Leveraging Gaussian Process Regression and Many-Objective Optimization Through Voting Scores for Fault Identification

Using piezoelectric impedance/admittance sensing for structural health monitoring is promising, owing to the simplicity in circuitry design as well as the high-frequency interrogation capability. The actual identification of fault location and severity using impedance/admittance measurements, nevertheless, remains to be an extremely challenging task. A first-principle-based structural model using finite element discretization requires high dimensionality to characterize the high-frequency response. As such, direct inversion using the sensitivity matrix usually yields an under-determined problem. Alternatively, the identification problem may be cast into an optimization framework, in which the fault parameters are identified through the repeated forward finite element analysis that is often computationally prohibitive. This paper presents an efficient data-assisted optimization approach for fault identification without using the finite element model iteratively. We formulate a many-objective optimization problem to identify the fault parameters, where response surfaces of impedance measurements are constructed through the Gaussian process-based calibration. To balance between the solution diversity and convergence, an epsilon-dominance-enabled many-objective simulated annealing algorithm is established. As multiple solutions are expected, a voting score calculation procedure is developed to further identify those solutions that yield better implications regarding a structural health condition. The effectiveness of the proposed approach is demonstrated by the systematic numerical and experimental case studies.