Uncertainty Quantification in the Assessment of the Characteristics of the Electromechanical Impedance Spectrum of a Rectangular Piezoelectric Patch

Document Type : Research Article

Authors

1 New Technologies Research Center (NTRC), Amirkabir University of Technology, Tehran

2 Department of Mechanical Engineering, Amirkabir University of Technology, Tehran

3 Faculty of Mechanical and Mechatronic Engineering, Shahrood University of Technology, Shahrood

Abstract

Electromechanical impedance spectroscopy can be used for damage localization by estimating the electromechanical impedance spectrum with numerical or analytical models. The existence of several sources of uncertainty, however, leads to a significant mismatch between the numerical and experimental results. Therefore, uncertainty quantification for high-frequency coupled electromechanical vibration response of the piezoelectric patch is necessary. Polynomial chaos expansion is an efficient method for assessing uncertainty when dealing with time-consuming models. For the probabilistic analysis of modal features of the impedance spectrum, surrogate models derived by polynomial chaos expansion were used. The statistical moments and probability distributions of the quantity of interest were computed analytically using surrogate models. By post-processing the coefficients of polynomial chaos expansion models with relatively minimal computing cost, global sensitivity analysis was performed to rank the relevance of input variable variation on response variance. According to the results, due to the common uncertainties in the material properties and geometry of the piezoelectric patch, the coefficient of variation in the peak amplitudes is substantially higher than the peak frequencies. In addition, modal frequencies are most sensitive to mechanical properties (compliance and density), whereas modal amplitudes are most sensitive to mechanical damping, electrical permittivity, and the piezoelectric constant.

