A Bayesian updating procedure for the electromechanical properties of piezoelectric energy harvesters

¹ Department of Mechanical Engeneering, Universidad de Chile, Beauchef 851, Santiago, Chile
² Department of Civil Engeneering, Universidad de Chile, Blanco Encalada 2002, Santiago, Chile

^* e-mail: patricio.peralta@ug.uchile.cl
^** e-mail: rafaelruiz@uchile.cl
^*** e-mail: vmeruane@ing.uchile.cl

Abstract

In the last decade, several numerical and analytic procedures have been proposed to predict the dynamic behavior of piezoelectric energy har- vesters (PEHs). Nevertheless, PEHs present characteristics that are di ffi cult to control in their manufacturing process, for example the electromechanical properties of the materials present variations up to 20% of their nominal val- ues. In that sense, the use of deterministic models to obtain accurate predictions implies to have full information about the geometry and the electromechanical properties. This work introduces a procedure to update the electromechani- cal properties of PEHs based on Bayesian updating techniques. The procedure requires the use of: (i) a predictive model, (ii) a prior multivariate probabilis- tic density function for the electromechanical properties, and (iii) experimen- tal measurements of the harvester response. The mode of the updated elec- tromechanical properties is identified adopting a Maximum a Posteriori esti- mate while the probability density function associated is obtained by applying a Laplace’s asymptotic approximation. The procedure is exemplified using the experimental characterization of 20 nominally identical PEHs. Results show the capability of the procedure to update not only the electromechanical proper- ties of each PEH but also the characteristics of the whole sample of harvesters (mandatory information for design purposes).