Orthogonal decomposition and transmission of nonstationary random processes

Abstract

A relatively simple and straightforward procedure is given for representing analytically defined or data-based covariance kernels of arbitrary random processes in a compact form that allows its convenient use in later analytical random vibration response studies. The method is based on the spectral decomposition of the random process by the orthogonal Karhuen Loeve expansion and the subsequent use of least-squares approaches to develop an approximating analytical fit for the eigenvectors of the underlying random process. The resulting compact analytical representation of the random process is then used to derive a closed-form solution for the nonstationary response of a damped SDOF harmonic oscillator. The utility of the method for representing the excitation and calculating the mean square response is illustrated by the use of an analytically-defined covariance kernel widely employed in random vibration studies. It is shown that the method offers the potential of being a useful tool for feature extraction of experimentally measured covariance kernels of nonstationary random processes.