An efficient computational method for estimating failure credibility by combining genetic algorithm and active learning Kriging

Failure credibility is popular in measuring safety degree of structure under fuzzy uncertainty due to its excellent property of self-duality. Existing methods for estimating failure credibility can be mainly divided into two categories, i.e., the simulation-based methods and the optimization-based methods. The simulation-based methods are universal and robust, but time-consuming in dealing with high-dimensional problems. The optimization-based methods are efficient and flexible, but the precision of the failure credibility estimate will be impacted by the local optimum solution resulted from some optimization techniques. Thus, in order to overcome the disadvantages of existing methods, an efficient method by combining genetic algorithm and active learning Kriging (AK-GA) is proposed to estimate failure credibility in this paper. Firstly, by use of the fuzzy simulation, the estimation of failure credibility is transformed into finding for the failure/safety sample that processes the maximum joint membership function (MF) from the fuzzy simulation pool, which makes the credibility estimation less difficult to be computed. Secondly, the genetic algorithm is used to find the failure/safety sample with maximum joint MF. Thirdly, to drastically improve the computational efficiency of the proposed method, active learning Kriging is embedded to accurately and efficiently distinguish the failure and safety sample in computing the fitness function of genetic algorithm. Four mathematical and engineering test examples are used to demonstrate the accuracy and efficiency of the proposed AK-GA for estimating failure credibility.