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The present work proposes a multi-stage optimization technique for damage detection of the thin plate-like structure using sparse modal data collected from the limited sensors. The response of the thin plate structures is obtained from a finite element model, which is developed with constant strain triangle elements. The iterated improved reduction system (IIRS) is applied to simulate the state of sparse sensors numerically. Next, the damage identification problem is formulated as a constrained optimization problem. A weighted linear combination of the natural frequencies and modes shapes of the structure is used to construct the objective function. The damage extent of each element is considered as the design variable. The formulated objective function is minimized by the proposed multi-stage strategy employing a hybrid metaheuristic algorithm, which is based on particle swarm optimization and gravitational search algorithm (PSOGSA). The algorithm identifies the healthy elements in each stage and eliminates them from the search space of the next stage. Thus, the search space dimension of the optimization problem reduces in each stage, and actual damaged elements are identified effectively. The efficiency of the proposed method is demonstrated through three numerical examples with different damage scenarios.

Damage identification of thin plates using multi-stage PSOGSA and incomplete modal data