Importance sampling for elasto-plastic systems using adapted process with deterministic control

A new importance sampling method is presented for computing the first passage probability of elasto-plastic systems under white noise 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. This causal property is responsible for maintaining the theoretical rigor of the resulting importance sampling procedure. It opens up great possibilities in the design of adapted process for variance reduction using importance sampling. In this work the adapted process is designed using concepts of deterministic optimal control. Numerical results show that the use of adapted process is particularly useful for hysteretic systems where hysteretic effects undermine the effectiveness of conventional importance sampling method based on fixed design points.