Deterministic integration algorithms for stochastic response computations of FE-systems

Abstract

An algorithm for the computation of the covariance matrix of the the stochastic response of linear and non-linear structures is introduced. General deterministic loading perturbed by discrete white noise is treated. The merits of the algorithm are most pronounced when dealing with large FE-models but is also competitive for MDOF-systems. The covariance matrix is represented by employing the Karhunen–Loéve expansion. The corresponding deterministic Karhunen–Loéve vectors can be integrated using the preferred deterministic step-by-step integration schemes, e.g. Newmark algorithm or other suitable deterministic schemes. Hence the procedure is not restricted to special integration procedures. A relatively small number m≪ n of Karhunen–Loéve vectors is, even for large FE-models, sufficient to represent accurately the covariance matrix which is generally a full symmetric quadratic matrix of dimension⩾2 n, where n denotes the number of DOF of the FE-model. Hence space reduction is introduced right from the beginning, leading to a feasible, and moreover efficient algorithm for large FE-models.