstractNote={In the paper, we discuss the development of a high-fidelity and surrogate model for a PZT bimorph used as an actuator for micro-air vehicles including Robobee. The models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. The actuator dynamics are initially modeled using the homogenized energy model (HEM) framework. This provides a comprehensive high-fidelity model, which can be inverted and implemented in real time for certain control regimes. To improve efficiency, we additionally discuss the development of data-driven models and focus on the implementation of a surrogate model based on a dynamic mode decomposition (DMD). Finally, we detail the design and implementation of a PI controller on the surrogate and high-fidelity models.}, booktitle={Proceedings of the asme conference on smart materials adaptive}, author={Bravo, N. and Smith, Ralph and Crews, J.}, year={2017} }
 @article{leon_smith_oates_miles_2017, title={Global Sensitivity Analysis for a Quantum Informed Ferroelectric Phase Field Model}, volume={10165}, ISSN={["1996-756X"]}, DOI={10.1117/12.2259945}, abstractNote={We consider global sensitivity analysis (GSA) for correlated parameters in a continuum phase-field model for ferroelectric materials. The model was previously calibrated using density functional theory (DFT) simulations. For single domain ferroelectric lead titanate crystals, GSA is employed to rank the sensitivity of phenomenological parameters governing the Landau energy surface. The sensitivity analysis is based on Sobol’s variance-based decomposition in which the component functions of the high-dimensional representation (HDMR) of the model are computed analytically. For the subset of parameters that are most correlated, high-order component functions and sensitivity indices are found to be significant.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2017}, author={Leon, Lider S. and Smith, Ralph C. and Oates, William S. and Miles, Paul}, year={2017} }
 @article{ştefănescu_schmidt_hite_smith_mattingly_2017, title={Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem}, volume={111}, ISSN={0029-5981}, url={http://dx.doi.org/10.1002/nme.5491}, DOI={10.1002/nme.5491}, abstractNote={We propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 × 180 m block of an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Owing to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms composed of mixed optimization techniques. For global optimization, we consider simulated annealing, particle swarm, and genetic algorithm, which rely solely on objective function evaluations; that is, they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo‐optimum point is obtained. This is subsequently utilized as the initial value by the deterministic implicit filtering method, which is able to find local extrema in non‐smooth functions, to finish the search in a narrow domain. These new hybrid techniques, combining global optimization and implicit filtering address, difficulties associated with the non‐smooth response, and their performances, are shown to significantly decrease the computational time over the global optimization methods. To quantify uncertainties associated with the source location and intensity, we employ the delayed rejection adaptive Metropolis and DiffeRential Evolution Adaptive Metropolis algorithms. Marginal densities of the source properties are obtained, and the means of the chains compare accurately with the estimates produced by the hybrid algorithms. Copyright © 2016 John Wiley & Sons, Ltd.}, number={10}, journal={International Journal for Numerical Methods in Engineering}, publisher={Wiley}, author={Ştefănescu, Răzvan and Schmidt, Kathleen and Hite, Jason and Smith, Ralph C. and Mattingly, John}, year={2017}, month={Feb}, pages={955–982} }
 @inproceedings{leon_smith_oates_miles_2017, title={Identifiability and active subspace analysis for a polydomain ferroelectric phase field model}, DOI={10.1115/smasis2017-3845}, abstractNote={We consider subset selection and active subspace techniques for parameters in a continuum phase-field polydomain model for ferroelectric materials. This analysis is necessary to mathematically determine the parameter subset or subspace critically affecting the response, prior to model calibration using either experimental or synthetic data constructed using density functional theory (DFT) simulations. For the 180° domain wall model, we employ identifiability analysis using a Fisher information matrix methodology, and subspace selection to determine the active subspace. We demonstrate the implementation and interpretation of techniques that accommodate the model structure and discuss results in the context of identifiable parameter subsets and active subspaces quantifying the strongest influence on the model output. Our results indicate that the governing domain wall gradient energy exchange parameter is most identifiable.}, booktitle={Proceedings of the asme conference on smart materials adaptive}, author={Leon, L. S. and Smith, Ralph and Oates, W. S. and Miles, P.}, year={2017} }
 @article{bravo_smith_crews_2017, title={Surrogate Model Development and Feedforward Control Implementation for PZT Bimorph Actuators Employed for Robobee}, volume={10165}, ISSN={["1996-756X"]}, DOI={10.1117/12.2259948}, abstractNote={In this paper, we discuss the development of models for PZT bimorph actuators used to power micro-air vehicles including Robobee. Due to the highly dynamic drive regimes required for the actuators, models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT. We first employ the homogenized energy model (HEM) framework to model the actuator dynamics. This provides a comprehensive model, which can be inverted and implemented for certain control regimes. We additionally discuss the development of data-driven models and focus on the implementation of a model based on a dynamic mode decomposition (DMD). Finally, we detail attributes of both approaches for uncertainty quantification and real-time control implementation.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2017}, author={Bravo, Nikolas and Smith, Ralph C. and Crews, John}, year={2017} }
 @article{miles_leon_smith_oates_2017, title={Uncertainty Analysis of Continuum Phase Field Modeling in 180 degrees Domain Wall Structures}, volume={10165}, ISSN={["1996-756X"]}, DOI={10.1117/12.2260130}, abstractNote={The evolution and formation of domain structures in ferroelectric materials is modeled using a continuum phase field approach and compared with density functional theory (DFT) using Bayesian uncertainty analysis. These simulations are carried out on the ferroelectric, lead titanate. Self-consistency between DFT and the continuum approach is advantageous when computing polydomain structures and domain wall dynamics. There is uncertainty in the phenomenological parameters related to the Landau energy, electrostriction, and twinned domain wall energy in single and polydomain ferroelectric crystals. To quantify the model parameter uncertainty associated with the phase field model, Bayesian statistics were used. Specifically, we will focus on estimating the value of the exchange parameters associated with polarization gradients. The phase field model predictions for the 180° domain wall energy are calibrated based upon DFT calculations. Model predictions of domain wall size are found to be on the same order as DFT calculations.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2017}, author={Miles, Paul and Leon, Lider and Smith, Ralph and Oates, William}, year={2017} }
 @inproceedings{miles_oates_leon_smith_2017, title={Uncertainty analysis of ferroelectric polydomain structures}, DOI={10.1115/smasis2017-3916}, abstractNote={Ferroelectric materials exhibit strong electromechanical behavior which has led to the production of a wide variety of adaptive structures and intelligent systems, ranging from structural health monitoring sensors, energy harvesting circuits, and flow control actuators. Given the large number of applications, accurate prediction of ferroelectric materials constitutive behavior is critical. This presents many challenges, including the need to predict behavior from electronic structures up to macroscropic continuum. Many of the structure-property relations in these materials can be accurately calculated using density functional theory (DFT). However, DFT is not necessarily conducive to the large scale computations required to solve these problems on a continuum scale. Introducing a phase field polarization order parameter is an alternative approach, which provides a means to simulate the length scale gap between nano- and microscale domain structure evolution. The introduction of the phase field approximation results in uncertainty. Bayesian statistical analysis is an ideal tool for quantifying the uncertainty associated with the continuum phase field model parameters. Analyses of monodomain structures allows for identification of Landau energy and electrostrictive stress parameters. Identifying the exchange parameters, which are proportional to the polarization gradients, requires consideration of polydomain structures. This is a nontrivial problem as domain wall structures are fully coupled between the Landau energy, electrostrictive, and exchange parameters. Accurately quantifying the uncertainty in the phase field parameters will provide insight into the nonlinear constitutive behavior.}, booktitle={Proceedings of the asme conference on smart materials adaptive}, author={Miles, P. and Oates, W. and Leon, L. and Smith, Ralph}, year={2017} }
 @article{nelson_azmy_gardner_mattingly_smith_worrall_dewji_2017, title={Validation and uncertainty quantification of detector response functions for a 1″×2″ NaI collimated detector intended for inverse radioisotope source mapping applications}, volume={410}, ISSN={0168-583X}, url={http://dx.doi.org/10.1016/j.nimb.2017.07.015}, DOI={10.1016/j.nimb.2017.07.015}, abstractNote={Detector response functions (DRFs) are often used for inverse analysis. We compute the DRF of a sodium iodide (NaI) nuclear material holdup field detector using the code named g03 developed by the Center for Engineering Applications of Radioisotopes (CEAR) at NC State University. Three measurement campaigns were performed in order to validate the DRF’s constructed by g03: on-axis detection of calibration sources, off-axis measurements of a highly enriched uranium (HEU) disk, and on-axis measurements of the HEU disk with steel plates inserted between the source and the detector to provide attenuation. Furthermore, this work quantifies the uncertainty of the Monte Carlo simulations used in and with g03, as well as the uncertainties associated with each semi-empirical model employed in the full DRF representation. Overall, for the calibration source measurements, the response computed by the DRF for the prediction of the full-energy peak region of responses was good, i.e. within two standard deviations of the experimental response. In contrast, the DRF tended to overestimate the Compton continuum by about 45–65% due to inadequate tuning of the electron range multiplier fit variable that empirically represents physics associated with electron transport that is not modeled explicitly in g03. For the HEU disk measurements, computed DRF responses tended to significantly underestimate (more than 20%) the secondary full-energy peaks (any peak of lower energy than the highest-energy peak computed) due to scattering in the detector collimator and aluminum can, which is not included in the g03 model. We ran a sufficiently large number of histories to ensure for all of the Monte Carlo simulations that the statistical uncertainties were lower than their experimental counterpart’s Poisson uncertainties. The uncertainties associated with least-squares fits to the experimental data tended to have parameter relative standard deviations lower than the peak channel relative standard deviation in most cases and good reduced chi-square values. The highest sources of uncertainty were identified as the energy calibration polynomial factor (due to limited source availability and NaI resolution) and the Ba-133 peak fit (only a very weak source was available), which were 20% and 10%, respectively.}, journal={Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms}, publisher={Elsevier BV}, author={Nelson, N. and Azmy, Y. and Gardner, R.P. and Mattingly, J. and Smith, R. and Worrall, L.G. and Dewji, S.}, year={2017}, month={Nov}, pages={1–15} }
 @article{schmidt_smith_2016, title={A PARAMETER SUBSET SELECTION ALGORITHM FORMIXED-EFFECTS MODELS}, volume={6}, ISSN={["2152-5099"]}, DOI={10.1615/int.j.uncertaintyquantification.2016016469}, abstractNote={Mixed-effects models are commonly used to statistically model phenomena that include attributes associated with a population or general underlying mechanism as well as effects specific to individuals or components of the general mechanism. This can include individual effects associated with data from multiple experiments. However, the parameterizations used to incorporate the population and individual effects are often unidentifiable in the sense that parameters are not uniquely specified by the data. As a result, the current literature focuses on model selection, by which insensitive parameters are fixed or removed from the model. Model selection methods that employ information criteria are applicable to both linear and nonlinear mixed-effects models, but such techniques are limited in that they are computationally prohibitive for large problems due to the number of possible models that must be tested. To limit the scope of possible models for model selection via information criteria, we introduce a parameter subset selection (PSS) algorithm for mixed-effects models, which orders the parameters by their significance. We provide examples to verify the effectiveness of the PSS algorithm and to test the performance of mixed-effects model selection that makes use of parameter subset selection.}, number={5}, journal={INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION}, author={Schmidt, Kathleen L. and Smith, Ralph C.}, year={2016}, pages={405–416} }
 @article{smith_anderson_hartl_atulasimha_sarles_wissa_shafer_2016, title={Adaptive and active materials: selected papers from the ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems (SMASIS 15) (Colorado Springs, CO, USA, 21-23 September 2015)}, volume={25}, ISSN={["1361-665X"]}, DOI={10.1088/0964-1726/25/10/100201}, number={10}, journal={SMART MATERIALS AND STRUCTURES}, author={Smith, Ralph C. and Anderson, Iain and Hartl, Darren and Atulasimha, Jayasimha and Sarles, Stephen A. and Wissa, Aimy and Shafer, Michael}, year={2016}, month={Oct} }
 @article{lewis_smith_williams_figueroa_2016, title={An information theoretic approach to use high-fidelity codes to calibrate low-fidelity codes}, volume={324}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2016.08.001}, abstractNote={For many simulation models, it can be prohibitively expensive or physically infeasible to obtain a complete set of experimental data to calibrate model parameters. In such cases, one can alternatively employ validated higher-fidelity codes to generate simulated data, which can be used to calibrate the lower-fidelity code. In this paper, we employ an information-theoretic framework to determine the reduction in parameter uncertainty that is obtained by evaluating the high-fidelity code at a specific set of design conditions. These conditions are chosen sequentially, based on the amount of information that they contribute to the low-fidelity model parameters. The goal is to employ Bayesian experimental design techniques to minimize the number of high-fidelity code evaluations required to accurately calibrate the low-fidelity model. We illustrate the performance of this framework using heat and diffusion examples, a 1-D kinetic neutron diffusion equation, and a particle transport model, and include initial results from the integration of the high-fidelity thermal-hydraulics code Hydra-TH with a low-fidelity exponential model for the friction correlation factor.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Lewis, Allison and Smith, Ralph and Williams, Brian and Figueroa, Victor}, year={2016}, month={Nov}, pages={24–43} }
 @inproceedings{hite_mattingly_schmidt_stelanescu_smith_2016, title={Bayesian metropolis methods applied to sensor networks for radiation source localization}, DOI={10.1109/mfi.2016.7849519}, abstractNote={We present an application of statistical techniques to the localization of an unknown gamma source in an urban environment. By formulating the problem as a task of Bayesian parameter estimation, we are able to apply Markov Chain Monte Carlo (MCMC) to generate a full posterior probability density estimating the source location and intensity based on counts reported from a distributed detector network. To facilitate the calibration procedure, we employ a simplified photon transport model with low computational cost and test the proposed methodology in a simulated urban environment, with calibration data generated using the radiation transport code MCNP. The Bayesian methodology is able to identify the source location and intensity along with providing a full posterior density.}, booktitle={2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)}, author={Hite, J. M. and Mattingly, J. K. and Schmidt, K. L. and Stelanescu, R. and Smith, Ralph}, year={2016}, pages={389–393} }
 @article{coleman_schmidt_smith_2016, title={Frequentist and Bayesian Lasso Techniques for Parameter Selection in Nonlinearly Parameterized Models}, volume={49}, ISSN={["2405-8963"]}, DOI={10.1016/j.ifacol.2016.10.201}, abstractNote={In this paper, we discuss the use of frequentist and Bayesian lasso (least absolute shrinkage and selection operator) techniques for parameter selection in nonlinearly parameterized models employed for control design. This is necessary to isolate the subset of identifiable or influential parameters, which can be uniquely calibrated from experimental data. We survey the performance of existing algorithms and present a new Bayesian lasso implementation based on the Delayed Rejection Adaptive Metropolis (DRAM) algorithm.}, number={18}, journal={IFAC PAPERSONLINE}, author={Coleman, Kayla D. and Schmidt, Kathleen and Smith, Ralph C.}, year={2016}, pages={416–421} }
