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.

失效可信度因其出色的自我对偶性而在模糊不确定性下测量结构的安全度方面广受欢迎。现有的估计故障可信度的方法主要可以分为两类，即基于仿真的方法和基于优化的方法。基于仿真的方法通用且健壮，但是在处理高维问题时非常耗时。基于优化的方法是高效且灵活的，但是故障可信度估计的精度将受到某些优化技术所产生的局部最优解的影响。因此，为克​​服现有方法的弊端，提出了一种结合遗传算法和主动学习克里格法（AK-GA）的有效方法来评估失效可信度。首先，通过使用模糊仿真，将故障可信度的估计转换为从模糊仿真池中查找处理最大联合隶属函数（MF）的故障/安全样本，这使得可信度估算的计算变得不那么困难。其次，使用遗传算法找到具有最大联合MF的失效/安全样本。第三，为了大大提高所提方法的计算效率，嵌入了主动学习Kriging算法，可以在计算遗传算法的适应度函数时准确有效地区分故障和安全样本。四个数学和工程测试示例用于证明所提出的AK-GA的准确性和效率，以评估故障可信度。失效可信度的估计被转换为从模糊仿真池中查找处理最大联合隶属函数（MF）的失效/安全样本，这使得可信度估计的计算变得不那么困难。其次，使用遗传算法找到具有最大联合MF的失效/安全样本。第三，为了大大提高所提方法的计算效率，嵌入了主动学习Kriging算法，可以在计算遗传算法的适应度函数时准确有效地区分故障和安全样本。四个数学和工程测试示例用于证明所提出的AK-GA的准确性和效率，以评估故障可信度。失效可信度的估计被转换为从模糊仿真池中查找处理最大联合隶属函数（MF）的失效/安全样本，这使得可信度估计的计算变得不那么困难。其次，使用遗传算法找到具有最大联合MF的失效/安全样本。第三，为了大大提高所提方法的计算效率，嵌入了主动学习Kriging算法，可以在计算遗传算法的适应度函数时准确有效地区分出故障和安全样本。四个数学和工程测试示例用于证明所提出的AK-GA的准确性和效率，以评估故障可信度。