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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