A stochastic harmonic function representation for non-stationary stochastic processes

Abstract

The time-domain representation of non-stationary stochastic processes is of paramount importance, in particular for response analysis and reliability evaluation of nonlinear structures. In the present paper a stochastic harmonic function (SHF) representation originally developed for stationary processes is extended to evolutionary non-stationary processes. Utilizing the new scheme, the time-domain representation of non-stationary stochastic processes is expressed as the linear combination of a series of stochastic harmonic components. Different from the classical spectral representation (SR), not only the phase angles but also the frequencies and their associated amplitudes, are treated as random variables. The proposed method could also be regarded as an extension of the classical spectral representation method. However, it is rigorously proved that the new scheme well accommodates the target evolutionary power spectral density function. Compared to the classical spectral representation method, moreover, the new scheme needs much fewer terms to be retained. The first four moments and the distribution properties, e.g., the asymptotical Gaussianity, of the simulated stochastic process via SHF representation are studied. Numerical examples are addressed for illustrative purposes, showing the effectiveness of the proposed scheme.