Time Dependent Reliability of Dynamic Systems Using Subset Simulation With Splitting Over a Series of Correlated Time Intervals

Abstract

Timedependent reliability is the probability that a system will perform its intended function successfully for a specified time. Unless many and often unrealistic assumptions are made, the accuracy and efficiency of timedependent reliability estimation are major issues which may limit its practicality. Monte Carlo simulation (MCS) is accurate and easy to use, but it is computationally prohibitive for high dimensional, long duration, timedependent (dynamic) systems with a low failure probability. This work is relevant to systems with random parameters excited by stochastic processes. Their response is calculated by time integrating a set of differential equations at discrete times. The limit state functions are, therefore, explicit in time and depend on timeinvariant random variables and timedependent stochastic processes. We present an improved subset simulation with splitting approach by partitioning the original high dimensional random process into a series of correlated, short duration, low dimensional random processes. Subset simulation reduces the computational cost by introducing appropriate intermediate failure subdomains to express the low failure probability as a product of larger conditional failure probabilities. Splitting is an efficient sampling method to estimate the conditional probabilities. The proposed subset simulation with splitting not only estimates the timedependent probability of failure at a given time but also estimates the cumulative distribution function up to that time with approximately the same cost. A vibration example involving a vehicle on a stochastic road demonstrates the advantages of the proposed approach.