Model parameter identification and model class selection in piezoelectric energy harvester based on bayesian inference

Abstract

The model updating of the electro-mechanical properties of Piezoelectric Energy Harvesters (PEHs) using experimental data within a Bayesian inference setting is discussed. The implementation requires: a predictive model for the harvester response; an assumption for its prediction error; a prior multivariate probabilistic density function for the electromechanical properties; and experimental measurements of the harvester response. Different approaches are compared with respect to the Bayesian model updating, including point estimates of the updated properties based on Maximum a Posteriori (MAP) and Maximum Likelihood Estimates (MLE), as well as a full description of the posterior density for the model characteristics, obtained through a Transitional Markov Chain Monte Carlo approach. A model class selection implementation is also discussed that allows for the consideration of some PEH properties as either deterministic or aleatoric (uncertain) variables. The overall framework offers an elegant approach to calibrate PEH numerical/analytical model or identify variability trends for the PEH manufacturing process.