Improving further importance sampling (IS) method for failure probability estimation

In structural reliability analysis, the traditional IS method can improve the sampling efficiency by moving the sampling center to the design point. We now present a truncated IS method that can further improve the traditional IS method. In the full paper we explain in some detail our truncated IS method; in this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is: the traditional IS method based on design point. The aim of the first topic is to facilitate the explanation of our truncated IS method. The second topic is: the truncated IS method. Its three subtopics are: the estimation of failure probability in truncated IS method (subtopic 2.1), the coefficient of variance (COV) of the estimated failure probability (subtopic 2.2) and the procedure of the truncated IS method (subtopic 2.3). In subtopic 2.1, we explain that the improved IS method adopts the truncated IS function to generate the importance samples outside a special hypersphere, which takes the mean point as the center of the hypersphere. In subtopic 2.2, we give eq. (14) in the full paper as the formula for calculating the COV. In subtopic 2.3, we give a 5-step procedure for truncated IS method. Finally we give three numerical examples, whose calculated results are given in Tables 1, 3 and 5 in the full paper. These results show preliminarily that, compared with the traditional IS method, the truncated IS method is more efficient in the following two cases: (1) in the case that the samples of the two methods are the same, the proposed truncated IS method has smaller COV of the failure probability estimation; (2) in the case that the precisions of two methods are the same, the proposed method needs less samples.