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References

[1] H. Mei, M.F. Haider, R. Joseph, A. Migot, V. Giurgiutiu, Recent advances in piezoelectric wafer active sensors for structural health monitoring applications, Sensors, 19(2) (2019) 383.
[2] A.F.G. Tenreiro, A.M. Lopes, L.F.M. da Silva, A review of structural health monitoring of bonded structures using electromechanical impedance spectroscopy, Structural Health Monitoring, 21(2) (2022) 228-249.
[3] N. Sepehry, F. Bakhtiari-Nejad, M. Shamshirsaz, Thermo-Electro Mechanical Impedance based Structural Health Monitoring: Euler-Bernoulli Beam Modeling, AUT Journal of Modeling and Simulation, 49(2) (2017) 143-152.
[4] N. Sepehry, M. Ehsani, W. Zhu, F. Bakhtiari-Nejad, Application of scaled boundary finite element method for vibration-based structural health monitoring of breathing cracks, Journal of Vibration and Control, 27(23-24) (2021) 2870-2886.
[5] N. Sepehry, M. Ehsani, M. Shamshirsaz, Free and forced vibration analysis of piezoelectric patches based on semi-analytic method of scaled boundary finite element method, Amirkabir Journal of Mechanical Engineering, 52(12) (2019) 3463-3484.
[6] N. Sepehry, M. Ehsani, M. Shamshirsaz, M. Sadighi, Contact acoustic nonlinearity identification via online vibro-acoustic modulation technique, Modares Mechanical Engineering, 20(7) (2020) 1719-1730
[7] D. Ai, H. Luo, H. Zhu, Diagnosis and validation of damaged piezoelectric sensor in electromechanical impedance technique, Journal of Intelligent Material Systems and Structures, 28(7) (2017) 837-850.
[8] C. Liang, F.P. Sun, C.A. Rogers, Coupled electro-mechanical analysis of adaptive material systems-determination of the actuator power consumption and system energy transfer, Journal of intelligent material systems and structures, 8(4) (1997) 335-343.
[9] Y.Y. Lim, C.K. Soh, Towards more accurate numerical modeling of impedance based high frequency harmonic vibration, Smart Materials and Structures, 23(3) (2014) 035017.
[10] N. Sepehry, M. Ehsani, M. Shamshirsaz, M. Sadighi, Online health monitoring of marine structures using electromechanical impedance spectroscopy: A simulation approach, in:  Journal of Solid and Fluid Mechanics, Shahrood University of Technology, 10 (2020) 67-76.
[11] S. Asadi, M. Shamshirsaz, Y.A. Vaghasloo, Bayesian in-situ parameter estimation of metallic plates using piezoelectric transducers, Smart Structures and Systems, An International Journal, 26(6) (2020) 735-751.
[12] J.E. Mottershead, M. Link, M.I. Friswell, The sensitivity method in finite element model updating: A tutorial, Mechanical systems and signal processing, 25(7) (2011) 2275-2296.
[13] R. Ghanem, H. Owhadi, D. Higdon, Handbook of uncertainty quantification, 2017.
[14] B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering and System Safety, 93(7) (2008) 964-979.
[15] N. Wiener, The homogeneous chaos, American Journal of Mathematics, 60(4) (1938) 897-936.
[16] D. Xiu, G.E. Karniadakis, The Wiener--Askey polynomial chaos for stochastic differential equations, SIAM journal on scientific computing, 24(2) (2002) 619-644.
[17] S. Oladyshkin, W. Nowak, Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion, Reliability Engineering & System Safety, 106 (2012) 179-190.
[18] X. Wan, G.E. Karniadakis, Beyond wiener-askey expansions: Handling arbitrary PDFs, Journal of Scientific Computing, 27(1-3) (2006) 455-464.
[19] R.G. Ghanem, P.D. Spanos, Stochastic finite elements: a spectral approach, 2003.
[20] M. Berveiller, B. Sudret, M. Lemaire, Stochastic finite element: A non intrusive approach by regression, European Journal of Computational Mechanics, 15(1-3) (2006) 81-92.
[21] M.D. Spiridonakos, E.N. Chatzi, Metamodeling of dynamic nonlinear structural systems through polynomial chaos NARX models, Computers and Structures, 157 (2015) 99-113.
[22] H.-p. Wan, W.-x. Ren, M.D. Todd, Arbitrary polynomial chaos expansion method for uncertainty quantification and global sensitivity analysis in structural dynamics, Mechanical Systems and Signal Processing, 142 (2020) 106732.
[23] X. Wei, H.-P. Wan, J. Russell, S. Živanović, X. He, Influence of mechanical uncertainties on dynamic responses of a full-scale all-FRP footbridge, Composite Structures, 223 (2019) 110964.
[24] J.A.S. Witteveen, S. Sarkar, H. Bijl, Modeling physical uncertainties in dynamic stall induced fluid–structure interaction of turbine blades using arbitrary polynomial chaos, Computers & structures, 85(11-14) (2007) 866-878.
