Structural Damage Diagnosis Based on Multi-Stage Sparrow Search Algorithm

This study proposes a Multi-Stage Sparrow Search Algorithm (MS-SSA) for precise structural damage identification. Initially, the structural static displacement sensitivity formulation is derived via the Sherman-Morrison-Woodbury formula, and an objective function is constructed by integrating the sensitivity equations with the L2-norm penalty. Subsequently, MS-SSA is implemented to sequentially achieve preliminary damage localization and accurate quantification. In the localization phase, a constrained narrow-bound search space is predefined to identify potential damage regions. Leveraging this feedback, the sensitivity equations are condensed, and the search boundaries are adaptively refined for the quantification phase, where SSA is reapplied to precisely determine damage severity while mitigating misjudgments. The MS-SSA framework exhibits two distinct advantages: (i) Phase I localization accelerates convergence by constraining the search space, as it does not target precise quantification; and (ii) the significant reduction in unknowns achieved by excluding intact elements in Phase II enables rapid convergence to the global optimum. Comparative studies against the Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), and standard SSA demonstrate that the proposed method effectively overcomes computational instability, slow convergence, and large errors inherent in swarm intelligence optimization for damage identification. Specifically, numerical case studies reveal that the identification error is reduced to merely 9%~22% of that associated with existing methods, with experimental validation confirming reductions to 18%~22%. Overall, the proposed approach achieves high-fidelity damage identification while eliminating false positives and false negatives.