Response probabilities of nonlinear random systems: a compartmental approach

In this paper, a compartmental approach is applied to the study of response behaviour of nonlinear systems subject to random external excitations and random parametric variations. A distinct advantage is that, while the underlying system is nonlinear, the compartmental equations governing the response probabilities are linear and homogeneous. The dimension of this system of equations, however, is large in general but its solution is facilitated by the fact that its coefficient matrix is sparse. Computational aspects and stability of the compartmental probabilities are studied in detail.