[25] R. Loendersloot, M. Ehsani, N. Sepehry, M. Shamshirsaz, Numerical Modelling of Stochastic Fatigue Damage Accumulation in Thick Composites, in:  European Workshop on Structural Health Monitoring, 2020, pp. 776-787.
[26] F. Bakhtiari-Nejad, N. Sepehry, M. Shamshirsaz, Polynomial chaos expansion sensitivity analysis for electromechanical impedance of plate, in:  Proceedings of the ASME Design Engineering Technical Conference, 2016, pp. 1-8.
[27] M.D. Spiridonakos, E.N. Chatzi, B. Sudret, Polynomial Chaos Expansion Models for the Monitoring of Structures under Operational Variability, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 2(3) (2016) 1-13.
[28] G. Capellari, E. Chatzi, S. Mariani, Cost–benefit optimization of structural health monitoring sensor networks, Sensors (Switzerland), 18(7) (2018) 1-22.
[29] S.S. Kucherenko, Global sensitivity indices for nonlinear mathematical models, Review, Wilmott Mag, 1 (2005) 56-61.
[30] P. Wei, Z. Lu, J. Song, Variable importance analysis: A comprehensive review, Reliability Engineering and System Safety, 142 (2015) 399-432.
[31] I.M. Sobol, Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Mathematics and Computers in Simulation, 55(1-3) (2001) 271-280.
[32] V. Giurgiutiu, A.N. Zagrai, Characterization of Piezoelectric Wafer Active Sensors, Journal of Intelligent Materials Systems and Structures, 11(12) (2000) 959-976.
[33] V. Giurgiutiu, Structural Health Monitoring with Piezoelectric Wafer Active Sensors: with Piezoelectric Wafer Active Sensors, 2007.
[34] J.L. Aurentz, L.N. Trefethen, Chopping a chebyshev series, ACM Transactions on Mathematical Software, 43(4) (2017) 1-25.
[35] R. Pachon, R.B. Platte, L.N. Trefethen, Piecewise-smooth chebfuns, IMA Journal of Numerical Analysis, 30(4) (2009) 898-916.
[36] R. Loendersloot, M. Ehsani, M. Shamshirsaz, Fatigue damage identification and remaining useful life estimation of composite structures using piezo wafer active transducers, in:  Advances in Asset Management and Condition Monitoring, 2020, pp. 485-497.
[37] C. Soize, R. Ghanem, Physical Systems With Random Uncertainties : Chaos Representations With Arbitrary Probability, 26(2) (2004) 395-410.
[38] O. Ditlevsen, H.O. Madsen, Structural reliability methods, Wiley New York, 1996.
[39] G. Blatman, B. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, Journal of Computational Physics, 230(6) (2011) 2345-2367.
[40] B. Sudret, A. Der-Kiureghian, Stochastic finite element methods and reliability, Rep. No. UCB/SEMM-2000, 8 (2000).
[41] B. Sudret, Polynomial chaos expansions and stochastic finite element methods, Risk and reliability in geotechnical engineering,  (2014) 265-300.
[42] R. Kohavi, A study of cross-validation and bootstrap for accuracy estimation and model selection, in:  Ijcai, (1995), 1137-1145.
[43] O. Chapelle, V. Vapnik, Y. Bengio, Model selection for small sample regression, Machine Learning, 48(1-3) (2002) 9-23.
[44] D.W. Scott, Multivariate density estimation and visualization, in:  Handbook of computational statistics, Springer, 2012, pp. 549-569.
[45] A. Janon, T. Klein, A. Lagnoux, M. Nodet, C. Prieur, Asymptotic normality and efficiency of two Sobol index estimators, ESAIM - Probability and Statistics, 18 (2014) 342-364.
[46] A. Saltelli, T. Homma, Importance measures in global sensitivity analysis of model output, Reliab. Eng. Sys. Safety, 52 (1996) 1-17.
[47] K. Konakli, B. Sudret, Global sensitivity analysis using low-rank tensor approximations, Reliability Engineering and System Safety, 156 (2016) 64-83.
[48] C.M.R. BDV, Numerical simulation for health monitoring of thin simply supported plate using PZT transducers, Materials Today: Proceedings, 45 (2021) 3492-3498.
[49] M.D. McKay, R.J. Beckman, W.J. Conover, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 42(1) (2000) 55-61.
[50] B.G.M. Husslage, G. Rennen, E.R. van Dam, D. den Hertog, Space-filling Latin hypercube designs for computer experiments, Optimization and Engineering, 12(4) (2010) 611-630.
[51] N. Pérez, M.A.B. Andrade, F. Buiochi, J.C. Adamowski, Identification of elastic, dielectric, and piezoelectric constants in piezoceramic disks, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 57(12) (2010) 2772-2783.
[52] W. Gautschi, Orthogonal polynomials (in Matlab), Journal of Computational and Applied Mathematics, 178(1-2 SPEC. ISS.) (2005) 215-234.
[53] S. Rahman, Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions, Journal of Engineering Mechanics, 135(12) (2009) 1439-1451.
Amirkabir Journal of Mechanical Engineering
Volume 54, Issue 10
January 2023
Pages 2351-2376

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