基于椭球凸模型的结构模糊可靠性分析

结构工程中不仅存在随机不确定性，还存在模糊不确定性。针对结构模糊可靠性问题，本文提出了一种基于模糊分解定理的超椭球凸模型响应面法，适用于隐式结构功能函数的模糊可靠性求解问题。首先，通过在置信水平0，1]內遍历隶属度值确定结构可靠度的可能性分布函数，将模糊变量转化成在置信水平0，1]下的区间变量；其次，建立超椭球凸集模型，同时将超椭球转换为单位超球体，得到非概率可靠度指标——表示为从原点到极限状态曲面的最短距离；最后，利用响应面法求解结构非概率可靠度，采用中心复合设计生成试验点，通过多次迭代找到原点到极限状态曲面的最短距离点求得可靠度指标，得到遍历置信水平的结构模糊可靠度。算例仿真表明了本文方法的有效性和精确性，为结构模糊可靠性分析与计算提供了一种可行途经。

Structural Fuzzy Reliability Analysis Based on Ellipsoidal Convex Model

There are not only random uncertainties in structural engineering, but also fuzzy uncertainties. Aiming at fuzzy reliability problem of implicit structure performance function, an ellipsoidal convex model-response surface method based on fuzzy decomposition theorem is proposed in this paper. Firstly, the fuzzy variable is transformed into the interval variable at the confidence level 0, 1] by determining the probability distribution function of the structural reliability. Secondly, the super ellipsoidal convex model is established, and the super ellipsoid is converted into a unit hyper sphere, and the non-probabilistic reliability index is obtained, which is expressed as the shortest distance from the origin to the limit state surface. Finally, the response surface method is used to solve the structural non-probabilistic reliability. The central composite design is used to generate the test points. The reliability index is obtained by finding the shortest distance point from the origin to the limit state surface through multiple iterations, and the structural fuzzy reliability of the traversal confidence level is obtained. The simulation of the examples shows the effectiveness and accuracy of the proposed method, which provides a feasible way for structural fuzzy reliability analysis and calculation.