Time-dependent system reliability analysis by adaptive importance sampling

A method for evaluating time-dependent reliability of a structural system subjected to stochastic loads is presented. Structural deterioration due to environmental stressors is also taken into account. An adaptive Monte Carlo simulation procedure combined with conditional expectation is proposed. The optimum common ratio of the standard deviation of an importance sampling variables to that of the corresponding original valuables is estimated iteratively as well as their mean values. Unlike systems evaluated by simple Monte Carlo simulations, the accuracy of the failure probability evaluated by adaptive importance sampling is relatively insensitive to the magnitude of the probability.