Smooth Karhunen–Loève decomposition to analyze randomly vibrating systems

This paper deals with the application of smooth Karhunen–Loève decomposition (SKLD) procedure applied to random fields. The SKLD is obtained by solving a generalized eigenproblem defined by combining the covariance matrix of the random field with that of the associated time-derivative random field. The main properties of the SKLD procedure thus obtained are described and compared with the classical Karhunen–Loève decomposition. The SKLD is then applied to the responses of randomly excited vibrating systems in order to perform modal analysis. The resulting SKLD characteristics are discussed, in the case of linear vibrating systems subjected to white noise excitation, in terms of normal modes.