A real-time approach to structural seismic response analysis

Abstract

This paper presents a real-time seismic response analysis method based on the Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD) theories. Initially, the damping matrix and ground motion load are incorporated using the parametric form of the solid dynamic equation. By leveraging the POD method, the computational challenge arising from the high number of parameters in the equation (one parameter for each degree of freedom of the entire model) is overcome, enabling the calculation of complex computational models. Subsequently, the proposed method's effectiveness, stability, and accuracy are demonstrated through the analysis of various seismic waves characterized by different magnitudes, durations, and frequencies. Furthermore, the method successfully achieves real-time response feedback of the structure to arbitrary seismic waves. Importantly, this approach exhibits significant potential for engineering applications.