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 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.

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.

Uncertainty Quantification of Viscoplastic Parameters for Grade 91 Steel Through Bayesian Analysis

2020 ◽  
Author(s):  
Aritra Chakraborty ◽  
M. C. Messner ◽  
T.-L. Sham
Keyword(s):  
Experimental Data ◽  
High Temperature ◽  
Initial Guess ◽  
Mcmc Methods ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Experimental Conditions ◽  
Materials Used ◽  
Grade 91 ◽  
Effective Component

Abstract Calibrating inelastic models for high temperature materials used in advanced reactor heat exchangers is a critical aspect in accurately predicting their deformation behavior under different loading conditions, and thus determining the corresponding failure times. The experimental data against which these models are calibrated often contains a wide degree of variability caused by heat-to-heat material property variations and general experimental uncertainty. Most often, model calibration is done against mean of these experimental data without considering this variability. In this work we aim to capture the bounds of the viscoplastic parameter uncertainties that enclose this observed scatter in the experimental data using Bayesian Markov Chain Monte Carlo (MCMC) methods. Bayesian inference provides a probabilistic framework that allows to coherently quantify parameter uncertainties based on some prior parameter distributions and the available data. To perform the statistical Bayesian MCMC analysis, a pre-calibrated model, fitted against mean of the experimental data, is used as an initial guess for the prior distribution and bounds, while further sampling is done using Meteropolis–Hastings algorithm for four Markov chains in tandem, to finally obtain the posterior distribution of the model parameters. Since different inelastic parameters are sensitive to different tests, data from multiple experimental conditions (tensile, and creep) are combined to capture the bounds in all the parameters. The developed statistical model reasonably captures the scatter observed in the experimental data. Quantifying uncertainty in inelastic models will improve high temperature engineering design practice and lead to safer, more effective component designs.

Constitutive Modeling of Porous Shape Memory Alloys Using Gurson–Tvergaard–Needleman Model Under Isothermal Conditions

2020 ◽  
Vol 12 (04) ◽  
pp. 2050038
Author(s):  
Xiang Zhu ◽  
Liangliang Chu ◽  
Guansuo Dui
Keyword(s):  
Experimental Data ◽  
Phase Transformation ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Strain Hardening ◽  
Constitutive Relationship ◽  
Model Parameters ◽  
Gtn Model ◽  
Critical Phase ◽  
Transformation Stress

Based on the Gurson–Tvergaard–Needleman (GTN) model, a constitutive relationship considering both the effects of strain hardening and hydrostatic stress for porous shape memory alloys (SMAs) is proposed. To capture the relationship between microscopic and mesoscopic behaviors, a representative volume element (RVE) containing an array of spherical voids is presented. In this paper, an approximate solution including strain hardening exponent [Formula: see text] is deduced by considering the porous SMA as a two phase composite with the SMA matrix and the second phase representing voids. The model parameters, [Formula: see text] and [Formula: see text], accounting for interactions between voids are investigated to take into account their influences on strain hardening, critical phase transformation stress and yield surface. In addition, the evolution equations of phase transformation are derived and then applied to the simulation of porous Ni–Ti SMAs with a porosity of 13%. Using the calibrated GTN model parameters, the critical phase transformation stress closer to experimental data is obtained. The predictions of stress–strain curve by the proposed constitutive model are found to be in excellent agreement with published experimental data and finite element results. The results prove that the model is capable of reproducing the features of porous SMAs such as superelasticity, tensile-compressive asymmetry and internal loops under uniaxial even combined loading conditions. A conclusion is drawn that the present constitutive relationship is powerful and useful for the analysis of porous SMAs.

scholarly journals Experimental studies of iron transformations kinetics and autocatalysis during its physicochemical removal from underground water

2021 ◽  
Author(s):  
S. Yu Martynov ◽  
V. L. Poliakov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Experimental Studies ◽  
Underground Water ◽  
Model Parameters ◽  
Kinetic Coefficients ◽  
Transfer Equations ◽  
The Mathematical Model ◽  
Autocatalytic Effect ◽  
Forms Of Iron

