@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{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{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{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{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{gao_miles_moura_hussaini_oates_2019, title={Uncertainty analysis of dielectric elastomer membranes under electromechanical loading}, volume={28}, ISSN={["1361-665X"]}, DOI={10.1088/1361-665X/aaedea}, abstractNote={The uncertainty in modeling finite deformation membrane electromechanics is analyzed by comparing low and high fidelity models against data on the dielectric elastomer VHB 4910. Both models include electrically and mechanically induced stress during transverse deformation of the membranes. The low fidelity model approximates deformation to be homogeneous while the high fidelity model includes a more accurate kinematic assumption of inhomogeneous deformation. We illustrate the importance of model fidelity with regards to parameter uncertainty and the associated propagation of errors in predicting membrane forces and charges in realistic actuator configurations. Both the low and high fidelity models are shown to accurately predict membrane forces and charges under different applied displacements and voltages. However, there are significant differences in the estimation of the dielectric constant used to model the membrane electromechanics. Bayesian statistics are used to quantify the uncertainty of the modeling approaches in light of both force–displacement and charge–voltage measurements. We quantify the hyperelastic, electromechanical coupling, and dielectric model uncertainties self-consistently using all mechanical and electrical experiments conducted on the 3M elastomer VHB 4910. We conclude that the low fidelity model is useful for system dynamic and control applications yet is limited in self-consistent predictions of both forces and charges from applied displacements and voltages. In comparison, the high fidelity model provides a more accurate description of the electromechanical coupling and dielectric constitutive behavior, but requires more computational power due to finite element discretization. In addition, the high fidelity modeling illustrates that a deformation dependent dielectric constant is necessary to self-consistently simulate both force–displacement and charge–voltage data.}, number={5}, journal={SMART MATERIALS AND STRUCTURES}, author={Gao, W. and Miles, P. R. and Moura, A. G. and Hussaini, M. Y. and Oates, W. S.}, year={2019}, month={May} }
 @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{solheim_stanisauskis_miles_oates_2018, title={Fractional Viscoelasticity of Soft Elastomers and Auxetic Foams}, volume={10596}, ISSN={["1996-756X"]}, DOI={10.1117/12.2296666}, abstractNote={Dielectric elastomers are commonly implemented in adaptive structures due to their unique capabilities for real time control of a structure’s shape, stiffness, and damping. These active polymers are often used in applications where actuator control or dynamic tunability are important, making an accurate understanding of the viscoelastic behavior critical. This challenge is complicated as these elastomers often operate over a broad range of deformation rates. Whereas research has demonstrated success in applying a nonlinear viscoelastic constitutive model to characterize the behavior of Very High Bond (VHB) 4910, robust predictions of the viscoelastic response over the entire range of time scales is still a significant challenge. An alternative formulation for viscoelastic modeling using fractional order calculus has shown significant improvement in predictive capabilities. While fractional calculus has been explored theoretically in the field of linear viscoelasticity, limited experimental validation and statistical evaluation of the underlying phenomena have been considered. In the present study, predictions across several orders of magnitude in deformation rates are validated against data using a single set of model parameters. Moreover, we illustrate the fractional order is material dependent by running complementary experiments and parameter estimation on the elastomer VHB 4949 as well as an auxetic foam. All results are statistically validated using Bayesian uncertainty methods to obtain posterior densities for the fractional order as well as the hyperelastic parameters.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES XII}, author={Solheim, Hannah and Stanisauskis, Eugenia and Miles, Paul and Oates, William}, year={2018} }