Effective design and characterization of flutter-based piezoelectric energy harvesters with discontinuous nonlinearities

The interest of this work is to describe a framework that allows the use of the well-known dynamic estimators in piezoelectric harvester (deterministic performance estimators) but taking into account the random error associated to the mathematical model and the uncertainties on the model parameters. The framework presented could be employed to perform Posterior Robust Stochastic Analysis, which is the case when the harvester can be tested or it is already installed and the experimental data is available. In particular, it is introduced a procedure to update the electromechanical properties of PEHs based on Bayesian updating techniques. The mean of the updated electromechanical properties are identified adopting a Maximum a Posteriori estimate while the probability density function associated is obtained by applying a Laplaces asymptotic approximation (updated properties could be expressed as a mean value together a band of confidence). The procedure is exemplified using the experimental characterization of 20 PEHs, all of them with same nominal characteristics. Results show the capability of the procedure to update not only the electromechanical properties of each PEH (mandatory information for the prediction of a particular PEH) but also the characteristics of the whole sample of harvesters (mandatory information for design purposes). The results reveal the importance to include the model parameter uncertainties in order to generate robust predictive tools in energy harvesting. In that sense, the present framework constitutes a powerful tool in the robust design and prediction of piezoelectric energy harvesters performance.

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

MATEC Web of Conferences ◽

10.1051/matecconf/201821105002 ◽

2018 ◽

Vol 211 ◽

pp. 05002

Author(s):

Patricio Peralta ◽

Rafael O. Ruiz ◽

Viviana Meruane

Keyword(s):

Density Function ◽

Bayesian Updating ◽

Experimental Characterization ◽

A Posteriori ◽

Electromechanical Properties ◽

Deterministic Models ◽

Energy Harvesters ◽

Piezoelectric Energy ◽

Updating Procedure

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).

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