 @article{lewis_smith_williams_2016, title={Gradient free active subspace construction using Morris screening elementary effects}, volume={72}, ISSN={["1873-7668"]}, DOI={10.1016/j.camwa.2016.07.022}, abstractNote={Among multivariate functions with high-dimensional input spaces, it is common for functions to vary more strongly in a few dominant directions related to a small number of highly influential parameters. In such cases, the input dimension may be greatly reduced by constructing a low-dimensional response space that is aligned with the directions of strongest dominance; this is the basis behind active subspace methods. Until recently, gradient-based methods have been employed to construct the active subspace. We introduce a gradient-free active subspace construction method that avoids the need to sample from the gradient, which may not be available, via construction of a coarse approximation to the gradient matrix by employing the concept of “elementary effects” from Morris screening procedures. In addition, we introduce the use of adaptive step sizes and directions, when constructing these elementary effects, to allow for more accuracy in locally sensitive regions while still covering a substantial amount of the input space. This increases algorithmic efficiency by avoiding function evaluations in directions in which the gradient is relatively flat. To demonstrate the method, we use an elliptic PDE example with two correlation lengths to illustrate the effects of differing rates of singular value decay. The gradient-free active subspace method is compared to a local sensitivity analysis using coordinate reduction. This problem is then modified to contain a clearly defined 10-dimensional active subspace for verification of our method on a more complex example.}, number={6}, journal={COMPUTERS & MATHEMATICS WITH APPLICATIONS}, author={Lewis, Allison and Smith, Ralph and Williams, Brian}, year={2016}, month={Sep}, pages={1603–1615} }
 @article{mcmahan_smith_2016, title={Parameter Estimation for Predictive Simulation of Oscillatory Systems with Model Discrepancy}, volume={49}, ISSN={["2405-8963"]}, DOI={10.1016/j.ifacol.2016.10.203}, abstractNote={A Bayesian framework provides a methodology in which inferences from measurement data can be used to bound the uncertainties in the predictive simulation of a physical system. The accuracy of these bounds relies on the satisfaction of statistical assumptions on the measurement error. Discrepancies between the model and the true physics can invalidate these assumptions. We examine the effect of such model discrepancies in the context of an oscillating cantilever beam. First we illustrate the influence of discrepancies in a simplified model of purely periodic signals and then we observe how discrepancies affect the accuracy of prediction uncertainty bounds using Bayesian parameter inference on a Euler-Bernoulli beam model. Our study shows small changes in the inference setup can result in significant differences in prediction accuracy and calls attention to important considerations for the practical application of Bayesian parameter estimation.}, number={18}, journal={IFAC PAPERSONLINE}, author={McMahan, Jerry A., Jr. and Smith, Ralph C.}, year={2016}, pages={428–433} }
 @article{wentworth_smith_banks_2016, title={Parameter Selection and Verification Techniques Based on Global Sens Analysis Illustrated for an HIV Model}, volume={4}, ISSN={["2166-2525"]}, DOI={10.1137/15m1008245}, abstractNote={We consider parameter selection and verification techniques for models having one or more parameters that are noninfluential in the sense that they minimally impact model outputs. We illustrate these techniques for a dynamic HIV model but note that the parameter selection and verification framework is applicable to a wide range of biological and physical models. To accommodate the nonlinear input to output relations, which are typical for such models, we focus on global sensitivity analysis techniques, including those based on the Pearson correlation coefficient, Sobol indices based on second-order model representations, and Morris indices, as well as a parameter selection technique based on standard errors. A significant objective is to provide verification strategies to assess the accuracy of those techniques, which we illustrate in the context of the HIV model.}, number={1}, journal={SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION}, author={Wentworth, Mami T. and Smith, Ralph C. and Banks, H. T.}, year={2016}, pages={266–297} }
 @article{oates_miles_leon_smith_2016, title={Uncertainty analysis of continuum scale ferroelectric energy landscapes using density functional theory}, volume={9800}, ISSN={["1996-756X"]}, DOI={10.1117/12.2219273}, abstractNote={Density functional theory (DFT) provides exceptional predictions of material properties of ideal crystal structures such as elastic modulus and dielectric constants. This includes ferroelectric crystals where excellent predictions of spontaneous polarization, lattice strain, and elastic moduli have been predicted using DFT. Less analysis has focused on quantifying uncertainty of the energy landscape over a broad range of polarization states in ferroelectric materials. This is non-trivial because the degrees of freedom contained within a unit cell are reduced to a single vector order parameter which is normally polarization. For example, lead titanate contains five atoms and 15 degrees of freedom of atomic nuclei motion which contribute to the overall unit cell polarization. Bayesian statistics is used to identify the uncertainty and propagation of error of a continuum scale, Landau energy function for lead titanate. Uncertainty in different parameters is quantified and this uncertainty is propagated through the model to illustrate error propagation over the energy surface. Such results are shown to have an impact in integration of quantum simulations within a ferroelectric phase field continuum modeling framework.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2016}, author={Oates, William S. and Miles, Paul and Leon, Lider and Smith, Ralph}, year={2016} }
 @article{fancher_han_levin_page_reich_smith_wilson_jones_2016, title={Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis}, volume={6}, ISSN={2045-2322}, url={http://dx.doi.org/10.1038/srep31625}, DOI={10.1038/srep31625}, abstractNote={Abstract}, number={1}, journal={Scientific Reports}, publisher={Springer Science and Business Media LLC}, author={Fancher, Chris M. and Han, Zhen and Levin, Igor and Page, Katharine and Reich, Brian J. and Smith, Ralph C. and Wilson, Alyson G. and Jones, Jacob L.}, year={2016}, month={Aug}, pages={31625} }
 @article{miles_hays_smith_oates_2015, title={Bayesian uncertainty analysis of finite deformation viscoelasticity}, volume={91}, ISSN={["1872-7743"]}, DOI={10.1016/j.mechmat.2015.07.002}, abstractNote={The viscoelasticity of the dielectric elastomer, VHB 4910, is experimentally characterized, modeled, and analyzed using Bayesian uncertainty analysis. Whereas these materials are known for their large-field induced deformation and broad applications in smart structures, the rate-dependent viscoelastic effects are not well understood. To address this issue, we quantify both the hyperelastic and viscoelastic constitutive behavior and use Bayesian uncertainty analysis to assess several key modeling attributes. Specifically, we compare an Ogden-based phenomenological model to a nonaffine hyperelastic model and couple hyperelasticity to both linear and nonlinear viscoelasticity. The utilization of Bayesian statistics is shown to provide insight into quantifying nonlinear viscoelasticity behavior as a function of internal state variables. The results are validated experimentally in the finite deformation regime over a range of stretch rates spanning four orders of magnitude (6.7×10-5–0.67 Hz). A unique set of hyperelastic parameters are identified, independent of the stretch rate. In addition, comparisons of the linear and nonlinear viscoelastic models demonstrate a reduction in modeling error by approximately a factor of three. Finally, the viscoelastic time constant is shown to produce an inverse stretch rate power law dependence regardless of which hyperelastic model is used.}, journal={MECHANICS OF MATERIALS}, author={Miles, Paul and Hays, Michael and Smith, Ralph and Oates, William}, year={2015}, month={Dec}, pages={35–49} }
 @article{hu_smith_burch_hays_oates_2014, title={A modeling and uncertainty quantification framework for a flexible structure with macrofiber composite actuators operating in hysteretic regimes}, volume={25}, ISSN={["1530-8138"]}, DOI={10.1177/1045389x13489781}, abstractNote={Macrofiber composites are low cost, durable, and flexible piezoceramic devices that are presently being considered for applications that include shape control of airfoils for improved flight performance, vibration, and noise suppression and energy harvesting. However, macrofiber composites also exhibit hysteresis and constitutive nonlinearities that need to be incorporated in models and model-based control designs to achieve their full capability. In this article, we combine constitutive relations, constructed using the homogenized energy model for ferroelectric hysteresis, with Euler–Bernoulli theory to construct a dynamic macrofiber composite model that quantifies a range of rate-dependent hysteretic behavior of macrofiber composites. Using homogenizing strategies, the macrofiber composite patch is treated as a monolithic material with effective parameters. We initially calibrate the model by estimating parameters through a least squares fit to a subset of the measured data. We find that the estimated parameters yield very accurate fits for quasi-static hysteresis. The estimated parameters also provide reasonably accurate predictions for a range of frequencies that include the first two harmonics. Second, we employ an adaptive Markov chain Monte Carlo algorithm to construct densities and analyze the correlation between parameters. The kernel density estimates derived from the Markov chain Monte Carlo chains imply that most of the model parameters exhibit non-Gaussian distributions.}, number={2}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Hu, Zhengzheng and Smith, Ralph C. and Burch, Nathanial and Hays, Michael and Oates, William S.}, year={2014}, month={Jan}, pages={204–228} }
 @inproceedings{wentworth_smith_2014, title={Construction of Bayesian prediction intervals for smart systems}, DOI={10.1115/smasis2013-3168}, abstractNote={In this paper, we employ adaptive Metropolis algorithms to construct densities for parameters and quantities of interest for models arising in the analysis of smart material structures. In the first step of the construction, MCMC algorithms are used to quantify the uncertainty in parameters due to measurement errors. We then combine uncertainties from the input parameters and measurement errors, and construct prediction intervals for the quantity of interest by propagating uncertainties through the models.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems - 2013, vol 1}, author={Wentworth, M. T. and Smith, Ralph}, year={2014} }
 @article{hu_smith_willert_kelley_2014, title={High-Dimensional Model Representations for the Neutron Transport Equation}, volume={177}, ISSN={["1943-748X"]}, DOI={10.13182/nse13-52}, abstractNote={Abstract The Boltzmann transport equation is used to model the neutron flux in a nuclear reactor. The solution of the transport equation is the neutron flux, which depends on a large number of material cross sections that can be on the order of thousands. These cross sections describe various types of possible interactions between neutrons, such as fission, capture, and scattering. The cross sections are measured experimentally and therefore have associated uncertainties. It is thus necessary to quantify how the uncertainty of the cross-section values is propagated through the model for the neutron flux. High-dimensional model representations (HDMRs) can be employed to systematically quantify input-output relations. It can, however, be computationally prohibitive to construct a surrogate model using the HDMR framework for a model that has thousands of parameters. In this paper, we introduce an algorithm that utilizes the New Morris Method to first reduce the parameter space to include only the significant individual and pairwise effects and then construct a surrogate model using a Cut-HDMR expansion within the reduced space. A unified index is introduced to facilitate the comparison of the significance of the model parameters. The accuracy and efficiency of the surrogate model is demonstrated using a one-dimensional neutron transport equation.}, number={3}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Hu, Zhengzheng and Smith, Ralph C. and Willert, Jeffrey and Kelley, C. T.}, year={2014}, month={Jul}, pages={350–360} }
 @inproceedings{lewis_mcmahan_smith_2014, title={Model calibration for beam models in the presence of model discrepancy}, DOI={10.1115/smasis2014-7722}, abstractNote={Piezoelectric, magnetic and shape memory alloy (SMA) materials offer unique capabilities for energy harvesting and reduced energy requirements in aerospace, aeronautic, automotive, industrial and biomedical applications. However, all of these materials exhibit creep, rate-dependent hysteresis, and constitutive nonlinearities that must be incorporated in models and model-based control designs to achieve their full potential. Furthermore, models and control designs must be constructed in a manner that incorporates parameter and model uncertainties and permits predictions with quantified uncertainties. In this presentation, we compare the Euler-Bernoulli and Timoshenko beam models for a cantilever beam with an applied PZT patch to illustrate parameter estimation in the presence of model discrepancy.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, 2014, vol 1}, author={Lewis, A. L. and McMahan, J. A. and Smith, Ralph}, year={2014} }
 @article{crews_smith_2014, title={Quantification of parameter and model uncertainty for shape memory alloy bending actuators}, volume={25}, ISSN={["1530-8138"]}, DOI={10.1177/1045389x13490842}, abstractNote={ In this article, we employ a Bayesian framework to estimate parameter and model uncertainty for shape memory alloy bending actuators. The Bayesian framework provides parameter densities, instead of ordinary least-squares optimal point estimates. Bayes’ rule relates a posterior parameter density to a prior density and likelihood. However, the posterior density is difficult to calculate directly for high-dimensional parameter spaces. Markov chain Monte Carlo methods overcome this difficulty indirectly by creating a Markov chain whose stationary density is the posterior. In this article, we utilize the Delayed Rejection Adaptive Metropolis algorithm for estimating parameter uncertainty. The shape memory alloy bending actuator is modeled using the homogenized energy framework, a computationally efficient and accurate model for various transductive materials. The model is summarized, and techniques for estimating the heat transfer parameters are presented. An algorithmic approach to quantifying uncertainty is useful for numerous reasons. The anticipated use is to quantify uncertainty for robust control algorithms. Robust control is an area of considerable research for smart materials such as shape memory alloy; however, the source of uncertainty is rarely quantified. The methods employed here would greatly aid in the design of robust controllers. }, number={2}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Crews, John H. and Smith, Ralph C.}, year={2014}, month={Jan}, pages={229–245} }
 @article{smith_wereley_myers_dragoni_ruggiero_loh_2014, title={Special Issue: 2012 ASME Conference on Smart Materials, Adaptive Structures, and Intelligent Systems Preface}, volume={25}, ISSN={["1530-8138"]}, DOI={10.1177/1045389x14535539}, abstractNote={The 2012 ASME Conference on Smart Materials, Adaptive Structures, and Intelligent Systems (SMASIS) was held from 19 to 21 September 2012, in Stone Mountain, GA. As in its prior incarnations, the conference was a highly successful and energetic forum in which to develop discussions and collaborations among the conference delegates in adaptive structures, intelligent systems, and structural health monitoring. Participants enjoyed the distinctive atmosphere at a special ‘‘Georgia on my Mind’’ pioneer banquet that was held in the Georgia Aquarium. Conference delegates enjoyed a wonderful dinner, after touring the world’s largest aquarium. With more than 10 million gallons of water, the Georgia Aquarium has more aquatic life than any other aquarium. The six distinct galleries within the Georgia Aquarium depict different aquatic habitats, ranging from arctic to tropical waters, featuring the largest collection of aquatic animals. This was a unique setting for the Pioneer Banquet! Symposium 4: Integrated System Design and Implementation}, number={9}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Smith, Ralph and Wereley, Norman M. and Myers, Oliver and Dragoni, Eugenio and Ruggiero, Eric and Loh, Kenneth J.}, year={2014}, month={Jun}, pages={1039–1040} }
 @book{smith_2014, place={Philadelphia}, title={Uncertainty Quantification: Theory, Implementation and Applications}, publisher={SIAM}, author={Smith, R.C.}, year={2014} }
