20. Model Class Selection and Model Parameter Identification on Piezoelectric Energy Harvesters

The dynamic behavior of piezoelectric energy harvesters has been widely studied in the last decade. Different deterministic modeling techniques and simplifications have been adopted to describe their electromechanical coupling effect in order to increase the accuracy on the output power estimation. Although it is a common practice to use deterministic models to predict the input-output (I/O) behavior of piezoelectric harvesters, perfect predictions are not expected since these devices are not exempt of uncertainties. The accuracy of the output estimation is affected mainly by the uncertainties on its electromechanical properties, requiring in many cases a parameter identification based on experimental measurements. In this context, two main questions arise: (1) how to properly perform the electromechanical properties identification and (2) how to select the most adequate prediction model. The interest of this work is to answer both questions employing a Bayesian inferential scheme. In particular, a model class selection is established employing predictive models with different grades of nonlinearities, while the updated model parameters are identified using a transitional Markov chain Monte Carlo over the device’s frequency response. Different recommendations to achieve the mentioned tasks are offered based on the number of experiments, the output type (voltage, electrical power, and displacement), and the method to identify the posterior distribution.