The system failure possibility of multi-mode structural system (referred to as system) under fuzzy uncertainty is the joint membership function of input vector at the system fuzzy design point, and it can reasonably measure the safety degree of the system. The system fuzzy simulation (S-FS) can be combined with adaptive Kriging model (AK-S-FS) to solve the system failure possibility. In the current AK-S-FS method, the system fuzzy design point is searched in the maximum value region of the fuzzy input vector corresponding to the 0 membership level, and its computational efficiency still needs to be improved. Thus, a hierarchical system fuzzy simulation combined with adaptive Kriging model (AK-HS-FS) method is proposed to improve the efficiency of searching the system fuzzy design point in this paper. The efficiency of the proposed AK-HS-FS method comes from the innovative strategies of three aspects. The first is the strategy of the hierarchical system fuzzy simulation (HS-FS). Compared with the S-FS with the system fuzzy design point searched roughly in the maximum possible value region, the strategy of the HS-FS is to exploratively expand the search region by transferring from a larger membership level to a smaller one. The overall search region of the system fuzzy design point can be reduced without losing the search accuracy in the HS-FS. The second is the strategy of the hierarchical training. Compared with training the system Kriging model in the combined candidate sample pool (CSP) of all layers, it is more time-saving to train the system Kriging model layer by layer in the hierarchical CSP. The third is the strategy of iteratively reducing the CSP. According to the properties of the system fuzzy design point and the probability properties of the Kriging prediction, the required time of training the system Kriging model can be further reduced by iteratively reducing the CSP, and the reduction of the CSP can ensure the accuracy without introducing any computational cost and complexity. The results of case studies fully verify that the AK-HS-FS is much more efficient than the AK-S-FS under satisfying the computational accuracy.

模糊不确定性下多模结构系统（简称系统）的系统失效可能性是输入向量在系统模糊设计点的联合隶属函数，它可以合理地衡量系统的安全程度。系统模糊仿真（S-FS）可以结合自适应克里金模型（AK-S-FS）解决系统故障的可能性。目前的AK-S-FS方法是在0隶属度对应的模糊输入向量的最大值区域搜索系统模糊设计点，其计算效率仍有待提高。为此，本文提出了一种结合自适应克里金模型(AK-HS-FS)的分层系统模糊仿真方法，以提高系统模糊设计点的搜索效率。所提出的 AK-HS-FS 方法的效率来自三个方面的创新策略。首先是层次系统模糊模拟（HS-FS）的策略。与在最大可能值区域粗略搜索系统模糊设计点的S-FS相比，HS-FS的策略是通过从较大的隶属度转移到较小的隶属度来探索性地扩大搜索区域。在不损失HS-FS搜索精度的情况下，可以减少系统模糊设计点的整体搜索区域。二是分级训练的策略。与在各层的组合候选样本池（CSP）中训练系统克里金模型相比，在分层CSP中逐层训练系统克里金模型更省时。三是迭代减少CSP的策略。根据系统模糊设计点的性质和克里金预测的概率性质，通过迭代减少CSP，可以进一步减少训练系统Kriging模型所需的时间，减少CSP可以保证精度而不引入任何计算成本和复杂性。案例研究的结果充分验证了在满足计算精度的情况下，AK-HS-FS 比 AK-S-FS 高效得多。并且CSP的减少可以在不引入任何计算成本和复杂度的情况下保证准确性。案例研究的结果充分验证了在满足计算精度的情况下，AK-HS-FS 比 AK-S-FS 高效得多。并且CSP的减少可以在不引入任何计算成本和复杂度的情况下保证准确性。案例研究的结果充分验证了在满足计算精度的情况下，AK-HS-FS 比 AK-S-FS 高效得多。