 @inproceedings{miles_hays_smith_oates_2014, title={Uncertainty analysis of a finite deformation viscoelastic model}, DOI={10.1115/smasis2014-7440}, abstractNote={The viscoelasticity of the dielectric elastomer, VHB 4910, is experimentally characterized, modeled, and analyzed using uncertainty quantification. These materials are known for their large field induced deformation and applications in smart structures, although the rate dependent viscoelastic effects are not well understood. To address this issue, we first quantify hyperelastic and viscoelastic model uncertainty by comparing a finite deformation viscoelastic model to uni-axial rate dependent experiments. The utilization of Bayesian statistics is shown to provide additional insight into different viscoelastic processes within elastomers. This is demonstrated by coupling two hyperelastic models, an Ogden model and a nonaffine model, to different types of viscoelastic models.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, 2014, vol 2}, author={Miles, P. and Hays, M. and Smith, Ralph and Oates, W. S.}, year={2014} }
 @inproceedings{mcmahan_smith_2014, title={ncertainty quantification for robust control design of smart material systems}, DOI={10.1115/smasis2013-3166}, abstractNote={The objective in robust control design is to provide mechanisms to achieve tracking or stabilization objectives in the presence of unmodeled dynamics. This is usually achieved by assuming worst case model discrepancies which can significantly degrade control authority if the uncertainty bounds are overly conservative. In this paper, we use uncertainty quantification techniques to construct densities for control outputs that can be used to derive optimal robust control designs. We illustrate the performance of these techniques in the context of systems with smart material actuators and sensors.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems - 2013, vol 1}, author={McMahan, J. A. and Smith, Ralph}, year={2014} }
 @article{matthews_smith_fiscus_2013, title={CONFIDENCE INTERVAL ESTIMATION FOR AN EMPIRICAL MODEL QUANTIFYING THE EFFECT OF SOIL MOISTURE AND PLANT DEVELOPMENT ON SOYBEAN (GLYCINE MAX (L.) MERR.) LEAF CONDUCTANCE}, volume={83}, ISSN={1311-8080 1314-3395}, url={http://dx.doi.org/10.12732/ijpam.v83i3.6}, DOI={10.12732/ijpam.v83i3.6}, abstractNote={In this work, we address uncertainty analysis for a model, pre- sented in a separate paper, quantifying the effect of soil moisture and plant age on soybean (Glycine max (L.) Merr.) leaf conductance. To achieve this we present several methods for confidence interval estimation. Estimation of confidence intervals for model parameters and predictions is investigated using asymptotic theory, Monte Carlo methods, and bootstrap methods. A compu- tationally feasible solution for estimating confidence intervals for model param- eters via asymptotic theory is unattainable. Confidence intervals for model}, number={3}, journal={International Journal of Pure and Apllied Mathematics}, publisher={Academic Publications}, author={Matthews, J.L. and Smith, R.C. and Fiscus, E.L.}, year={2013}, month={Mar} }
 @article{kenz_banks_smith_2013, title={Comparison of Frequentist and Bayesian Confidence Analysis Methods on a Viscoelastic Stenosis Model}, volume={1}, ISSN={2166-2525}, url={http://dx.doi.org/10.1137/130917867}, DOI={10.1137/130917867}, abstractNote={We compare the performance of three methods for quantifying uncertainty in model parameters: asymptotic theory, bootstrapping, and Bayesian estimation. We study these methods on an existing model for one-dimensional wave propagation in a viscoelastic medium, as well as corresponding data from lab experiments using a homogeneous, tissue-mimicking gel phantom. In addition to parameter estimation, we use the results from the three algorithms to quantify complex correlations between our model parameters, which are best seen using the more computationally expensive bootstrapping or Bayesian methods. We also hold constant the parameter causing the most complex correlation, obtaining results from all three methods which are more consistent than those obtained when estimating all parameters. Concerns regarding computational time and algorithm complexity are incorporated into a discussion on differences between the frequentist and Bayesian perspectives.}, number={1}, journal={SIAM/ASA Journal on Uncertainty Quantification}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kenz, Zackary R. and Banks, H. T. and Smith, Ralph C.}, year={2013}, month={Jan}, pages={348–369} }
 @inproceedings{crews_smith_hannen_2013, title={Development of robust control algorithms for shape memory alloy bending actuators}, DOI={10.1115/smasis2012-7989}, abstractNote={In this paper, we present a systematic approach to developing robust control algorithms for a single-tendon shape memory alloy (SMA) bending actuator. Parameter estimation and uncertainty quantification are accomplished using Bayesian techniques. Specifically, we utilize Markov Chain Monte Carlo (MCMC) methods to estimate parameter uncertainty. The Bayesian parameter estimation results are used to construct a sliding mode control (SMC) algorithm where the bounds on uncertainty are used to guarantee controller robustness. The sliding mode controller utilizes the homogenized energy model (HEM) for SMA. The inverse HEM compensates for hysteresis and converts a reference bending angle to a reference temperature. Temperature in the SMA actuator is estimated using an observer, and the sliding mode controller ensures that the observer temperature tracks the reference temperature. The SMC is augmented with proportional-integral (PI) control on the bending angle error.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol 1}, author={Crews, J. H. and Smith, Ralph and Hannen, J. C.}, year={2013}, pages={391–400} }
 @inproceedings{hu_smith_burch_hays_oates_2013, title={Homogenized energy model and markov chain Monte Carlo simulations for macro fiber composites operating in broadband regimes}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol 1}, author={Hu, Z. Z. and Smith, R. C. and Burch, N. and Hays, M. and Oates, W. S.}, year={2013}, pages={321–327} }
 @article{mcmahan_crews_smith_2013, title={Inversion algorithms for the homogenized energy model for hysteresis in ferroelectric and shape memory alloy compounds}, volume={24}, DOI={10.1177/1045389x12471868}, abstractNote={Ferroelectric and ferromagnetic materials have the advantage of broadband and dual actuator and sensor capabilities. Ferroelastic compounds such as shape memory alloys have large energy densities and are biocompatible. However, to take full advantage of these properties, it is necessary to employ models and control designs that account for the rate-dependent hysteresis, creep, and constitutive nonlinearities inherent to the materials. Inverse compensation is one technique that achieves this purpose. We present an inversion algorithm based on a binary search of a discretized input grid and apply this to the homogenized energy model for modeling hysteresis. The inversion algorithm is shown to provide a reasonable balance between accuracy and computational speed. Numerical examples are presented for three specific cases of the homogenized energy model.}, number={15}, journal={Journal of Intelligent Material Systems and Structures}, author={McMahan, J. A. and Crews, J. H. and Smith, Ralph}, year={2013}, pages={1796–1821} }
 @article{crews_mcmahan_smith_hannen_2013, title={Quantification of parameter uncertainty for robust control of shape memory alloy bending actuators}, volume={22}, ISSN={["1361-665X"]}, DOI={10.1088/0964-1726/22/11/115021}, abstractNote={In this paper, we employ Bayesian parameter estimation techniques to derive gains for robust control of smart materials. Specifically, we demonstrate the feasibility of utilizing parameter uncertainty estimation provided by Markov chain Monte Carlo (MCMC) methods to determine controller gains for a shape memory alloy bending actuator. We treat the parameters in the equations governing the actuator’s temperature dynamics as uncertain and use the MCMC method to construct the probability densities for these parameters. The densities are then used to derive parameter bounds for robust control algorithms. For illustrative purposes, we construct a sliding mode controller based on the homogenized energy model and experimentally compare its performance to a proportional-integral controller. While sliding mode control is used here, the techniques described in this paper provide a useful starting point for many robust control algorithms.}, number={11}, journal={SMART MATERIALS AND STRUCTURES}, author={Crews, John H. and McMahan, Jerry A. and Smith, Ralph C. and Hannen, Jennifer C.}, year={2013}, month={Nov} }
 @article{matthews_fiscus_smith_heitman_2013, title={Quantifying Plant Age and Available Water Effects on Soybean Leaf Conductance}, volume={105}, ISSN={0002-1962}, url={http://dx.doi.org/10.2134/agronj2012.0263}, DOI={10.2134/agronj2012.0263}, abstractNote={Given the ever‐present threat of drought and the knowledge that water availability is the strongest limiting factor in vegetation growth, it is important to characterize the effect of water limitations on agricultural production. In this study, a small field plot technique for controlling soil moisture content suitable for physiological research in moist, humid areas was tested. We characterized the effect of water stress on total leaf conductance (gl) for two distinct determinate soybean [Glycine max (L.) Merr.] genotypes. Based on these findings, a model of gl as a function of plant age and soil moisture content was formulated and validated. The dependency of gl on plant age was well represented by a parabolic function that increased throughout the vegetative period, peaked around anthesis, and decreased throughout the reproductive period and senescence. A sigmoidal function explained the relation of gl to plant‐available soil water content. This new empirical model effectively quantifies the response of gl to plant‐available soil water and plant age with a functional form similar to the abscisic acid related Tardieu–Davies model.}, number={1}, journal={Agronomy Journal}, publisher={Wiley}, author={Matthews, Jessica L. and Fiscus, Edwin L. and Smith, Ralph C. and Heitman, Joshua L.}, year={2013}, month={Jan}, pages={28–36} }
 @inproceedings{mcmahan_smith_2013, title={Sliding mode control for inverse compensated hysteretic smart systems}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol 1}, author={McMahan, J. A. and Smith, R. C.}, year={2013}, pages={335–344} }
 @inproceedings{blaircum_smith_2013, title={The homogenized energy model for characterizing magnetization and strains in ferromagnetic materials}, DOI={10.1115/smasis2012-8137}, abstractNote={Ferromagnetic materials exhibit rate-dependent hysteresis, creep and constitutive nonlinearities due to their inherent domain structure. For model-based control applications, these non-linear attributes must be incorporated in a models in a manner that facilitates model calibration and real-time control implementation. In this paper, we present a homogenized energy model for these materials. This is a multiscale framework that quantifies energy at the domain level and then employs stochastic homogenization techniques to provide macroscopic models that are highly efficient to implement. The accuracy of models will be validated using a variety of experimental data.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol 1}, author={Blaircum, L. Van and Smith, Ralph}, year={2013}, pages={489–496} }
 @inproceedings{hu_smith_2012, title={A strain model for piezoelectric materials operating in highly hysteretic regimes}, DOI={10.1115/smasis2011-5073}, abstractNote={Piezoelectric materials exhibit hysteresis in the field-strain relation at essentially all drive levels. Furthermore, this non-linear relation is dependent upon both prestresses and dynamic stresses generated during employment of the materials. The accurate characterization of this nonlinear and hysteretic material behavior is critical for material characterization, device design, and model-based control design. In this paper, we will discuss the characterization of hysteresis using the homogenized energy model (HEM) framework. At the mesoscale, energy relations characterizing field and stress-dependent 90 and 180 degree switching are used to develop fundamental kernels or hysterons. Material and field nonhomogeneities are subsequently incorporated by assuming that certain parameters are manifestations of underlying densities. This yields a macroscopic model that accurately characterizes the fundamental material behavior yet is sufficiently efficient for optimization and control implementation. Attributes of the model will be illustrated through comparison to experimental data.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent systems (SMASIS 2011), vol 2}, author={Hu, Z. Z. and Smith, Ralph}, year={2012}, pages={241–249} }
 @article{hu_smith_ernstberger_2012, title={Data-driven techniques to estimate parameters in a rate-dependent ferromagnetic hysteresis model}, volume={407}, ISSN={["1873-2135"]}, DOI={10.1016/j.physb.2011.06.084}, abstractNote={Abstract The quantification of rate-dependent ferromagnetic hysteresis is important in a range of applications including high speed milling using Terfenol-D actuators. There exist a variety of frameworks for characterizing rate-dependent hysteresis including the magnetic model in Ref. [2] , the homogenized energy framework, Preisach formulations that accommodate after-effects, and Prandtl–Ishlinskii models. A critical issue when using any of these models to characterize physical devices concerns the efficient estimation of model parameters through least squares data fits. A crux of this issue is the determination of initial parameter estimates based on easily measured attributes of the data. In this paper, we present data-driven techniques to efficiently and robustly estimate parameters in the homogenized energy model. This framework was chosen due to its physical basis and its applicability to ferroelectric, ferromagnetic and ferroelastic materials.}, number={9}, journal={PHYSICA B-CONDENSED MATTER}, author={Hu, Zhengzheng and Smith, Ralph C. and Ernstberger, Jon M.}, year={2012}, month={May}, pages={1394–1398} }
 @article{crews_smith_pender_hannen_buckner_2012, title={Data-driven techniques to estimate parameters in the homogenized energy model for shape memory alloys}, volume={23}, ISSN={["1530-8138"]}, DOI={10.1177/1045389x12453965}, abstractNote={ The homogenized energy model is a unified framework for modeling hysteresis in ferroelectric, ferromagnetic, and ferroelastic materials. The homogenized energy model framework combines energy analysis at the lattice level with stochastic homogenization techniques, based on the assumption that quantities such as interaction and coercive fields are manifestations of underlying densities, to construct macroscopic material models. In this article, we focus on the homogenized energy model for shape memory alloys. Specifically, we develop techniques for estimating model parameters based on attributes of measured data. Both the local (mesoscopic) and macroscopic models are described, and the model parameters’ relationship to the material’s response is discussed. Using these relationships, techniques for estimating model parameters are presented. The techniques are applied to constant-temperature stress–strain and resistance–strain data. These estimates are used in two manners. In one method, the estimates are considered fixed and only the homogenized energy model density functions are optimized. For SMA, the HEM incorporates densities for the interaction and relative stress (the width of the hysteresis loop). In the second method, the estimates are included in the optimization algorithm. Both cases are compared to experimental data at various temperatures, and the optimized model parameters are compared to the initial estimates. }, number={17}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Crews, John H. and Smith, Ralph C. and Pender, Kyle M. and Hannen, Jennifer C. and Buckner, Gregory D.}, year={2012}, month={Nov}, pages={1897–1920} }
 @inproceedings{crews_smith_2012, title={Density function optimization for the homogenized energy model of shape memory alloys}, DOI={10.1115/smasis2011-5036}, abstractNote={In this paper, we present two methods for optimizing the density functions in the homogenized energy model (HEM) of shape memory alloys (SMA). The density functions incorporate the polycrystalline behavior of SMA by accounting for material inhomogeneities and localized interaction effects. One method represents the underlying densities for the relative stress and interaction stress as log-normal and normal probability density functions, respectively. The optimal parameters in the underlying densities are found using a genetic algorithm. A second method represents the densities as a linear parameterization of log-normal and normal probability density functions. The optimization algorithm determines the optimal weights of the underlying densities. For both cases, the macroscopic model is integrated over the localized constitutive behavior using these densities. In addition, the estimation of model parameters using experimental data is described. Both optimized models accurately and efficiently quantify the SMA’s hysteretic dependence on stress and temperature, making the model suitable for use in real-time control algorithms.}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems (SMASIS 2011), vol 1}, author={Crews, J. H. and Smith, Ralph}, year={2012}, pages={371–379} }
