Data Sampling — Importance Sampling
Importance sampling is used in reliability analyses that contain an importance region (the region defined by the relationship between the QoIs and the thresholds for a reliability analysis) in the input parameter space. Although Monte Carlo analysis can be applied to reliability analysis with desired accuracy, the response of the limit state is analyzed with a large number of samples, which can be time consuming and expensive, especially for problems with low probability of importance. In reliability analysis, by default, a multimodal adaptive importance sampling method is used in combination with the AGP surrogate model. The AGP model provides information about the initial location of the importance region in the input parameter space, which ensures efficiency in constructing the multimodal sampling density. The importance sampling method starts with using the representative points (the points located near the limit state where the QoIs are equal to the thresholds) from adaptive GP with the highest probability density to iteratively construct a multimodal sampling density with the representative points. After the multimodal sample density converged, the importance sampling method iteratively samples on the multimodal sampling density function and computes the probability of the reliability analysis until convergence. The probability computed with importance sampling is defined as
where xi are the points sampled with the multimodal sampling density, N is the number of samples, φ is the multimodal sampling density, f is the original input distributions density, and I is an operator that evaluates to 1 if the reliability criteria is satisfied and 0 otherwise. You can specify the initial number of samples, maximum number of samples, and relative tolerance for the importance sampling method.
If the relative tolerance is not satisfied for the importance sampling, you can try to increase the initial number of samples and the maximum number of samples. Given that an accurate AGP model has been built for the problem, the importance sampling method can be used without recomputation of COMSOL model evaluations. More details about the importance sampling method are described in Ref. 4.