Hierarchical Bayesian Approach for Model Parameter Updating in Piezoelectric Energy Harvesters

This work proposes a hierarchical Bayesian framework to identify electromechanical properties of Piezoelectric Energy Harvesters (PEHs) and associated uncertainties based on experimental frequency response functions (FRFs). The framework allows the use of experimental data from multiple devices, potentially defined by different electromechanical properties. In the proposed hierarchical scheme, the FRF dispersion experimentally observed in groups of PEHs is explicitly modeled as a consequence of uncertainties in the model parameters rather than as a consequence of only the model prediction error typically used in classical Bayesian scheme. The Transitional Markov Chain Monte Carlo (TMCMC) method is used to establish the full posterior distribution of the model parameters. Preference towards selection of the hierarchical scheme is further confirmed by using Bayesian model class selection to compare the posterior probabilities of selecting the hierarchical or the classical scheme. The proposed framework is applied to identification of model parameters for both a single device and groups of devices. Results show that the proposed hierarchical scheme present significant advantages compared to other Bayesian based approaches for PEHs. First, it extracts more information about the model parameters using the same experimental observations (i.e., extract information at both device and group level); second, it accounts for the model parameter uncertainties across different devices; third, it could be used to identify objective priors for classical Bayesian approach.