 @article{smith_hu_2012, title={Homogenized energy model for characterizing polarization and strains in hysteretic ferroelectric materials: Material properties and uniaxial model development}, volume={23}, ISSN={["1530-8138"]}, DOI={10.1177/1045389x12453967}, abstractNote={ Ferroelectric materials, such as lead zirconate titanate, lanthanum-doped lead zirconate titanate, and BaTiO3, are being considered, or are already being employed, for a large number of applications including nanopositioning, high-speed valves for fuel injectors, ultrasonic transducers, high-speed camera shutters and autofocusing mechanisms, energy harvesting, and pico air vehicle design. Their advantages include nanometer positioning resolution, broadband frequency responses, moderate power requirements, the capability for miniaturization, and complementary actuator and sensor capabilities. However, they also exhibit creep, rate-dependent hysteresis, and constitutive nonlinearities at essentially all drive levels due to their noncentrosymmetric nature. In this article, we model the hysteretic dependence of strains and polarizations on input fields and stresses using the homogenized energy model framework. At the domain level, the minimization of the Gibbs energy densities yields linear constitutive relations. Nonlinearities and hysteresis due to dipole switching are modeled at the grain level using the Boltzmann theory to specify the evolution of dipole fractions that serve as internal variables. In the final step of the development, stochastic homogenization, based on the assumption that interaction fields and driving forces are manifestations of underlying densities, is used to construct nonlinear constitutive relations for the bulk material. It is demonstrated that these relations are amenable to subsequent development of distributed system models. The article includes significant discussion regarding the mechanisms that produce hysteresis in ferroelectric materials. The capability of the framework for characterizing various hysteretic phenomena, including creep and various rate dependencies, is illustrated by validation with lead zirconate titanate and lanthanum-doped lead zirconate titanate data. }, number={16}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Smith, Ralph C. and Hu, Zhengzheng}, year={2012}, month={Nov}, pages={1833–1867} }
 @article{crews_smith_2012, title={Modeling and Bayesian Parameter Estimation for Shape Memory Alloy Bending Actuators}, volume={8342}, ISSN={["1996-756X"]}, DOI={10.1117/12.914792}, abstractNote={In this paper, we employ a homogenized energy model (HEM) for shape memory alloy (SMA) bending actuators. Additionally, we utilize a Bayesian method for quantifying parameter uncertainty. The system consists of a SMA wire attached to a flexible beam. As the actuator is heated, the beam bends, providing endoscopic motion. The model parameters are fit to experimental data using an ordinary least-squares approach. The uncertainty in the fit model parameters is then quantified using Markov Chain Monte Carlo (MCMC) methods. The MCMC algorithm provides bounds on the parameters, which will ultimately be used in robust control algorithms. One purpose of the paper is to test the feasibility of the Random Walk Metropolis algorithm, the MCMC method used here.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2012}, author={Crews, John H. and Smith, Ralph C.}, year={2012} }
 @article{mcmahan_smith_2012, title={Sliding Mode Control Design for Hysteretic Ferroelectric Materials}, volume={8342}, ISSN={["0277-786X"]}, DOI={10.1117/12.914631}, abstractNote={Ferroelectric materials are attractive for use in a wide range of applications due to their unique transduction capabilities. However, taking full advantage of these capabilities requires a control design which accounts for the materials' inherent hysteretic behavior. A common approach is to partially cancel the hysteretic effects in the system by employing an approximate inversion algorithm in the control input, resulting in an almost linear system. Using a recently developed modification to the homogenized energy model for ferroelectric materials, we combine this method with a sliding mode control design to track a reference trajectory even in the presence of modeling and inversion errors. Numerical simulations illustrate the effectiveness of the design.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2012}, author={McMahan, Jerry A. and Smith, Ralph C.}, year={2012} }
 @article{hu_smith_ernstberger_2012, title={The homogenized energy model for characterizing polarization and strains in hysteretic ferroelectric materials: Implementation algorithms and data-driven parameter estimation techniques}, volume={23}, ISSN={["1530-8138"]}, DOI={10.1177/1045389x12453968}, abstractNote={ Ferroelectric materials, such as lead zirconate titanate, lanthanum-doped lead zirconate titanate, lead manganese niobate, and BaTiO3, provide unique actuator and sensor capabilities for applications including nanopositioning, high-speed valves and fuel injectors, camera focusing and shutter mechanisms, ultrasonic devices for biomedical imaging and treatment, and energy harvesting devices. However, to achieve the full potential of the materials, it is necessary to develop and employ models that quantify the creep, rate-dependent hysteresis, and constitutive nonlinearities that are intrinsic to the materials due to their domain structure. The success of models requires that they be highly efficient to implement since real-time applications can require kilo hertz to mega hertz rates. The calibration of models for specific materials, devices, and applications requires efficient and robust parameter estimation algorithms. Finally, control designs can be facilitated by models that admit efficient and robust approximate inversion. The homogenized energy model is a multiscale, micromechanical framework that quantifies a range of hysteretic phenomena intrinsic to ferroelectric, ferromagnetic, and ferroelastic materials. In this article, we present highly efficient implementation and parameter estimation algorithms for the ferroelectric model. This includes techniques to construct analytic Jacobians and data-driven algorithms to determine initial parameter estimates to facilitate subsequent optimization. The efficiency of these algorithms facilitates material and device characterization and provides the basis for constructing efficient and robust inverse algorithms for model-based control design. The model implementation, calibration, and validation are illustrated using rate-dependent lead zirconate titanate data and single-crystal BaTiO3 data. }, number={16}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Hu, Zhengzheng and Smith, Ralph C. and Ernstberger, Jon}, year={2012}, month={Nov}, pages={1869–1894} }
 @article{mcmahan_smith_2011, title={Adaptive Control Design for Hysteretic Smart Systems}, volume={7978}, ISSN={["1996-756X"]}, DOI={10.1117/12.884621}, abstractNote={Ferroelectric and ferromagnetic actuators are being considered for a range of industrial, aerospace, aeronautic and biomedical applications due to their unique transduction capabilities. However, they also exhibit hysteretic and nonlinear behavior that must be accommodated in models and control designs. If uncompensated, these effects can yield reduced system performance and, in the worst case, can produce unpredictable behavior of the control system. In this paper, we address the development of adaptive control designs for hysteretic systems. We review an MRAC-like adaptive control algorithm used to track a reference trajectory while computing online estimates for certain model parameters. This method is incorporated in a composite control algorithm to improve the tracking capabilities of the system. Issues arising in the implementation of these algorithms are addressed, and a numerical example is presented, comparing the results of each method.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2011}, author={McMahan, Jerry A. and Smith, Ralph C.}, year={2011} }
 @article{hu_smith_stuebner_hays_oates_2011, title={Statistical Parameter Estimation for Macro Fiber Composite Actuators using the Homogenized Energy Model}, volume={7978}, ISSN={["0277-786X"]}, DOI={10.1117/12.884622}, abstractNote={Macro Fiber Composites (MFC) are planar actuators comprised of PZT fibers embedded in an epoxy matrix that is sandwiched between electrodes. Due to their construction, they exhibit significant durability and flexibility in addition to being lightweight and providing broadband inputs. They are presently being considered for a range of applications including positioning and control of membrane mirrors and configurable aerospace structures. However, they also exhibit hysteresis and constitutive nonlinearities that must be incorporated in models to achieve the full potential of the devices. In this paper, we discuss the development of a model that quantifies the hysteresis and constitutive nonlinearities in a manner that promotes subsequent control design. The constitutive model is constructed using the homogenized energy framework for ferroelectric hysteresis and used to develop resulting system models. The performance of the models is validated with experimental data.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2011}, author={Hu, Zhengzheng and Smith, Ralph C. and Stuebner, Michael and Hays, Michael and Oates, William S.}, year={2011} }
 @article{oates_zrostlik_eichhorn_smith_2010, title={A Non-linear Optimal Control Design using Narrowband Perturbation Feedback for Magnetostrictive Actuators}, volume={21}, ISSN={["1530-8138"]}, DOI={10.1177/1045389x10386398}, abstractNote={ Non-linear optimal and narrowband feedback control designs are developed and experimentally implemented on a magnetostrictive Terfenol-D actuator. The non-linear optimal control design incorporates a non-linear and hysteretic ferromagnetic homogenized energy model within an optimal control formulation to reduce displacement tracking errors and increase bandwidth. Improvements in robustness in the steady-state regime are achieved by utilizing narrowband feedback. A narrowband filter is implemented by treating the nonlinear and hysteretic magnetostrictive constitutive behavior as higher-order harmonic disturbances which are mitigated by tuning the narrowband filter to penalize these harmonics for displacement tracking control problems. The control designs are then combined into a hybrid optimal controller with perturbation narrowband feedback. Both transient and steady-state tracking control is assessed to illustrate performance attributes in different operating regimes. Narrowband perturbation feedback is shown to mitigate errors in the steady-state operating regime, while non-linear optimal control provides enhanced tracking control in the transient regime. The hybrid control design is relevant to a broad number of smart material actuators that exhibit non-linear and hysteretic field-coupled constitutive behavior. }, number={16}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Oates, William S. and Zrostlik, Rick and Eichhorn, Scott and Smith, Ralph}, year={2010}, month={Nov}, pages={1681–1693} }
 @article{proctor_richards_shen_skorczewski_wang_zhang_zhong_massad_smith_2010, title={Design of RF MEMS Switches without Pull-in Instability}, volume={7644}, ISSN={["1996-756X"]}, DOI={10.1117/12.848045}, abstractNote={Micro-electro-mechanical systems (MEMS) switches for radio-frequency (RF) signals have certain advantages over solid-state switches, such as lower insertion loss, higher isolation, and lower static power dissipation. Mechanical dynamics can be a determining factor for the reliability of RF MEMS. The RF MEMS ohmic switch discussed in this paper consists of a plate suspended over an actuation pad by four double-cantilever springs. Closing the switch with a simple step actuation voltage typically causes the plate to rebound from its electrical contacts. The rebound interrupts the signal continuity and degrades the performance, reliability and durability of the switch. The switching dynamics are complicated by a nonlinear, electrostatic pull-in instability that causes high accelerations. Slow actuation and tailored voltage control signals can mitigate switch bouncing and effects of the pull-in instability; however, slow switching speed and overly-complex input signals can significantly penalize overall system-level performance. Examination of a balanced and optimized alternative switching solution is sought. A step toward one solution is to consider a pull-in-free switch design. In this paper, determine how simple RC-circuit drive signals and particular structural properties influence the mechanical dynamics of an RF MEMS switch designed without a pull-in instability. The approach is to develop a validated modeling capability and subsequently study switch behavior for variable drive signals and switch design parameters. In support of project development, specifiable design parameters and constraints will be provided. Moreover, transient data of RF MEMS switches from laser Doppler velocimetry will be provided for model validation tasks. Analysis showed that a RF MEMS switch could feasibly be designed with a single pulse waveform and no pull-in instability and achieve comparable results to previous waveform designs. The switch design could reliably close in a timely manner, with small contact velocity, usually with little to no rebound even when considering manufacturing variability.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2010}, author={Proctor, W. Cyrus and Richards, Gregory P. and Shen, Chongyi and Skorczewski, Tyler and Wang, Min and Zhang, Jingyan and Zhong, Peng and Massad, Jordan E. and Smith, Ralph}, year={2010} }
 @article{stuebner_smith_2010, title={Inverse Model Construction for Control Implementation of Macro Fiber Composite Actuators Operating in Hysteretic Regimes}, volume={7644}, ISSN={["0277-786X"]}, DOI={10.1117/12.848256}, abstractNote={Macro Fiber Composite (MFC) actuators utilize PZT fibers embedded in an epoxy matrix for structural actuation. Due to their construction, they are lightweight and provide broadband inputs. Significant advantages of MFC actuators are their high performance, durability, and flexibility when compared to traditional piezoceramic actuators. They are presently being considered for a range of applications including positioning of membrane mirrors and structural control in the aerospace and automotive industry. However, they exhibit varying degrees of hysteresis and constitutive nonlinearities throughout their operating range that must be incorporated in models to achieve the full capabilities of the materials. In this paper, hysteresis is modeled using the homogenized energy model. The inverse model is then used to construct an inverse compensator framework suitable for subsequent control design. The performance of the inverse compensator is illustrated through a numerical example.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2010}, author={Stuebner, Michael and Smith, Ralph C.}, year={2010} }
 @article{may_smith_2010, title={Proper Orthogonal Decomposition with Updates for Efficient Control Design in Smart Material Systems}, volume={7644}, ISSN={["0277-786X"]}, DOI={10.1117/12.847579}, abstractNote={Proper orthogonal decomposition (POD) is a basis reduction technique that allows simulations of complicated systems to be calculated at faster speeds with minimal loss of accuracy. The reduced order basis is created from a set of system data called snapshots. The speed and information retention of POD make it an attractive method to implement reduced-order models of smart material systems. This can allow for the modeling of larger systems and the implementation of real time control, which may be impossible when using the full-order system. There are times when the dynamics of a system can change during a simulation, and the addition of more information to the set of snapshots would be beneficial. The implementation of control on a system is a time when adding new snapshots to the collection can increase the accuracy of the model. Using updates allows more flexibility when trying to balance the accuracy and the speed of the simulation. By updating the POD basis at specific times throughout the interval, we can increase the accuracy of the model and control by using a greater amount of the information given by the snapshots, while we can increase the speed of the simulation during times when using less information will still result in sufficient accuracy.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2010}, author={May, Stephen F. and Smith, Ralph C.}, year={2010} }
 @article{demetriou_ito_smith_2009, title={Adaptive techniques for the MRAC, adaptive parameter identification, and on-line fault monitoring and accommodation for a class of positive real infinite dimensional systems}, volume={23}, ISSN={["1099-1115"]}, DOI={10.1002/acs.1058}, abstractNote={Abstract}, number={2}, journal={INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING}, author={Demetriou, Michael A. and Ito, Kazufumi and Smith, Ralph C.}, year={2009}, month={Feb}, pages={193–215} }
 @article{oates_evans_smith_dapino_2009, title={Experimental implementation of a hybrid nonlinear control design for magnetostrictive actuators}, volume={131}, DOI={10.21236/ada459020}, number={4}, journal={Journal of Dynamic Systems, Measurement, and Control}, author={Oates, W. S. and Evans, P. G. and Smith, Ralph and Dapino, M. J.}, year={2009} }
 @inbook{banks_smith_2009, title={Numerical Techniques for Simulation, Parameter Estimation, and Noise Control in Structural Acoustic Systems}, ISBN={9780511530180}, url={http://dx.doi.org/10.1017/cbo9780511530180.006}, DOI={10.1017/cbo9780511530180.006}, abstractNote={A model for a 3-D structural acoustic system, currently being used for parameter estimation and control experiments in the Acoustics Division, NASA Langley Research Center, is presented. This system consists of a hard-walled cylinder with a flexible circular plate at one end. An exterior noise source causes vibrations in the plate which in turn lead to unwanted noise inside the cylinder. Control is implemented through the excitation of piezoceramic patches bonded to the plate which generate in-plane forces and/or bending moments in response to an input voltage.}, booktitle={Dynamics and Control of Distributed Systems}, publisher={Cambridge University Press}, author={Banks, H. T. and Smith, R. C.}, editor={Tzou, H. S. and Bergman, L. A.Editors}, year={2009}, month={Dec}, pages={202–263} }
