Stochastic control approach to reliability of elasto-plastic structures

An importance sampling method is presented for computing the first passage probability of elasto-plastic structures under stochastic excitations. The importance sampling distribution corresponds to shifting the mean of the excitation to an \'adapted\' stochastic process whose future is determined based on information only up to the present. A stochastic control approach is adopted for designing the adapted process. The optimal control law is determined by a control potential, which satisfies the Bellman\'s equation, a nonlinear partial differential equation on the response state-space. Numerical results for a single-degree-of freedom elasto-plastic structure shows that the proposed method leads to significant improvement in variance reduction over importance sampling using design points reported recently.