Probabilistic Multi-Objective Inverse Analysis for Damage Identification Using Piezoelectric Impedance Measurement Under Uncertainties

Piezoelectric impedance sensing is promising for highly accurate damage identification because of its high-frequency active interrogative nature and simplicity in data acquisition. To fully unleash the potential, effective inverse analysis is needed in order to pinpoint the damage location and identify the severity. The inverse analysis, however, may be underdetermined since there exists a very large number of unknowns (i.e., locations and severity levels) to be solved in a finite element model but only limited measurements are available in actual practice. To uncover the true damage scenario, an inverse analysis strategy built upon the multi-objective optimization, which aims at matching the multiple sets of measurements with model predictions in the damage parametric space, can be formulated to identify a small set of solutions. This solution set then allows the incorporation of empirical knowledge to facilitate final decision-making. The main disadvantage of the conventional inverse analysis strategy is that it overlooks uncertainties that exist in both baseline structural modeling and actual measurements. To address this, in this research, we formulate a probabilistic multi-objective optimization-based inverse analysis framework, which is fundamentally built upon the differential evolution Markov chain Monte Carlo (DEMC) technique. The new approach can yield the Pareto optimal set (solutions) and the respective Pareto front, which are represented in a probabilistic sense to account for uncertainties. Comprehensive case studies with experimental investigations are conducted to demonstrate the effectiveness of this new approach.