Stochastic analysis of linear structures subjected to multicorrelated filtered noises

A procedure is proposed to evaluate the mean square response of a linear system subjected to a multicorrelated, stationary or non-stationary, filtered vector process. By applying Ito's method, the multicorrelated stochastic process is considered as a white noise filtered by a set of first order linear differential equations. A closed form solution is given for the estimation of the cross-covariance matrix in the time domain, for the stationary case. Also presented is a step-by-step solution procedure to evaluate the evolutive cross-covariance matrix, for the non-stationary case. Numerical results are given for the seismic analysis of structures placed on layered soil, and idealized as a lumped mass system subjected to a white noise process at the bedrock.