@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{kirschmeier_pash_gianikos_medina_gopalarathnam_bryant_2020, title={Aeroelastic inverse: Estimation of aerodynamic loads during large amplitude limit cycle oscillations}, volume={98}, ISSN={["0889-9746"]}, DOI={10.1016/j.jfluidstructs.2020.103131}, abstractNote={This paper presents an algorithm to compute the aerodynamic forces and moments of an aeroelastic wing undergoing large amplitude heave and pitch limit cycle oscillations. The technique is based on inverting the equations of motion to solve for the lift and moment experienced by the wing. Bayesian inferencing is used to estimate the structural parameters of the system and generate credible intervals on the lift and moment calculations. The inversion technique is applied to study the affect of mass coupling on limit cycle oscillation amplitude. Examining the force, power, and energy of the system, the reasons for amplitude growth with wind speed can be determined. The results demonstrate that the influence of mass coupling on the pitch–heave difference is the driving factor in amplitude variation. The pitch–heave phase difference not only controls how much aerodynamic energy is transferred into the system but also how the aerodynamic energy is distributed between the degrees of freedom.}, journal={JOURNAL OF FLUIDS AND STRUCTURES}, author={Kirschmeier, Benjamin and Pash, Graham and Gianikos, Zachary and Medina, Albert and Gopalarathnam, Ashok and Bryant, Matthew}, year={2020}, month={Oct} }
 @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} }