Stable parameters identification for rational approximation of Single degree of freedom frequency response function of semi‐infinite medium

Abstract

The rational approximation is an important tool for establishing a dynamic analysis model in time domain for semi‐infinite water and soil. It accurately represents the interaction between the semi‐infinite medium and an engineering structure. Current research on rational approximation method focuses mainly on the establishment of time‐domain analysis models. However, the stability, accuracy, and calculation efficiency of the rational approximation model cannot be guaranteed simultaneously. Based on linear system control theory, this work decomposes the continuous‐time rational approximation (CRA) and the discrete‐time rational approximation (DRA) into a combination of first‐ and second‐order subsystems, and the stability boundaries for the identified parameters are established according to the stability conditions of each subsystem. A genetic algorithm and a sequential quadratic programming algorithm are used to construct a parameter identification method that can ensure stability in the time domain. Through parameter identification of complex frequency response functions, it is demonstrated that the method proposed in this work can guarantee the stability and accuracy simultaneously, and the calculation efficiency is also substantially improved over that of the existing methods.