Calibration of Design Response Spectrum Based on Improved Particle Swarm Algorithm

This paper proposes two improved algorithms, the DE-PSO algorithm, which combines differential evolution and phased strategy, and the hybrid particle swarm optimization algorithm integrating whale algorithm (WOAPSO), which combines the whale optimization mechanism. Compared to traditional calibration methods (such as the Newmark three- and two-parameter methods), which rely on empirical simplified models, adapting them to the complex seismic nonstationarity and multipeak characteristics is difficult. However, although intelligent optimization algorithms, such as particle swarm optimization (PSO) and differential evolution (DE) have improved calibration accuracy in recent years, insufficient convergence stability and low computational efficiency, among other problems, persist. Therefore, based on experiments, the performances of these algorithms were compared with those of standard PSO, traditional DE, and other algorithms. The results demonstrate the significant superiority of DE-PSO and WOAPSO. In 50 repeated experiments, the fitness standard deviation (STD) was significantly reduced, and the algorithms achieved rapid convergence by the mid-iteration stage, which effectively resolves the issues of premature convergence and local oscillation tendencies inherent in the standard Particle Swarm Optimization algorithm. Regarding the key parameters (Tg, βmax, γ) of the standard, the STD of the improved algorithm approached zero, verifying its strong adaptability to multimodal optimization problems. Furthermore, the DE-PSO algorithm had the best performance in balancing computational efficiency and stability, with a convergence speed that is three times faster than that of standard DE algorithm while maintaining the lowest parameter volatility. This study provides an efficient algorithmic tool for the rapid analysis of strong motion records and the efficient calibration of design response spectra, which has implications for the seismic optimization design of complex structures and can be guided by regulations, contributing to engineering seismic practice.