Structural Damage Identification Using PID-Based Search Algorithm: A Control-Theory Inspired Application

Abstract

This study employs a PID (Proportion, Integral, Differential)-based search algorithm (PSA) to achieve structural damage identification (SDI), localization, and quantification. We developed finite element programs for a 10-element simply supported beam, a 21-element truss, and a 7-story steel frame, assigning damage factors to each element as design variables. The Relative Frequency Change Rate (RFCR) and Modal Assurance Criterion (MAC) were calculated as objective functions for PSA iteration; comparative studies were then conducted against Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Simulated Annealing (SA) in terms of damage identification accuracy, computational efficiency, and noise robustness. Results demonstrate that PSA achieves exceptional damage localization accuracy within 1% error in severity under noise-free conditions. With 1–3% noise, PSA maintains precise damage localization despite minor severity estimation errors, while other algorithms exhibit false positives in intact elements. Within the fixed number of iterations, PSA outperforms GA and PSO in computational efficiency. Although SA shows faster computation, it significantly compromises identification accuracy and fails in damage detection. The regularization term enables PSA to maintain noise-resistant damage identification even in a 70-element frame structure, demonstrating its potential for robust damage assessment across diverse structural types, scales, and noisy environments.