Importance Sampling & SMC

Reliability-based design of structures is carried out through several Monte Carlo methods. The general Crude Monte Carlo (CMC) method is not accurate for small probabilities of failure with a limit on the number of samples because of expensive simulations. This is why several ways have been devised to improve the accuracy of estimation through methods like separable Monte Carlo (SMC) and importance sampling.

The failure criterion in structural problems is generally defined as the response exceeding the capacity. SMC can be used if the response and capacity are independent of each other.

Importance sampling for reliability analysis can be highly efficient with a good choice of new sampling distributions. However, in practice, implementing importance sampling can be quite challenging. Even when a sampling distribution is selected that preferentially samples in the failure region, the accuracy of the probability of failure may not significantly improve for fewer number of samples due to computational budget.

Figure showing the importance sampling procedure

To take advantage of both SMC and importance sampling, a combined method (ImpSMC) has been developed which is shown to give a much higher accuracy as compared each of them individually. This combined method has been applied to some engineering examples to demonstrate its effectiveness. Further information about this work can be found in the paper Separable Monte Carlo Combined with Importance Sampling for Variance Reduction.