scholarly journals Bayesian Framework to Quantify Uncertainties in Piezoelectric Energy Harvesters

2018 ◽  
Author(s):  
Patricio Peralta ◽  
Rafael O. Ruiz ◽  
Viviana Meruane
Keyword(s):  
Mean Value ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Electromechanical Properties ◽  
Energy Harvesters ◽  
A Posteriori Estimate ◽  
Piezoelectric Energy ◽  
The Mathematical Model ◽  
Maximum A Posteriori Estimate

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.

Tuning Nonlinear Model Parameters in Piezoelectric Energy Harvesters to Match Experimental Data

2020 ◽  
Author(s):  
Alejandro Poblete ◽  
Patricio Peralta ◽  
Rafael Ruiz
Keyword(s):  
Experimental Data ◽  
Stochastic Analysis ◽  
Constitutive Relationship ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Electromechanical Properties ◽  
Bayesian Techniques ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
The Mathematical Model

Abstract A framework that allows for the use of well-known dynamic estimators in piezoelectric harvesters (PEHs) (i.e., deterministic performance estimators) and that accounts for the random error associated with the mathematical model and the uncertainties of model parameters is described presented here. This framework may be employed for Posterior Robust Stochastic analysis, such as when a harvester can be tested or is already installed and the experimental data are available. In particular, the framework detailed here was introduced to update the electromechanical properties of PEHs using Bayesian techniques. The updated electromechanical properties were identified by adopting a Transitional Markov Chain Monte Carlo. A well-known device with a nonlinear constitutive relationship was employed for experiments in this study, and the results demonstrated the capability of the proposed framework to update nonlinear electromechanical properties. The importance of including model parameter uncertainties to generate robust predictive tools was also supported by the results. Therefore, this framework constitutes a powerful tool for the robust design and prediction of PEH performance.

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

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).

Framework to Quantify Uncertainties in Piezoelectric Energy Harvesters

2016 ◽  
Author(s):  
Rafael O. Ruiz ◽  
Viviana Meruane
Keyword(s):  
Model Parameters ◽  
Response Functions ◽  
Incomplete Knowledge ◽  
Energy Harvesters ◽  
Uncertain Variables ◽  
Piezoelectric Energy ◽  
Posterior Analysis ◽  
The Mathematical Model ◽  
Probability Density Function Pdf ◽  
Prior Analysis

The interest of this work is to describe a framework to propagate uncertainties in piezoelectric energy harvesters (PEHs). The uncertainties are related to the random error associated to the mathematical model adopted, incomplete knowledge of the model parameters and the randomness nature of the excitation. The framework presented could be employed to conduct Prior and Posterior Robust Stochastic predictions. The prior analysis assumes a known Probability Density Function (PDF) for the uncertain variables while the posterior analysis calculates this PDF by adopting a Bayesian updating technique. The framework is particularized to evaluate the behavior of the Frequency Response Functions (FRFs) in PEHs while its implementation is illustrated by the use of a unimorph PEH. Results reveal the importance to include the model parameters uncertainties in the estimation of the FRFs. In that sense, the present framework constitutes a powerful tool in the robust design and prediction of PEH’s performance.

A Nonlinear Piezoelectric Energy Harvester from the Vibration of Magnetic Levitation

2013 ◽  
Vol 860-863 ◽  
pp. 594-598
Author(s):  
Zu Yao Wang
Keyword(s):  
Energy Harvester ◽  
Magnetic Levitation ◽  
Electric Energy ◽  
Response Analysis ◽  
Frequency Response Analysis ◽  
Energy Harvesters ◽  
Multi Scale ◽  
The Past ◽  
Piezoelectric Energy ◽  
The Mathematical Model

Vibration-based energy harvester has been widely investigated during the past years. In .order to improve the power-generating ability and enlarge the frequency range of energy harvesters, this paper presents the design and analysis of a new magneto electric energy harvester that uses Terfenol-D/PZT/Terfenol-D laminate to harvest energy from nonlinear vibrations created by magnetic levitation. The mathematical model of the proposed harvester is derived and used in a parametric study. By multi-scale analysis, the frequency-response analysis of the system is obtained and discussed here. It is shown that the systems nonlinearity can broaden the harvesters working bandwidth, thus makes the harvester suitable to work in practical cases.

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