Reliability Assessment of Uncertain Linear Systems Subjected to Random Vibrations

This paper provides a formulation to calculate the probability of first-passage failure for uncertain linear systems subjected to random vibrations. This probability is a function of the service life and failure rate for a given failure threshold. For a linear system subjected to random vibrations, the first passage probability can be computed based on the Root Mean Square (RMS) response of the displacement and the velocity. However, when the system also presents uncertainties in its parameters (e.g., stiffness or damping), the calculation of the failure rate, which is the basis for the computation of the probability of first-passage failure, can nolonger be performed with typical random vibration methods. This is because the RMS response of the displacement and the velocity will change depending on the distribution of the system’s parameters. This paper presents an approach to calculate the probability of first-passage failure of a stochastic system subjected to random vibrations by efficiently approximating the failure rate of the system using a Kriging surrogate model which is adaptively updated using ageneralized max-min scheme. This enables the efficient computation of the total probability of first-passage failure of a stochastic linear system subjected to random vibrations. The approach is applied to a single-degree-of-freedom (SDOF) system, and two finite element models subjected to random inputs.