 @article{oates_smith_2009, title={Optimal Tracking Using Magnetostrictive Actuators Operating in Nonlinear and Hysteretic Regimes}, volume={131}, ISSN={["0022-0434"]}, DOI={10.1115/1.3072093}, abstractNote={Abstract}, number={3}, journal={JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME}, author={Oates, William S. and Smith, Ralph C.}, year={2009}, month={May} }
 @article{stuebner_atulasimha_smith_2009, title={Quantification of hysteresis and nonlinear effects on the frequency response of ferroelectric and ferromagnetic materials}, volume={18}, ISSN={["1361-665X"]}, DOI={10.1088/0964-1726/18/10/104019}, abstractNote={Ferroelectric (e.g., PZT and PMN) and ferromagnetic (e.g., Terfenol-D) materials exhibit high energy densities, broadband drive capabilities, and the capacity for both actuating and sensing. This makes them attractive as compact transducers for a wide range of applications. However, the materials also exhibit hysteresis and constitutive nonlinearities, at all drive levels, that must be quantified and accommodated to achieve stringent tracking requirements. Whereas considerable effort has been made on model development and understanding these materials in the parameter space and time domain, comprehensive quantification of these effects in the frequency domain is currently lacking. In this paper, we employ the homogenized energy model, in combination with thin beam theory, to quantify the frequency domain behavior of ferroelectric and ferromagnetic materials. This model combines energy analysis at the lattice level with stochastic homogenization techniques to provide a framework that effectively quantifies the effect of hysteresis, constitutive nonlinearities, bias fields and AC drive levels on the material dynamics in both the time and frequency domains. Aspects of the model are illustrated and validated through numerical and experimental examples.}, number={10}, journal={SMART MATERIALS AND STRUCTURES}, author={Stuebner, M. and Atulasimha, J. and Smith, R. C.}, year={2009}, month={Oct} }
 @article{braun_smith_2008, title={High Speed Model Implementation and Inversion Techniques for Ferroelectric and Ferromagnetic Transducers}, volume={19}, ISSN={["1530-8138"]}, DOI={10.1177/1045389X07085638}, abstractNote={ Ferroelectric and ferromagnetic materials are employed as both actuators and sensors in a wide variety of applications including fluid pumps, nanopositioning stages, sonar transducers, vibration control, ultrasonic sources, and high-speed milling. They are attractive because the resulting transducers are solid-state and often very compact. However, the coupling of field to mechanical deformation, which makes these materials effective transducers, also introduces hysteresis and time-dependent behavior that must be accommodated in device designs and models before the full potential of compounds can be realized. In this article, we present highly efficient modeling techniques to characterize hysteresis and constitutive nonlinearities in ferroelectric and ferromagnetic compounds and model inversion techniques which permit subsequent linear control designs. }, number={11}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Braun, T. R. and Smith, R. C.}, year={2008}, month={Nov}, pages={1295–1310} }
 @article{oates_smith_2008, title={Nonlinear optimal control techniques for vibration attenuation using magnetostrictive actuators}, volume={19}, ISSN={["1530-8138"]}, DOI={10.1177/1045389X06074159}, abstractNote={This article addresses the development of a nonlinear control design for attenuating structural vibrations using magnetostrictive transducers operating in nonlinear and highly hysteretic operating regimes. We consider as a prototype a thin plate subjected to exogenous pressure waves and controlled via Terfenol-D transducers at the plate edges; however, the methodology is sufficiently general to encompass a wide range of structures and magnetic transducer designs. Hysteresis inherent to the transducer materials is quantified using a homogenized energy framework and the resulting nonlinear constitutive relations are used to construct a PDE representation and corresponding finite dimensional model of the structural system. We employ optimal control theory to construct nonlinear open loop control inputs which accommodate the hysteresis inherent to the transducers but are not robust with regard to unmodeled dynamics or disturbances. Robustness is incorporated by employing perturbation techniques to provide linear feedback laws acting on measured disturbances. As illustrated via numerical examples, the resulting hybrid control design provides excellent control authority and robustness for transducers operating in hysteretic and nonlinear regimes.}, number={2}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Oates, William S. and Smith, Ralph C.}, year={2008}, month={Feb}, pages={193–209} }
 @article{ball_smith_kim_seelecke_2007, title={A stress-dependent hysteresis model for ferroelectric materials}, volume={18}, ISSN={["1530-8138"]}, DOI={10.1177/1045389X07070937}, abstractNote={ This article addresses the development of a homogenized energy model which characterizes the ferroelastic switching mechanisms inherent to ferroelectric materials in a manner suitable for subsequent transducer and control design. In the first step of the development, we construct Helmholtz and Gibbs energy relations which quantify the potential and electrostatic energy associated with 90 and 180 dipole orientations. Equilibrium relations appropriate for homogeneous materials in the absence or presence of thermal relaxation are respectively determined by minimizing the Gibbs energy or balancing the Gibbs and relative thermal energies using Boltzmann principles. In the final step of the development, stochastic homogenization techniques are employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds. Attributes and limitations of the characterization framework are illustrated through comparison with experimental PLZT data. }, number={1}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Ball, Brian L. and Smith, Ralph C. and Kim, Sang-Joo and Seelecke, Stefan}, year={2007}, month={Jan}, pages={69–88} }
 @article{lenczner_smith_2007, title={A two-scale model for an array of AFM's cantilever in the static case}, volume={46}, ISSN={["1872-9479"]}, DOI={10.1016/j.mcm.2006.12.028}, abstractNote={The primary objective of this paper is to present a simplified model for an array of Atomic Force Microscopes (AFMs) operating in static mode. Its derivation is based on the asymptotic theory of thin plates initiated by P. Ciarlet and P. Destuynder and on the two-scale convergence introduced by M. Lenczner which generalizes the theory of G. Nguetseng and G. Allaire. As an example, we investigate in full detail a particular configuration, which leads to a very simple model for the array. Aspects of the theory for this configuration are illustrated through simulation results. Finally the formulation of our theory of two-scale convergence is fully revisited. All the proofs are reformulated in a significantly simpler manner.}, number={5-6}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Lenczner, M. and Smith, R. C.}, year={2007}, month={Sep}, pages={776–805} }
 @article{demetriou_ito_smith_2007, title={Adaptive monitoring and accommodation of nonlinear actuator faults in positive real infinite dimensional systems}, volume={52}, ISSN={["1558-2523"]}, DOI={10.1109/TAC.2007.910694}, abstractNote={We consider a class of positive real infinite dimensional systems which are subjected to incipient actuator faults. The actuator fault is modeled as a time varying transition from an initial (linear or nonlinear) map into another unknown nonlinear map at the onset of the fault occurrence. An infinite dimensional adaptive detection observer is utilized to generate a residual signal in order to detect the fault occurrence and to assist in the fault accommodation. This is done via an automated control reconfiguration which utilizes information on the new actuator map and adjusts the controller via a right inverse of the actuator map. A robust modification is utilized in order to avoid false alarms caused by unmodelled dynamics. An example is included to illustrate the applicability of the proposed scheme}, number={12}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Demetriou, Michael A. and Ito, Kazufumi and Smith, Ralph C.}, year={2007}, month={Dec}, pages={2332–2338} }
 @article{nealis_smith_2007, title={Model-based robust control design for magnetostrictive transducers operating in hysteretic and nonlinear regimes}, volume={15}, ISSN={["1558-0865"]}, DOI={10.1109/TCST.2006.883235}, abstractNote={This paper addresses the development of robust control designs for high-performance smart material transducers operating in nonlinear and hysteretic regimes. While developed in the context of a magnetostrictive transducer used for high-speed, high-accuracy milling, the resulting model-based control techniques can be directly extended to systems utilizing piezoceramic or shape memory alloy compounds due to the unified nature of models used to quantify hysteresis and nonlinearities inherent to all of these materials. When developing models and corresponding inverse filters or compensators, significant emphasis is placed on the utilization of the material's physics to provide the accuracy and efficiency required for real-time implementation of resulting model-based control designs. In the material models, this is achieved by combining energy analysis with stochastic homogenization techniques, whereas the efficiency of forward algorithms is combined with monotonicity properties of the material behavior to provide highly efficient inverse algorithms. These inverse filters are then incorporated in H2 and Hinfin theory to provide robust control algorithms capable of providing high-accuracy tracking even though the actuators are operating in nonlinear and hysteretic regimes. Through numerical examples, it is illustrated that the robust designs incorporating inverse compensators can achieve the required tracking tolerance of 1-2 mum for the motivating milling application, whereas robust designs which treat the uncompensated hysteresis and nonlinearities as unmodeled disturbances cannot achieve design specifications}, number={1}, journal={IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY}, author={Nealis, James M. and Smith, Ralph C.}, year={2007}, month={Jan}, pages={22–39} }
 @article{smith_dapino_braun_mortensen_2006, title={A homogenized energy framework for ferromagnetic hysteresis}, volume={42}, ISSN={["1941-0069"]}, DOI={10.1109/TMAG.2006.875717}, abstractNote={This paper focuses on the development of a homogenized energy model which quantifies certain facets of the direct magnetomechanical effect. In the first step of the development, Gibbs energy analysis at the lattice level is combined with Boltzmann principles to quantify the local average magnetization as a function of input fields and stresses. A macroscopic magnetization model, which incorporates the effects of polycrystallinity, material nonhomogeneities, stress-dependent interaction fields, and stress-dependent coercive behavior, is constructed through stochastic homogenization techniques based on the tenet that local coercive and interaction fields are manifestations of underlying distributions rather than constants. The resulting framework incorporates previous ferromagnetic hysteresis theory as a special case in the absence of applied stresses. Attributes of the framework are illustrated through comparison with previously published steel and iron data}, number={7}, journal={IEEE TRANSACTIONS ON MAGNETICS}, author={Smith, Ralph C. and Dapino, Marcelo J. and Braun, Thomas R. and Mortensen, Anthony P.}, year={2006}, month={Jul}, pages={1747–1769} }
 @article{smith_dapino_2006, title={A homogenized energy model for the direct magnetomechanical effect}, volume={42}, ISSN={["0018-9464"]}, DOI={10.1109/TMAG.2006.875705}, abstractNote={This paper focuses on the development of a homogenized energy model which quantifies certain facets of the direct magnetomechanical effect. In the first step of the development, Gibbs energy analysis at the lattice level is combined with Boltzmann principles to quantify the local average magnetization as a function of input fields and stresses. A macroscopic magnetization model, which incorporates the effects of polycrystallinity, material nonhomogeneities, stress-dependent interaction fields, and stress-dependent coercive behavior, is constructed through stochastic homogenization techniques based on the tenet that local coercive and interaction fields are manifestations of underlying distributions rather than constants. The resulting framework incorporates previous ferromagnetic hysteresis theory as a special case in the absence of applied stresses. Attributes of the framework are illustrated through comparison with previously published steel and iron data}, number={8}, journal={IEEE TRANSACTIONS ON MAGNETICS}, author={Smith, Ralph C. and Dapino, Marcelo J.}, year={2006}, month={Aug}, pages={1944–1957} }
 @article{smith_seelecke_dapino_ounaies_2006, title={A unified framework for modeling hysteresis in ferroic materials}, volume={54}, ISSN={["1873-4782"]}, DOI={10.1016/j.jmps.2005.08.006}, abstractNote={This paper addresses the development of a unified framework for quantifying hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials. Because the mechanisms which produce hysteresis vary substantially at the microscopic level, it is more natural to initiate model development at the mesoscopic, or lattice, level where the materials share common energy properties along with analogous domain structures. In the first step of the model development, Helmholtz and Gibbs energy relations are combined with Boltzmann theory to construct mesoscopic models which quantify the local average polarization, magnetization and strains in ferroelectric, ferromagnetic and ferroelastic materials. In the second step of the development, stochastic homogenization techniques are invoked to construct unified macroscopic models for nonhomogeneous, polycrystalline compounds exhibiting nonuniform effective fields. The combination of energy analysis and homogenization techniques produces low-order models in which a number of parameters can be correlated with physical attributes of measured data. Furthermore, the development of a unified modeling framework applicable to a broad range of ferroic compounds facilitates material characterization, transducer development, and model-based control design. Attributes of the models are illustrated through comparison with piezoceramic, magnetostrictive and shape memory alloy data and prediction of material behavior.}, number={1}, journal={JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS}, author={Smith, RC and Seelecke, S and Dapino, M and Ounaies, Z}, year={2006}, month={Jan}, pages={46–85} }
 @article{hatch_smith_de_salapaka_2006, title={Construction and experimental implementation of a model-based inverse filter to attenuate hysteresis in ferroelectric transducers}, volume={14}, ISSN={["1558-0865"]}, DOI={10.1109/TCST.2006.883195}, abstractNote={Hysteresis and constitutive nonlinearities are inherent properties of ferroelectric transducer materials due to the noncentrosymmetric nature of the compounds. In certain regimes, these effects can be mitigated through restricted input fields, charge- or current-controlled amplifiers, or feedback designs. For general operating conditions, however, these properties must be accommodated in models, transducer designs, and model-based control algorithms to achieve the novel capabilities provided by the compounds. In this paper, we illustrate the construction of inverse filters, based on homogenized energy models, which can be used to approximately linearize the piezoceramic transducer behavior for linear design and control implementation. Attributes of the inverse filters are illustrated through numerical examples and experimental open loop control implementation for an atomic force microscope stage}, number={6}, journal={IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY}, author={Hatch, Andrew G. and Smith, Ralph C. and De, Tathagata and Salapaka, Murti V.}, year={2006}, month={Nov}, pages={1058–1069} }
 @article{braun_smith_2006, title={Efficient implementation algorithms for homogenized energy models}, volume={18}, ISSN={["0935-1175"]}, DOI={10.1007/s00161-006-0015-8}, abstractNote={The homogenized energy framework quantifying ferroelectric and ferromagnetic hysteresis is increasingly used for comprehensive material characterization and model-based control design. For operating regimes in which thermal relaxation mechanisms and stress-dependencies are negligible, existing algorithms are sufficiently efficient to permit device optimization and the potential for real-time control implementation. In this paper, we develop algorithms employing lookup tables which permit the high speed implementation of formulations which incorporate relaxation mechanisms and electromechanical coupling. Aspects of the algorithms are illustrated through comparison with experimental data.}, number={3-4}, journal={CONTINUUM MECHANICS AND THERMODYNAMICS}, author={Braun, Thomas R. and Smith, Ralph C.}, year={2006}, month={Sep}, pages={137–155} }
