Uncertainty quantification in the assessment of the characteristics of the electromechanical impedance spectrum of a rectangular piezoelectric patch

Electromechanical impedance spectroscopy is among the most effective technologies for online damage detection in maintenance.This technique 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 (PCE) 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 PCE 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.