The classical radial point interpolation method (RPIM) is a powerful meshfree numerical technique for engineering computation. In the original RPIM, the moving support domain for the quadrature point is usually employed for the field function approximation, but the local supports of the nodal shape functions are always not in alignment with the integration cells constructed for numerical integration. This misalignment can result in additional numerical integration error and lead to a loss in computation accuracy. In this work, a modified RPIM (M-RPIM) is proposed to address this issue. In the present M-RPIM, the misalignment between the constructed integration cells and the nodal shape function supports is successfully overcome by using a fixed support domain that can be easily constructed by the geometrical center of the integration cell. Several numerical examples of free vibration analysis are conducted to evaluate the abilities of the present M-RPIM and it is found that the computation accuracy of the original RPIM can be markedly improved by the present M-RPIM.

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.