A Novel Efficient Method for Simulating Non-Stationary Random Processes Combining Generalized Harmonic Wavelet and Stochastic Harmonic Function

Abstract

Integrating the general expression of the generalized harmonic wavelet (GHW)-based spectral representation method (SRM) and the idea of stochastic harmonic function (SHF), a novel stochastic generalized harmonic wavelet (SGHW) method for fully nonstationary stochastic processes, is established. The advantages of the proposed method are (1) a stochastic process with accurate probability information can be obtained by retaining fewer components. A smaller number of components greatly reduces the number of random variables. Fewer random variables also reduce the difficulty of random process analysis. The superior fitting effect between evolutionary power spectral density (EPSD) obtained from the samples using the SGHW method and the EPSD model proves the validity and effectiveness of the SGHW method. (2) The proposed method contains more accurate probability information and has a higher computational efficiency. The comparisons of relative errors and computational time between the SGHW method and the SRM demonstrate the accuracy and efficiency of the proposed method.