Abstract The mathematical model of physicochemical iron removal from groundwater was developed. It consists of three interrelated compartments. The results of the experimental research provide information in support of the first two compartments of the mathematical model. The dependencies for the concentrations of the adsorbed ferrous iron and deposited hydroxide concentrations are obtained as a result of the exact solution of the system of the mass transfer equations for two forms of iron in relation to the inlet surface of the bed. An analysis of the experimental data of the dynamics of the deposit accumulation in a small bed sample was made, using a special application that allowed to select the values of the kinetic coefficients and other model parameters based on these dependencies. We evaluated the autocatalytic effect on the dynamics of iron ferrous and ferric forms. The verification of the mathematical model was carried out involving the experimental data obtained under laboratory and industrial conditions.

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.

Combustion in Ni–Al system with Cu additive (powder or rod) Experiment and mathematical model

2020 ◽  
pp. 33-43
Author(s):  
O. V. Lapshin ◽  
A. M. Shul’pekov ◽  
R. M. Gabbasov ◽  
V. D. Kitler
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Relative Density ◽  
Aluminum Matrix ◽  
Kinetic Constants ◽  
Model Parameters ◽  
Nickel Aluminum ◽  
Copper Melt ◽  
Analytical Formulas ◽  
The Mathematical Model

Experimental studies were carried out with theoretical calculations of wave synthesis in the Ni–Al–Cu system were performed using the mathematical model developed. Approximate analytical formulas were obtained for synthesis performance evaluation. The inverse problem method was used to get kinetic constants that determine process dynamics based on the experimental data and analytical relationships. It is shown that the combustion front propagation velocity increases monotonically with an increase in the reaction sample relative density in the range of relative density values of 0.4 to 0.6. The depth of copper melt penetration from the center of the sample into the nickel-aluminum matrix depends on the relative density of the sample and copper wire diameter: higher densities and larger diameters lead to an increase in the liquid-phase impregnation area. The rate of nickel and aluminum powder frame wetting with copper melt is limited by the synthesis wave speed. Based on the experimental data and analytical ratios, we estimated the effective kinetic constants describing the high-temperature synthesis of the Ni + Al reaction mixture in the presence of copper additives. The thermal effect of the NiAl intermetallic formation reaction and the preexponential factor in the chemical transformation equation are calculated, the exponent value in the ratio for the mixture thermal conductivity is established; a constant determining the process of nickel-aluminum matrix impregnation with copper melt is found. The macroscopic approach used to analyze the NiAl intermetallic synthesis makes it possible to determine all the desired physicochemical characteristics and model parameters. The mathematical model is suitable for predictive estimates and experimental data analysis in the macroscopic approximation. Approximate analytical formulas are obtained for calculating the NiAl intermetallic synthesis characteristics. They allow for calculating the through channel characteristics and can be used in the design of NiAl products.

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).

Performance of Galloping Piezoelectric Energy Harvesters With Square Bluff Body

2013 ◽  
Author(s):  
Felix Ewere ◽  
Gang Wang
Keyword(s):  
Experimental Data ◽  
Wind Tunnel ◽  
Mechanical Model ◽  
Bluff Body ◽  
Energy Harvester ◽  
Approximate Solutions ◽  
Wind Tunnel Tests ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Physical Insight

In this paper, we investigate a galloping piezoelectric energy harvester (GPEH) with a square bluff body. Comprehensive wind tunnel tests are conducted and experimental data are used to validate our analytical approximate solutions, which are derived from a coupled aero-electro-mechanical model. In addition, the effects of impact disturbances using a bump are investigated. The goal is to improve the performance of baseline GPEH. We expect to collect physical insight to design an optimal nonlinear GPEH configuration by placing bumps accordingly. Lessons learnt from this study will be used to improve the performance of future nonlinear GPEHs and lead to a practical device.

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