 @article{braun_smith_dapino_2006, title={Experimental validation of a homogenized energy model for magnetic after-effects}, volume={88}, ISSN={["1077-3118"]}, DOI={10.1063/1.2188595}, abstractNote={In this letter, we experimentally validate the ability of a recently developed ferromagnetic hysteresis model to characterize magnetic after-effects in ferromagnetic materials. The modeling framework, which combines energy analysis at the lattice level with stochastic homogenization techniques to accommodate material, stress, and field nonhomogeneities, quantifies after-effects through a balance of the Gibbs and relative thermal energies. Attributes of the framework are illustrated through fits to experimental steel data.}, number={12}, journal={APPLIED PHYSICS LETTERS}, author={Braun, TR and Smith, RC and Dapino, MJ}, year={2006}, month={Mar} }
 @article{smith_hatch_de_salapaka_del rosario_raye_2006, title={Model development for atomic force microscope stage mechanisms}, volume={66}, ISSN={["1095-712X"]}, DOI={10.1137/05063307X}, abstractNote={In this paper, we develop nonlinear constitutive equations and resulting system models quantifying the nonlinear and hysteretic field‐displacement relations inherent to lead zirconate titanate (PZT) devices employed in atomic force microscope stage mechanisms. We focus specifically on PZT rods utilizing $d_{33}$ motion and PZT shells driven in $d_{31}$ regimes, but the modeling framework is sufficiently general to accommodate a variety of drive geometries. In the first step of the model development, lattice‐level energy relations are combined with stochastic homogenization techniques to construct nonlinear constitutive relations which accommodate the hysteresis inherent to ferroelectric compounds. Second, these constitutive relations are employed in classical rod and shell relations to construct system models appropriate for presently employed nanopositioner designs. The capability of the models for quantifying the frequency‐dependent hysteresis inherent to the PZT stages is illustrated through comparison...}, number={6}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Smith, Ralph C. and Hatch, Andrew G. and De, Tathagata and Salapaka, Murti V. and Del Rosario, Ricardo C. H. and Raye, Julie K.}, year={2006}, pages={1998–2026} }
 @article{matthews_lada_weiland_smith_leo_2006, title={Monte Carlo simulation of a solvated ionic polymer with cluster morphology}, volume={15}, ISSN={["0964-1726"]}, DOI={10.1088/0964-1726/15/1/048}, abstractNote={A multiscale modeling approach for the prediction of material stiffness of the ionic polymer Nafion is presented. Traditional rotational isomeric state theory is applied in combination with a Monte Carlo methodology to develop a simulation model of the conformation of Nafion polymer chains on a nanoscopic level from which a large number of end-to-end chain lengths are generated. The probability density function of end-to-end distances is then estimated and used as an input parameter to enhance existing energetics-based macroscale models of ionic polymer behavior. Several methods for estimating the probability density function are compared, including estimation using Johnson distributions, Bézier distributions, and cubic splines.}, number={1}, journal={SMART MATERIALS & STRUCTURES}, author={Matthews, JL and Lada, EK and Weiland, LM and Smith, RC and Leo, DJ}, year={2006}, month={Feb}, pages={187–199} }
 @article{smith_hatch_mukherjee_liu_2005, title={A homogenized energy model for hysteresis in ferroelectric materials: General density formulation}, volume={16}, ISSN={["1045-389X"]}, DOI={10.1177/1045389X05054789}, abstractNote={ In this article, we construct a framework for modeling hysteresis and constitutive nonlinearities in ferroelectric compounds based on energy analysis at mesoscopic scales in combination with stochastic homogenization techniques to construct macroscopic models. In the first step of the development, previous analysis is used to construct Helmholtz and Gibbs energy relations at the lattice level. This provides local polarization relations that can be extrapolated to provide constitutive models for certain homogeneous, single crystal compounds. To incorporate material and field nonhomogeneities, as well as the effects of polycrystallinity, certain parameters in the local models are assumed to be manifestations of underlying distributions having densities which must be identified for a given compound. Two techniques for estimating the unknown densities are presented, and the accuracy of the resulting model is illustrated for both symmetric major loops and biased minor loops through fits and predictions with experimental PZT4 and PZT5H data. }, number={9}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Smith, RC and Hatch, AG and Mukherjee, B and Liu, SF}, year={2005}, month={Sep}, pages={713–732} }
 @article{massad_smith_2005, title={A homogenized free energy model for hysteresis in thin-film shape memory alloys}, volume={489}, ISSN={["1879-2731"]}, DOI={10.1016/j.tsf.2005.04.079}, abstractNote={Thin-film shape memory alloys (SMAs) have become excellent candidates for microactuator fabrication in microelectromechanical systems due to their capability to achieve very high work densities, produce large deformations, and generate high stresses. In general, the material behavior of SMAs is nonlinear and hysteretic. To achieve the full potential of SMA actuators, it is necessary to develop models that characterize the nonlinearities and hysteresis inherent to the constituent materials. We develop a model that quantifies the nonlinearities and hysteresis inherent to SMAs. The fully thermomechanical model is based on free energy principles combined with stochastic homogenization techniques. It predicts rate-dependent, polycrystalline SMA behavior, and it accommodates heat transfer issues pertinent to thin-film SMAs. The main advantages of this model are that it admits a simple, low-order formulation suitable for implementation and subsequent control design, and that most of the model parameters are identifiable directly from standard measurements. We illustrate aspects of the model through comparison with thin-film SMA superelastic and shape memory effect hysteresis data.}, number={1-2}, journal={THIN SOLID FILMS}, author={Massad, JE and Smith, RC}, year={2005}, month={Oct}, pages={266–290} }
 @article{seelecke_kim_ball_smith_2005, title={A rate-dependent two-dimensional free energy model for ferroelectric single crystals}, volume={17}, ISSN={["1432-0959"]}, DOI={10.1007/s00161-005-0207-7}, abstractNote={The one-dimensional free energy model for ferroelectric materials developed by Smith et al. [29–31] is generalized to two dimensions. The two-dimensional free energy potential proposed in this paper consists of four energy wells that correspond to four variants of the material. The wells are separated by four saddle points, representing the barriers for 90°-switching processes, and a local maximum, across which 180°-switching processes take place. The free energy potential is combined with evolution equations for the variant fractions based on the theory of thermally activated processes. The model is compared to recent measurements on BaTiO3 single crystals by Burcsu et al. [8], and predicitions are made concerning the response to the application of in-plane multi-axial electric fields at various frequencies and loading directions. The kinetics of the 90°- and 180°-switching processes are discussed in detail.}, number={4}, journal={CONTINUUM MECHANICS AND THERMODYNAMICS}, author={Seelecke, S and Kim, SJ and Ball, BL and Smith, RC}, year={2005}, month={Dec}, pages={337–350} }
 @article{smith_hom_2005, title={A temperature-dependent constitutive model for relaxor ferroelectrics}, volume={16}, ISSN={["1045-389X"]}, DOI={10.1177/1045389x05051699}, abstractNote={ This paper addresses the development of a temperature-dependent constitutive model for relaxor ferroelectric materials. These compounds exhibit a diffuse transition region between the paraelectric and ferroelectric phases due to the chemical heterogeneity of the materials. At low temperatures, the materials exhibit significant dielectric hysteresis in the relation between the applied field E and the macroscopic polarization P, with the degree of hysteresis decreasing as the temperature increases to freezing temperature Tf. Above the freezing temperature, the relation is single-valued, but nonlinear. }, number={5}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Smith, RC and Hom, CL}, year={2005}, month={May}, pages={433–448} }
 @article{weiland_lada_smith_leo_2005, title={Application of rotational isomeric state theory to ionic polymer stiffness predictions}, volume={20}, ISSN={["0884-2914"]}, DOI={10.1557/JMR.2005.0292}, abstractNote={Presently, rotational isomeric state (RIS) theory directly addresses polymer chain conformation as it relates to mechanical response trends. The primary goal of this work is to explore the adaptation of this methodology to the prediction of material stiffness. This multiscale modeling approach relies on ionomer chain conformation and polymer morphology and thus has potential as both a predictive modeling tool and a synthesis guide. The Mark–Curro Monte Carlo methodology is applied to generate a statistically valid number of end-to-end chain lengths via RIS theory for four solvated Nafion® cases. For each case, a probability density function for chain length is estimated using various statistical techniques, including the classically applied cubic spline approach. It is found that the stiffness prediction is sensitive to the fitting strategy. The significance of various fitting strategies, as they relate to the physical structure of the polymer, are explored so that a method suitable for stiffness prediction may be identified.}, number={9}, journal={JOURNAL OF MATERIALS RESEARCH}, author={Weiland, LM and Lada, EK and Smith, RC and Leo, DJ}, year={2005}, month={Sep}, pages={2443–2455} }
 @article{smith_hatch_2005, title={Parameter estimation techniques for a class of nonlinear hysteresis models}, volume={21}, ISSN={["1361-6420"]}, DOI={10.1088/0266-5611/21/4/011}, abstractNote={This paper addresses the development of parameter estimation techniques for a class of models used to characterize hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials employed in a wide range of actuators and sensors. These models are formulated as integral equations with known kernels and unknown densities to be identified through least-squares techniques. Due to the compactness of the integral operators, the resulting discretized models inherit ill-posedness which must be accommodated through regularization. The accuracy of regularized finite-dimensional models is illustrated through comparison with experimental data.}, number={4}, journal={INVERSE PROBLEMS}, author={Smith, RC and Hatch, AG}, year={2005}, month={Aug}, pages={1363–1377} }
 @book{smith_2005, place={Philadelphia}, title={Smart Material Systems: Model Development}, publisher={SIAM}, author={Smith, R.C.}, year={2005} }
 @article{v.n. melnik_smith_shillor_2005, title={The Fourth World Congress of Nonlinear Analysts: Modelling, control and analysis of coupled problems, processes and phenomena}, volume={63}, ISSN={0362-546X}, url={http://dx.doi.org/10.1016/j.na.2005.01.041}, DOI={10.1016/j.na.2005.01.041}, number={5-7}, journal={Nonlinear Analysis: Theory, Methods & Applications}, publisher={Elsevier BV}, author={V.N. Melnik, Roderick and Smith, Ralph and Shillor, Meir}, year={2005}, month={Nov}, pages={e1421–e1423} }
 @article{massad_smith_2003, title={A  domain wall model for hysteresis in ferroelastic materials}, volume={14}, DOI={10.1177/104538903035235}, number={7}, journal={Journal of Intelligent Material Systems and Structures}, author={Massad, J. E. and Smith, Ralph}, year={2003}, pages={455–471} }
 @article{smith_seelecke_ounaies_smith_2003, title={A Free Energy Model for Hysteresis in Ferroelectric Materials}, volume={14}, ISSN={1045-389X 1530-8138}, url={http://dx.doi.org/10.1177/1045389x03038841}, DOI={10.1177/1045389X03038841}, abstractNote={ This paper provides a theory for quantifying the hysteresis and constitutive nonlinearities inherent to piezoceramic compounds through a combination of free energy analysis and stochastic homogenization techniques. In the first step of the model development, Helmholtz and Gibbs free energy relations are constructed at the lattice or domain level to quantify the relation between the field and polarization in homogeneous, single crystal compounds which exhibit uniform effective fields. The effects of material nonhomogeneities, polycrystallinity, and variable effective fields are subsequently incorporated through the assumption that certain physical parameters, including the local coercive and effective fields, are randomly distributed and hence manifestations of stochastic density functions associated with the material. Stochastic homogenization in this manner provides low-order macroscopic models with effective parameters that can be correlated with physical properties of the data. This facilitates the identification of parameters for model construction, model updating to accommodate changing operating conditions, and control design utilizing model-based inverse compensators. Attributes of the model, including the guaranteed closure of biased minor loops in quasistatic drive regimes, are illustrated through examples. }, number={11}, journal={Journal of Intelligent Material Systems and Structures}, publisher={SAGE Publications}, author={Smith, Ralph C. and Seelecke, Stefan and Ounaies, Zoubeida and Smith, Joshua}, year={2003}, month={Nov}, pages={719–739} }
 @article{smith_dapino_seelecke_2003, title={Free energy model for hysteresis in magnetostrictive transducers}, volume={93}, ISSN={["1089-7550"]}, DOI={10.1063/1.1524312}, abstractNote={This article addresses the development of a free energy model for magnetostrictive transducers operating in hysteretic and nonlinear regimes. Such models are required both for material and system characterization and for model-based control design. The model is constructed in two steps. In the first, Helmholtz and Gibbs free energy relations are constructed for homogeneous materials with constant internal fields. In the second step, the effects of material nonhomogeneities and nonconstant effective fields are incorporated through the construction of appropriate stochastic distributions. Properties of the model are illustrated through comparison and prediction of data collected from a typical Terfenol-D transducer.}, number={1}, journal={JOURNAL OF APPLIED PHYSICS}, author={Smith, RC and Dapino, MJ and Seelecke, S}, year={2003}, month={Jan}, pages={458–466} }
 @book{smith_demetriou_2003, title={Research Directions in Distributed Parameter Systems}, ISBN={9780898715484 9780898717525}, url={http://dx.doi.org/10.1137/1.9780898717525}, DOI={10.1137/1.9780898717525}, abstractNote={Research Directions in Distributed Parameter Systems is composed of eleven chapters, written by experts in their respective fields, on topics ranging from control of the Navier-Stokes equations to nondestructive evaluation - all of which are modeled by distributed parameters systems. Written by the plenary speakers for the Conference on Future Directions in Distributed Parameter Systems (October 2000), the volume addresses the state of the art, open questions, and important research directions in applications modeled by partial differential equations and delay systems, with the ultimate goal of passing along these perspectives to researchers in the field.}, publisher={Society for Industrial and Applied Mathematics}, author={Smith, Ralph and Demetriou, M.}, editor={Smith, Ralph C. and Demetriou, Michael A.Editors}, year={2003}, month={Jan} }
 @article{dapino_smith_calkins_flatau_2002, title={A coupled magnetomechanical model for magnetostrictive transducers and its application to Villari-effect sensors}, volume={13}, DOI={10.1177/104538902032737}, number={11}, journal={Journal of Intelligent Material Systems and Structures}, author={Dapino, M. J. and Smith, Ralph and Calkins, F. T. and Flatau, A. B.}, year={2002}, pages={737–747} }
 @article{bortz_rubio_banks_cain_smith_2002, title={Control of Open Bay Acoustics by Harmonic Mass Injection}, volume={1}, ISSN={1475-472X 2048-4003}, url={http://dx.doi.org/10.1260/1475472021502677}, DOI={10.1260/1475472021502677}, abstractNote={ Aircraft with internal carriage of weapons systems require active control strategies to limit high amplitude open bay acoustic resonances and to optimize structure requirements and weapon reliability in an enlarged separation envelope. This paper is focused on communicating an investigation into the use of numerical simulations combined with Proper Orthogonal Decomposition (POD) to optimize an active control system for an aircraft weapons bay application. Issues addressed include characterizing shear layer and wake resonant responses, optimal steady blowing rates, the effect of open loop harmonic perturbations, use of POD for post processing data to reduce storage requirements, and the use of the Nelder-Mead optimization procedure. Comparison of the wake and shear layer responses shows why no aircraft would ever want to experience a wake response. This study intends to develop flow instability suppression strategies that may be scalable for implementation in a weapons bay application. A lower Reynolds number flow is considered here, which can be modeled numerically with the computational resources currently available. As the essential flow physics of some cavity instabilities are mainly inviscid, it is expected that control techniques for the shear-layer instability mode may be reasonably scaled. This work focuses primarily on a freestream flow at M=0.85 with a cavity of aspect ratio L/D = 4.5. The results include the use of steady blowing injection up to M = 0.9 and harmonic forcing perturbations ranging in amplitude from M=0.005 to M=0.45. In the parameter space examined mass injection (displacement effect) has the largest effect and momentum considerations are minor. The best observed forcing reduced the buffet loading metrics by approximately 17 dB. }, number={1}, journal={International Journal of Aeroacoustics}, publisher={SAGE Publications}, author={Bortz, D. M. and Rubio, A. D. and Banks, H. T. and Cain, A. B. and Smith, R. C.}, year={2002}, month={Jan}, pages={65–81} }
