Reliability assessment of nonlinear MDOF systems subject to evolutionary stochastic excitation

An approximate analytical technique for determining the survival probability and first-passage probability density function (PDF) of nonlinear multi-degree-of-freedom (MDOF) structural systems subject to a non-stationary stochastic excitation vector is developed. The proposed technique can be construed as a two-stage approach. First, relying on statistical linearization and utilizing a dimension reduction approach the nonlinear n-degree-of-freedom system is cast/decoupled into (n) effective single-degree-of-freedom (SDOF) linear time-variant (LTV) systems corresponding to each and every degree of freedom of the original MDOF system. Second, an approximate technique based on stochastic averaging is employed in conjunction with the time-varying stiffness and damping elements of the effective SDOF LTV oscillator for determining the survival probability and first-passage PDF of the nonlinear MDOF system. Overall, the technique appears to be efficient and versatile since it can handle readily, at a low computational cost, a wide range of nonlinear/hysteretic behaviors as well as various stochastic excitation forms, even of the fully non-stationary in time and frequency kind. A 3-DOF structural system exhibiting hysteresis following the Bouc-Wen model is included as a numerical example. The reliability of the technique is demonstrated by pertinent Monte Carlo simulations.