An Improved MPP-Based Importance Sampling Method for Reliability Analysis

Importance sampling (IS) as an efficient technique in Monte Carlo probability simulation has been widely applied for high reliability system analysis, which can greatly reduce the simulation numbers and improve the efficiency. Among the IS methods, Most Probable point (MPP)-based Importance Sampling Method (MISM) has gained wide attention because of its effectiveness and easy implementation. However, the traditional MISM uses the Acceptance-Rejection (A-R) technique to sample points from the important regions. The uniform distribution is often set as the proposal distribution and its value is equal to the value of the point in the Probability Density Function (PDF) where the first-order derivative is zero. This brings about efficiency-scarified problems when the derivative exceeds the sampling interval in different dimensional cases. Moreover, in order to increase the efficiency by use of the A-R process, it often performs the variable transformation (e.g. log-transformation). Unfortunately, it doesn’t work while the PDF of the random variables is not a log-concave function. In this paper, two feasible strategies were proposed to solve these drawbacks. The first strategy is that we set the maximal value of the PDF as the value of the uniform function, which is obtained by calculating all samples point by point in the target interval. It can be applied to any dimensions as an instructional strategy. The other one is that a well-designed normal distribution function, instead of the uniform distribution function, is used as the proposal distribution to avoid transformation of the variables. Finally, two numerical examples are given to illustrate the effectiveness and accuracy of the proposed method.