Quantification of parameter and model uncertainty for shape memory alloy bending actuators

Abstract

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.