失效概率函数求解的高效算法

An efficient method was developed to obtain the failure probability function which combines the fractional moment-based maximum entropy method and the surrogate model method. The idea of the process is to build the failure probability function iteratively by the active learning Kriging method. Firstly, a crude failure probability function was established by using a few training samples. Then the training samples which violate the restraints of the learning function were added to update the failure probability function until the accuracy of the problem was satisfied. The fractional moment-based maximum entropy method was used to get the failure probability sample for every distribution parameter's training sample. The samples of the failure probability could be evaluated efficiently and accurately for the optimization strategy in the fractional moment-based maximum entropy method, which could approximate the probability density function of the response effectively, and the fractional moments were estimated by the dimensional reduction method. Two examples were illustrated in the end to compare several methods such as the Bayes method, the Monte Carlo method, and so on. From the numerical results, it can be seen that the proposed method can accurately solve the problem with complex performance function and can reduce the computational cost significantly.