Probabilistic inverse problem and system uncertainties for damage detection in piezoelectrics

Abstract This paper provides a probabilistic formulation to design a monitoring setup for damage detection in piezoelectric plates, solving a model-based identification inverse problem (IP). The IP algorithm consists on the minimization of a cost functional defined as the quadratic-difference between experimental and trial measurements simulated by the finite element method. The motivation of this work comes from the necessity for a more rational design criteria applied to damage monitoring of piezoelectric materials. In addition, it is very important for the solving of the inverse problem to take into account the random nature of the system to be solved in order to obtain accurate and reliable solutions. In this direction, two investigations are considered. For the first, the experimental measurements are simulated combining a finite element and a Monte Carlo analysis, both validated with already published results. Then, an uncertainty analysis is used to obtain the statistical distribution of the simulated experimental measurements, while a sensitivity analysis is employed to find out the influence of the uncertainties in the model parameters related to the measurement noise. Upon the study of the measurements, they are used as the input for the damage identification IP which produces the location and extension of a defect inside a piezoelectric plate. For the second investigation, a probabilistic IP approach is developed to determine the statistical distribution and sensitivities of the IP solutions. This novel approach combines the Monte Carlo and the IP algorithm, considering the trial measurements as random. In conclusion, the analysis demonstrates that in order to improve the quality of the damage characterization, only a few material parameters have to be controlled at the experimental stage. It is important to note that this is not an experimental study, however, it can be considered as a first step to design a rational damage identification experimental device, controlling the variables that increase the noise level and decrease the accuracy of the IP solution.

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