Decoupling of Evolutionary Power Spectral Density and Its Engineering Applications

In order to improve the simulation efficiency of nonstationary processes and simplify the structural response analysis under nonstationary excitations, evolutionary power spectral density (EPSD) was approximately decoupled into the linear summation of products of the squared modulus of Fourier transform of wavelet function at different scales and associated time coefficients, i.e., a generally modulated nonstationary process was transformed into the summation of a number of uniformly modulated nonstationary processes. The decoupled EPSD was applied to engineering fields, including the simulation of nonstationary processes and the stochastic response analysis of structures. The research results show that the decoupled EPSD has a satisfactory accuracy. The simulation efficiency of nonstationary stochastic processes is generally improved for dozens of times by using the fast Fourier transform (FFT). The estimated autocorrelation function of simulated samples agrees very well with the target function. The stochastic response analysis of structures is simplified, and the calculated responses using the proposed method have small errors compared with the targets.