 @article{smith_2001, title={Inverse compensation for hysteresis in magnetostrictive transducers}, volume={33}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(00)00245-4}, abstractNote={This paper addresses the development of inverse compensation techniques for a class of ferromagnetic transducers including magnetostrictive actuators. If unaccommodated, the hysteresis and nonlinear dynamics can produce severe loss of control authority and potential instabilities when the actuators are incorporated in control design. In this work, hysteresis is modeled through the domain wall theory originally proposed by Jiles and Atherton [1]. This model is based on the quantification of the energy required to translate domain walls pinned at inclusions in the material with the magnetization at a given field level specified through the solution of an ordinary differential equation. A complementary differential equation is then employed to compute the inverse which can be used to compensate for hysteresis and nonlinear dynamics in control design. The performance of the inverse compensator and its employment in LQR control design are illustrated through numerical examples.}, number={1-3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Smith, RC}, year={2001}, pages={285–298} }
 @article{dapino_smith_faidley_flatau_2000, title={A coupled structural-magnetic strain and stress model for magnetostrictive transducers}, volume={11}, DOI={10.1106/MJ6A-FBP9-9M61-0E1F}, abstractNote={ This paper addresses the modeling of strains and forces generated by magnetostrictive transducers in response to applied magnetic fields. The magnetostrictive effect is modeled by considering both the rotation of magnetic moments in response to the field and the elastic vibrations in the transducer. The former is modeled with the Jiles-Atherton model of ferromagnetic hysteresis in combination with a quartic magnetostriction law. The latter is modeled through force balancing which yields a PDE system with magnetostrictive inputs and boundary conditions given by the specific transducer design. The solution to this system provides both rod displacements and forces. The calculated forces are used to quantify the magnetomechanical effect in the transducer core, i.e., the stress-induced magnetization changes. This is done by considering a “law of approach” to the anhysteretic magnetization. The resulting model provides a representation of the bidirectional coupling between the magnetic and elastic states. It is demonstrated that the model accurately characterizes the magnetic hysteresis in the material, as well as the strains and forces output by the transducer under conditions typical of engineering applications. }, number={2}, journal={Journal of Intelligent Material Systems and Structures}, author={Dapino, M. J. and Smith, Ralph and Faidley, L. E. and Flatau, A. B.}, year={2000}, pages={135–152} }
 @article{smith_ounaies_2000, title={A domain wall model for hysteresis in piezoelectric materials}, volume={11}, ISSN={["1045-389X"]}, DOI={10.1177/104538900772664413}, number={1}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Smith, RC and Ounaies, Z}, year={2000}, month={Jan}, pages={62–79} }
 @article{piquette_smith_2000, title={Analysis and comparison of four anhysteretic polarization models for lead magnesium niobate}, volume={108}, ISSN={["0001-4966"]}, DOI={10.1121/1.1310670}, abstractNote={Four anhysteretic polarization models that have been used in the literature to evaluate data acquired from lead magnesium niobate (PMN) are analyzed and compared. Derivations of two of the models from assumed spatial distributions of dipole energy states, using first physical principles, are presented. A third model is derived from a suitable integral averaging calculation. These derivations are used as the basis for developing an integral equation for determining an energy-state distribution that produces a fourth model, which was not originally formulated in terms of an assumed distribution. A new polarization function is also presented. Excellent approximations to each of the four polarization functions of interest can be deduced from this new polarization function by adjusting the numerical value of just a single parameter. An application of two of the models to data is presented. It is shown that it can be necessary to consider a sample to be an admixture of two distinct species of poles, in the sense that two polarization functions must be added together in order to accommodate the data.}, number={4}, journal={JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA}, author={Piquette, JC and Smith, RC}, year={2000}, month={Oct}, pages={1651–1662} }
 @article{calkins_smith_flatau_2000, title={Energy-based hysteresis model for magnetostrictive transducers}, volume={36}, ISSN={["0018-9464"]}, DOI={10.1109/20.825804}, abstractNote={This paper addresses the modeling of hysteresis in magnetostrictive transducers in the context of control applications that require an accurate characterization of the relation between input currents and strains output by the transducer. This relation typically exhibits significant nonlinearities and hysteresis because of inherent properties of magnetostrictive materials. The characterization considered here is based on the Jiles-Atherton mean field model for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. As demonstrated by comparison with experimental data, the magnetization model very adequately quantifies both major and minor loops under various operating conditions. The combined model can then be used to accurately characterize output strains at moderate drive levels. The advantages of this model lie in the small number (six) of required parameters and its flexibility under a variety of operating conditions.}, number={2}, journal={IEEE TRANSACTIONS ON MAGNETICS}, author={Calkins, FT and Smith, RC and Flatau, AB}, year={2000}, month={Mar}, pages={429–439} }
 @book{gremaud_li_smith_tran_2000, place={Philadelphia}, title={Industrial Mathematics: The 1998 CRSC Workshop}, ISBN={0898714672}, publisher={SIAM}, year={2000} }
 @book{industrial mathematics: the 1998 crsc workshop_2000, publisher={SIAM}, year={2000} }
 @article{chandrasekaran_lindner_smith_2000, title={Optimized design of switching amplifiers for piezoelectric actuators}, volume={11}, ISSN={["1045-389X"]}, DOI={10.1106/XFC7-PD82-LDFC-T2R9}, abstractNote={The formulation and solution of an optimization problem for the design of a current controlled switching power amplifier to drive a piezoelectric actuator is the subject of this paper. The design is formulated as a continuous optimization problem. A detailed model that includes the anhysteretic nonlinearity between the electric field and polarization is developed and is coupled with a dynamic model of the amplifier. The design specifications are formulated as optimization constraints. The objective function is chosen to be the weight of the inductor. Optimization results are presented to demonstrate the efficiency of the proposed design methodology.}, number={11}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Chandrasekaran, S and Lindner, DK and Smith, RC}, year={2000}, month={Nov}, pages={887–901} }
 @article{banks_rosario_smith_2000, title={Reduced-order model feedback control design: Numerical implementation in a thin shell model}, volume={45}, ISSN={["0018-9286"]}, DOI={10.1109/9.867024}, abstractNote={Reduced-order models employing the Lagrange and popular proper orthogonal decomposition (POD) reduced-basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actuators. Donnell-Mushtari equations, modified to include Kelvin-Voigt damping, are used to model the system dynamics. Basis functions constructed from Fourier polynomials tensored with cubic splines are employed in the Galerkin expansion of the full-order model. Reduced-basis elements are then formed from full order approximations of the exogenously excited shell taken at different time instances. Numerical examples illustrating the features of the reduced-basis methods are presented. As a first step toward investigating the behavior of the methods when implemented in physical systems, the use of reduced-order model feedback control gains in the full order model is considered and numerical examples are presented.}, number={7}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Banks, HT and Rosario, RCH and Smith, RC}, year={2000}, month={Jul}, pages={1312–1324} }
 @article{dapino_smith_flatau_2000, title={Structural magnetic strain model for magnetostrictive transducers}, volume={36}, ISSN={["0018-9464"]}, DOI={10.1109/20.846217}, abstractNote={This paper addresses the modeling of strains generated by magnetostrictive transducers in response to applied magnetic fields. The measured strains depend on both the rotation of moments within the material in response to the field and the elastic properties of the material. The magnetic behavior is characterized by considering the Jiles-Atherton mean field theory for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. Elastic properties must be incorporated to account for the dynamics of the material as it vibrates. This is modeled by force balancing, which yields a wave equation with magnetostrictive inputs. The validity of the resulting transducer model is illustrated by comparison with experimental data.}, number={3}, journal={IEEE TRANSACTIONS ON MAGNETICS}, author={Dapino, MJ and Smith, RC and Flatau, AB}, year={2000}, month={May}, pages={545–556} }
 @article{smith_hom_1999, title={Domain wall theory for ferroelectric hysteresis}, volume={10}, ISSN={["1530-8138"]}, DOI={10.1106/LJBM-RW18-MXW1-QXD0}, abstractNote={This paper addresses the modeling of hysteresis in ferroelectric materials through consideration of domain wall bending and translation. The development is considered in two steps. First, dielectric constitutive relations are obtained through consideration of Langevin, Ising spin and preferred orientation theories with domain interactions incorporated through mean field relations. This yields a model for the anhysteretic polarization that occurs in the absence of domain wall pinning. Second, hysteresis is incorporated through the consideration of domain wall dynamics and the quantification of energy losses due to inherent inclusions or pinning sites within the material. This yields a model analogous to that developed by Jiles and Atherton for ferromagnetic materials. The viability of the model is illustrated through comparison with experimental data from a PMN-PT-BT actuator operating at a temperature within the ferroelectric regime.}, number={3}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Smith, RC and Hom, CL}, year={1999}, month={Mar}, pages={195–213} }
 @article{smith_1998, title={A nonlinear optimal control method for magnetostrictive actuators}, volume={9}, ISSN={["1045-389X"]}, DOI={10.1177/1045389X9800900608}, abstractNote={This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent in the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.}, number={6}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Smith, RC}, year={1998}, month={Jun}, pages={468–486} }
 @article{smith_1998, title={Hysteresis Modeling in Magnetostrictive Materials Via Preisach Operators}, volume={8}, number={2}, journal={Journal of Mathematical Systems, Estimation and Control}, author={Smith, R.C.}, year={1998} }
 @article{del rosario_smith_1998, title={LQR control of thin shell dynamics: Formulation and numerical implementation}, volume={9}, ISSN={["1045-389X"]}, DOI={10.1177/1045389X9800900408}, abstractNote={ A PDE-based feedback control method for thin cylindrical shells with surface-mounted piezoceramic actuators is presented. Donnell-Mushtari equations modified to incorporate both passive and active piezoceramic patch contributions are used to model the system dynamics. The well-posedness of this model and the associated LQR problem with an unbounded input operator are established through analytic semigroup theory. The model is discretized using a Galerkin expansion and basis functions constructed from Fourier polynomials tensored with cubic splines, and convergence criteria for the associated approximate LQR problem are established. The effectiveness of the method for attenuating the coupled longitudinal, circumferential and transverse shell displacements is illustrated through a set of numerical examples. }, number={4}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Del Rosario, RCH and Smith, RC}, year={1998}, month={Apr}, pages={301–320} }
 @article{banks_demetriou_smith_1998, title={Utilization of coupling effects in compensator design for structural acoustic systems}, volume={103}, ISSN={["0001-4966"]}, DOI={10.1121/1.421205}, abstractNote={The quantification and utilization of coupling effects in a prototypical structural acoustic system are examined in this paper. In typical systems, the coupling mechanisms are manifested in two ways. The first leads to the transfer of energy from an ambient field to an adjacent structure and is often responsible for exogenous structural excitation. The second involves the transfer of energy from the vibrating structure to an adjacent field. This is the source of structure-borne noise and is ultimately the mechanism through which structural actuators are utilized to attenuate noise. The examples presented here demonstrate that in fully coupled systems, both mechanisms should be incorporated to accurately model system dynamics. The examples also illustrate advantages and limitations of compensators which utilize the accurate modeling of the structural coupling.}, number={2}, journal={JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA}, author={Banks, HT and Demetriou, MA and Smith, RC}, year={1998}, month={Feb}, pages={872–887} }
 @article{smith_1997, title={A Galerkin Method for Linear PDE Systems in Circular Geometries with Structural Acoustic Problems}, volume={18}, ISSN={1064-8275 1095-7197}, url={http://dx.doi.org/10.1137/s1064827594268531}, DOI={10.1137/s1064827594268531}, abstractNote={A Galerkin method for systems of PDEs in circular geometries is presented with motivating problems being drawn from structural, acoustic, and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximating the system dynamics with modifications included to incorporate the analytic solution decay near the coordinate singularity. This provides an efficient method which retains its accuracy throughout the circular domain without degradation at the singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coefficients, transform methods for the problems are not investigated. While the specific method is developed for the 2-D wave equation on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the flexibility of the method when approximating the dynamics of more complex systems.}, number={2}, journal={SIAM Journal on Scientific Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Smith, Ralph C.}, year={1997}, month={Mar}, pages={371–402} }
 @article{banks_smith_zhang_1997, title={Damage Detection as Inverse Problems for Distributed Parameter Systems: Computational Approaches}, volume={8}, journal={International Journal of Applied Electromagnetics and Mechanics}, author={Banks, H.T. and Smith, R.C. and Zhang, Y.}, year={1997}, pages={61–76} }
 @article{banks_smith_brown_silcox_metcalf_1997, title={Experimental confirmation of a PDE-based approach to design of feedback controls}, volume={35}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012995285909}, abstractNote={Issues regarding the experimental implementation of PDE-based controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surface-mounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vector-valued initial value problem. Optimal control theory is used to determine continuous-time voltages to the patches, and the approximations needed to facilitate discrete-time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady-state vibrations through these techniques are presented.}, number={4}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Banks, HT and Smith, RC and Brown, DE and Silcox, RJ and Metcalf, VL}, year={1997}, month={Jul}, pages={1263–1296} }
 @article{smith_bowers_vogel_1997, title={Numerical Recovery of Material Parameters in Euler-Bernoulli Beam Models}, volume={7}, number={2}, journal={Journal of Mathematical Systems, Estimation and Control}, author={Smith, R.C. and Bowers, K.L. and Vogel, C.R.}, year={1997}, pages={157–195} }
 @article{rosario_smith_1997, title={Spline approximation of thin shell dynamics}, volume={40}, DOI={10.1002/(sici)1097-0207(19970815)40:15<2807::aid-nme192>3.0.co;2-h}, abstractNote={Abstract : A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material nonhomogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method.}, number={15}, journal={International Journal for Numerical Methods in Engineering}, author={Rosario, R. C. Del and Smith, Ralph}, year={1997}, pages={2807–2840} }
