Electromechanical properties identification for groups of piezoelectric energy harvester based on Bayesian inference

A framework that allows the use of well-known dynamic estimators to infer the electromechanical properties in Piezoelectric Energy Harvesters (PEHs) is presented here. The framework is based on Bayesian inference applied over experimental results obtained from Frequency Response Functions (FRFs). The posterior probability density function is approximated adopting the Transitional Markov Chain Monte Carlo algorithm. A similar approach has been developed recently to perform the electromechanical properties updating for a single PEH. However, our results show that the former approach is not suitable to update the properties associated to a set of PEHs since it mismatches the normalized FRF. The proposed framework extends the previous formulation to solve this issue. The likelihood function is modified to account for a predictive model with three outputs obtained by manipulating the information available in the FRF. The proposed framework in this contribution can be used by manufacturers to update the nominal properties of groups of devices and, simultaneously, to identify the variability induced by the manufacturing process.