Uncertainties propagation and global sensitivity analysis of the frequency response function of piezoelectric energy harvesters

Abstract

The goal of this work is to describe a framework to propagate uncertainties in piezoelectricenergy harvesters(PEHs). These uncertainties are related to the incomplete knowledge of themodel parameters. The framework presented could be employed to conduct prior robuststochastic predictions. The prior analysis assumes a known probability density function for theuncertain variables and propagates the uncertainties to the output voltage. The framework isparticularized to evaluate the behavior of the frequency response functions(FRFs)in PEHs,while its implementation is illustrated by the use of different unimorph and bimorph PEHssubjected to different scenarios: free of uncertainties, common uncertainties, and uncertainties asa product of imperfect clamping. The common variability associated with the PEH parametersare tabulated and reported. A global sensitivity analysis is conducted to identify the Sobolindices. Results indicate that the elastic modulus, density, and thickness of the piezoelectric layerare the most relevant parameters of the output variability. The importance of including the modelparameter uncertainties in the estimation of the FRFs is revealed. In this sense, the presentframework constitutes a powerful tool in the robust design and prediction of PEH performance.