Importance sampling using adapted process for hysteretic structures

Abstract eng:
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’ process whose future is determined based on information only up to the present. The adapted process is designed using stochastic control techniques. The resulting optimal control law is determined by a control potential that satisfies the Bellman’s equation, a nonlinear partial differential equation on the response state-space. Numerical results for a single-degree-of freedom elastoplastic structure shows that the proposed method leads to significant improvement in variance reduction over importance sampling using design points reported recently.

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