 @article{banks_smith_brown_metcalf_silcox_1997, title={THE ESTIMATION OF MATERIAL AND PATCH PARAMETERS IN A PDE-BASED CIRCULAR PLATE MODEL}, volume={199}, ISSN={0022-460X}, url={http://dx.doi.org/10.1006/jsvi.1996.0649}, DOI={10.1006/jsvi.1996.0649}, abstractNote={Abstract The estimation of material and patch parameters for a system involving a circular plate, to which piezoceramic are bonded, is considered. A partial differential equation (PDE) model for the thin circular plate is used with the passive and active contributions from the patches included in the internal and external bending moments. This model contains piecewise constant parameters describing the density, flexural rigidity, Poisson ratio and Kelvin-Voigt damping for the system, as well as patch constants and a coefficient for viscous air damping. Examples demonstrating the estimation of these parameters with experimental acceleration data and a variety of inputs to the experimental plate are presented. By using a physically derived PDE model to describe the system, parameter sets consistent across experiments are obtained, even when phenomena such as damping due to electric circuits affect the system dynamics.}, number={5}, journal={Journal of Sound and Vibration}, publisher={Elsevier BV}, author={Banks, H.T. and Smith, R.C. and Brown, D.E. and Metcalf, V.L. and Silcox, R.J.}, year={1997}, month={Feb}, pages={777–799} }
 @article{banks_demitriou_smith_1996, title={An H∞/MinMax Periodic Control in a 2-D Structural Acoustic Model with Piezoceramic Actuators}, volume={41}, ISSN={0018-9286}, url={http://dx.doi.org/10.1109/9.508899}, DOI={10.1109/9.508899}, abstractNote={A feedback control computational methodology for reducing acoustic sound pressure levels in a two-dimensional cavity with a flexible boundary (a beam) is investigated. The control is implemented in this model through voltages to piezoceramic patches on the beam which are excited in a manner (out-of-phase) so as to produce pure bending moments. The incorporation of the output feedback control in this system leads to a problem with unbounded input and output terms. By writing the resulting system as an abstract Cauchy equation, the problem of reducing interior pressure levels can be posed in the context of an H/sub /spl infin///MinMax time-domain state-space formulation. A summary of extensive computational efforts comparing output feedback to full state feedback and investigating the effect of the number and location of sensors on performance of the control is presented.}, number={7}, journal={IEEE Transactions on Automatic Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Banks, H.T. and Demitriou, M.A. and Smith, R.C.}, year={1996}, month={Jul}, pages={943–959} }
 @article{banks_smith_wang_1996, title={Inverse problems in smart material structures}, volume={4}, ISSN={0928-0219 1569-3945}, url={http://dx.doi.org/10.1515/jiip.1996.4.5.371}, DOI={10.1515/jiip.1996.4.5.371}, number={5}, journal={Journal of Inverse and Ill-Posed Problems}, publisher={Walter de Gruyter GmbH}, author={Banks, H. T. and Smith, R. C. and Wang, Y.}, year={1996} }
 @article{banks_smith_1996, title={Parameter estimation in a structural acoustic system with fully nonlinear coupling conditions}, volume={23}, ISSN={0895-7177}, url={http://dx.doi.org/10.1016/0895-7177(96)00002-7}, DOI={10.1016/0895-7177(96)00002-7}, abstractNote={A methodology for estimating physical parameters in a class of structural acoustic systems is presented. The general model under consideration consists of an interior cavity which is separated from an exterior disturbance by an enclosing elastic structure. Piezoceramic patches are bonded to or embedded in the structure; these can be used both as actuators and sensors in applications ranging from the control of interior noise levels to the determination of structural flaws through nondestructive evaluation techniques. The presence and excitation of the patches, however, changes the geometry and material properties of the structure as well as involves unknown patch parameters, thus necessitating the development of parameter estimation techniques which are applicable in this coupled setting. In developing a framework for approximation, parameter estimation and implementation, strong consideration is given to the fact that the input operator is unbonded due to the discrete nature of the patches. Moreover, the model is weakly nonlinear as a result of the coupling mechanism between the structural vibrations and the interior acoustic dynamics. Within this context, an illustrating model is given, well-posedness and approximation results are discussed and an applicable parameter estimation methodology is presented. The scheme is then illustrated through several numerical examples with simulations modeling a variety of commonly used structural acoustic techniques for system excitation and data collection.}, number={4}, journal={Mathematical and Computer Modelling}, publisher={Elsevier BV}, author={Banks, H.T. and Smith, R.C.}, year={1996}, month={Feb}, pages={17–50} }
 @article{banks_demetriou_smith_1996, title={Robustness studies for H∞ feedback control in a structural acoustic model with periodic excitation}, volume={6}, ISSN={1049-8923 1099-1239}, url={http://dx.doi.org/10.1002/(sici)1099-1239(199606)6:5<453::aid-rnc222>3.0.co;2-5}, DOI={10.1002/(sici)1099-1239(199606)6:5<453::aid-rnc222>3.0.co;2-5}, abstractNote={Results from an extensive study on the robustness of an H∞ compensator for a 2-D structural acoustic model are presented. The effects of frequency uncertainties in an exogenous signal are studied for both the case where the signal is contained in the controller formulation and the case where it is excluded. Delays are inserted in the input and/or output signals and their effect on the controller performance is recorded. A comparison between the standard LQG/Kalman filter and the H∞/Min-Max compensator reveals no significant differences in the overall controller performance. Modifications in the controller structure are studied to see whether loss of information (the tracking variable) that must be calculated a priori would result in performance degradation. This study provides valuable insight into the computational and implementational issues that arise when dealing with the control of large and complex systems that are governed by partial differential equations.}, number={5}, journal={International Journal of Robust and Nonlinear Control}, publisher={Wiley}, author={Banks, H. T. and Demetriou, M. A. and Smith, R. C.}, year={1996}, month={Jun}, pages={453–478} }
 @book{banks_smith_wang_1996, place={Paris/Chichester}, title={Smart Material Structures: Modeling, Estimation and Control}, publisher={Masson/John Wiley}, author={Banks, H.T. and Smith, R.C. and Wang, Y.}, year={1996} }
 @inbook{banks_smith_1995, title={Active Control of Acoustic Pressure Fields Using Smart Material Technologies}, ISBN={9781461275695 9781461225263}, ISSN={0940-6573}, url={http://dx.doi.org/10.1007/978-1-4612-2526-3_1}, DOI={10.1007/978-1-4612-2526-3_1}, abstractNote={An overview describing the use of piezoceramic patches in reducing noise in a structural acoustics setting is presented. The passive and active contributions due to patches which are bonded to an Euler-Bernoulli beam or thin shell are briefly discussed and the results are incorporated into a 2-D structural acoustics model. In this model, an exterior noise source causes structural vibrations which in turn lead to interior noise as a result of nonlinear fluid/structure coupling mechanisms. Interior sound pressure levels. are reduced via patches bonded to the flexible boundary (a beam in this case) which generate pure bending moments when an out-of-phase voltage is applied. Wellposedness results for the infinite dimensional system are discussed and a Galerkin scheme for approximating the system dynamics is outlined. Control is implemented by using LQR optimal control theory to calculate gains for the linearized system and then feeding these gains back into the nonlinear system of interest. The effectiveness of this strategy for this problem is illustrated in an example.}, booktitle={Flow Control}, publisher={Springer New York}, author={Banks, H. T. and Smith, R. C.}, year={1995}, pages={1–33} }
 @article{banks_smith_wang_1995, title={The modeling of piezoceramic patch interactions with shells, plates, and beams}, volume={53}, ISSN={0033-569X 1552-4485}, url={http://dx.doi.org/10.1090/qam/1330657}, DOI={10.1090/qam/1330657}, abstractNote={General models describing the interactions between one or a pair of piezoceramic patches and elastic substructures consisting of a cylindrical shell, plate, or beam are presented. In each case, the contributions to the internal moments and forces due to the presence of the patches are carefully discussed. In addition to these material contributions, the input of voltage to the patches produces mechanical strains that lead to external moments and forces. These external loads depend on the material properties of the patch, the geometry of patch placement, and the voltage. The internal and external moments and forces due to the patches are then incorporated into the equations of motion, which yields models describing the dynamics of the combined structure. These models are sufficiently general to allow for potentially different patch voltages, which implies that they can be suitably employed when using piezoceramic patches for controlling system dynamics when both extensional and bending vibrations are present.}, number={2}, journal={Quarterly of Applied Mathematics}, publisher={American Mathematical Society (AMS)}, author={Banks, H. T. and Smith, R. C. and Wang, Yun}, year={1995}, month={Jun}, pages={353–381} }
 @article{banks_smith_1995, title={Well-Posedness of a Model for Structural Acoustic Coupling in a Cavity Enclosed by a Thin Cylindrical Shell}, volume={191}, ISSN={0022-247X}, url={http://dx.doi.org/10.1016/s0022-247x(85)71117-1}, DOI={10.1016/s0022-247x(85)71117-1}, abstractNote={A fully coupled mathematical model describing the interactions between a vibrating thin cylindrical shell and an enclosed acoustic field is presented. Because the model will ultimately be used in control applications involving piezoceramic actuators, the loads and material contributions resulting from piezoceramic patches bonded to the shell are included in the discussion. Theoretical and computational issues lead to the consideration of a weak form of the modeling set of partial differential equations (PDEs) and through the use of a semigroup formulation, well-posedness results for the system model are obtained.}, number={1}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Banks, H.T. and Smith, R.C.}, year={1995}, month={Apr}, pages={1–25} }
 @article{smith_banks_1994, title={Feedback control of noise in a 2-D nonlinear structural acoustics model}, volume={1}, ISSN={1078-0947}, url={http://dx.doi.org/10.3934/dcds.1995.1.119}, DOI={10.3934/dcds.1995.1.119}, abstractNote={A time domain feedback control methodology for reducing sound pressure 
levels in a nonlinear 2-D structural acoustics application is presented. The 
interior noise in this problem is generated through vibrations of one wall of the 
cavity (in this case a beam), and control is implemented through the excitation of 
piezoceramic patches which are bonded to the beam. These patches are mounted 
in pairs and are wired so as to create pure bending moments which directly affect 
the manner in which the structure vibrates. Th application of control in 
this manner leads to an unbounded control input term and the implications of 
this are discussed. The coupling between the beam vibrations and the interior 
acoustic response is inherently nonlinear, and this is addressed when developing 
a control scheme for the problem. Gains for the problem are calculated using a 
periodic LQR theory and are then fed back into the nonlinear system with results 
being demonstrated by a set of numerical examples. In particular, these examples 
demonstrate the viability of the method in cases involving excitation involving 
a large number of frequencies through both spatially uniform and nonuniform 
exterior forces.}, number={1}, journal={Discrete and Continuous Dynamical Systems}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Smith, R.C. and Banks, H.T.}, year={1994}, month={Oct}, pages={119–149} }
 @article{banks_silcox_smith_1994, title={Modeling and Control of Acoustic Structure Interaction Problems Via Piezoceramic Actuators: 2-D Numerical Examples}, volume={116}, ISSN={0739-3717}, url={http://dx.doi.org/10.1115/1.2930440}, DOI={10.1115/1.2930440}, abstractNote={The modeling and active control of acoustic pressure in a 2-D cavity with a flexible boundary (a beam) is considered. Control is implemented in the model via piezoceramic patches on the beam, which are excited in a manner so as to produce pure bending moments. Approximation techniques are discussed and, by writing the resulting system as an abstract Cauchy equation, the problem of reducing interior pressure fluctuations can be posed in the context of an LQR time domain state space formulation. Examples illustrating the dynamic behavior of the coupled system, as well as demonstrating the viability of the control method on a variety of problems with periodic forcing functions, are presented.}, number={3}, journal={Journal of Vibration and Acoustics}, publisher={ASME International}, author={Banks, H. T. and Silcox, R. J. and Smith, R. C.}, year={1994}, pages={386} }
 @article{banks_fang_silcox_smith_1993, title={Approximation Methods for Control of Structural Acoustics Models with Piezoceramic Actuators}, volume={4}, ISSN={1045-389X 1530-8138}, url={http://dx.doi.org/10.1177/1045389x9300400113}, DOI={10.1177/1045389x9300400113}, abstractNote={ The active control of acoustic pressure in a 2-D cavity with a flexible boundary (a beam) is considered. Specifically, this control is implemented via piezoceramic patches on the beam which produce pure bending moments. The incorporation of the feedback control in this manner leads to a system with an unbounded input term. Approximation methods in the context of an LQR state space formulation are discussed and numerical results demonstrating the effectiveness of this approach in computing feedback controls for noise reduction are presented. }, number={1}, journal={Journal of Intelligent Material Systems and Structures}, publisher={SAGE Publications}, author={Banks, H.T. and Fang, W. and Silcox, R.J. and Smith, R.C.}, year={1993}, month={Jan}, pages={98–116} }
 @inbook{banks_smith_1993, place={Philadelphia}, title={Models for Control in Smart Material Structures}, booktitle={Identification and Control in Systems Governed by Partial Differential Equations}, publisher={SIAM}, author={Banks, H.T. and Smith, R.C.}, year={1993}, pages={26–44} }
 @article{smith_bowers_1993, title={Sinc-Galerkin estimation of diffusivity in parabolic problems}, volume={9}, ISSN={0266-5611 1361-6420}, url={http://dx.doi.org/10.1088/0266-5611/9/1/007}, DOI={10.1088/0266-5611/9/1/007}, abstractNote={A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear parabolic partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an appropriate value of the regularization parameter is briefly discussed, and numerical examples are given which demonstrate the applicability of the method both for problems with noise-free data as well as for those whose data contain white noise.}, number={1}, journal={Inverse Problems}, publisher={IOP Publishing}, author={Smith, R C and Bowers, K L}, year={1993}, month={Feb}, pages={113–135} }
 @article{smith_bowers_lund_1992, title={A fully Sinc-Galerkin method for Euler-Bernoulli beam models}, volume={8}, ISSN={0749-159X 1098-2426}, url={http://dx.doi.org/10.1002/num.1690080207}, DOI={10.1002/num.1690080207}, abstractNote={Abstract}, number={2}, journal={Numerical Methods for Partial Differential Equations}, publisher={Wiley}, author={Smith, Ralph C. and Bowers, Kenneth L. and Lund, John}, year={1992}, month={Mar}, pages={171–202} }
 @article{mcarthur_smith_lund_bowers_1992, title={The Sinc-Galerkin method for parameter-dependent self-adjoint problems}, volume={50}, ISSN={0096-3003}, url={http://dx.doi.org/10.1016/0096-3003(92)90125-k}, DOI={10.1016/0096-3003(92)90125-k}, abstractNote={The Sinc-Galerkin method is being applied to a growing number of diverse problems in ordinary and partial differential equations including both forward and inverse (parameter recovery) problems. As a result of these continuing extensions, the treatment of parameter-dependent problems needs to be thoroughly investigated. Two specific questions considered here are the incorporation of various nonhomogeneous boundary conditions and the treatment of a variable parameter. The latter topic is particularly important for inverse problems that arise when numerically estimating physical parameters. The point of view taken emphasizes the maintenance of the classical exponential convergence rate. The techniques described are suitable both for the direct problem and for the parameter estimation problem. Numerical results are presented to substantiate the accuracy of the method.}, number={2-3}, journal={Applied Mathematics and Computation}, publisher={Elsevier BV}, author={McArthur, Kelly M. and Smith, Ralph C. and Lund, John and Bowers, Kenneth L.}, year={1992}, month={Mar}, pages={175–202} }
 @article{smith_bogar_bowers_lund_1991, title={The Sinc-Galerkin Method for Fourth-Order Differential Equations}, volume={28}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0728041}, DOI={10.1137/0728041}, abstractNote={The Sinc-Galerkin method originally proposed by Stenger is extended to handle fourth-order ordinary differential equations. The exponential convergence rate of the method, $O(e^{ - \kappa \sqrt M } )$ is carefully developed and the special features of the discrete system are described. Spectral properties and conditioning of the associated matrices are given. The appropriate choice of weight function in the Galerkin inner product is discussed with primary emphasis given to choices that are best suited to fourth-order partial differential equations. Numerical results are included to help illustrate the parameter selections made and confirm the efficiency and accuracy of the method.}, number={3}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Smith, Ralph C. and Bogar, Gary A. and Bowers, Kenneth L. and Lund, John}, year={1991}, month={Jun}, pages={760–788} }