ANALYSIS OF NONSTATIONARY RANDOM PROCESSES USING SMOOTH DECOMPOSITION

Orthogonal decompositions provide a powerful tool for stochastic dynamics analysis. The most popular decomposition is the Karhunen-Loeve decomposition (KLD), also called proper orthogonal decomposition. KLD is based on the eigenvectors of the correlation matrix of the random field. Recently, a modified KLD called smooth Karhunen-Loeve decomposition (SD) has appeared in the literature. It is based on a generalized eigenproblem defined from the covariance matrix of the random process and the covariance matrix of the associated time-derivative random process. SD appears to be an interesting tool to extend modal analysis. Although it does not satisfy the optimality relation of KLD, and maybe is not as good a candidate for building reduced models as KLD is, SD gives access to the modal vectors independently of the mass distribution. In this paper, the main properties of SD for nonstationary random processes are explored. A discrete nonlinear system is studied through its linearization, for uncorrelated and correlated excitation, and the SD of the nonlinear system and of the linearization are compared. It seems that SD detects not only mass inhomogeneities but also nonlinearities.