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Local sensitivity analysis of failure possibility and its universal solution by fuzzy simulation
Structural and Multidisciplinary Optimization ( IF 3.6 ) Pub Date : 2021-04-10 , DOI: 10.1007/s00158-021-02879-2
Lu Wang , Guijie Li , Zhenzhou Lu , Kaixuan Feng

Failure possibility (FP) is widely used to measure safety degree of structure in the presence of fuzzy uncertainty, but how to quantify the effect of fuzzy distribution parameter on FP is seldom investigated. For searching the important parameter to FP and guiding the FP-based design optimization, the local sensitivity of FP (LS-FP) is firstly defined by the partial derivative of FP with respect to the fuzzy distribution parameter in this paper. Then, the analytical solution is derived for the LS-FP in special cases; a universal algorithm is proposed to solve LS-FP by use of the fuzzy simulation. The proposed universal algorithm includes three creative steps. The first is explicitly expressing FP as the joint membership function of the fuzzy inputs at the fuzzy most possible failure point (F-MPP) by use of the fuzzy simulation, on which LS-FP can be equivalently transformed as the partial derivative of F-MPP with respect to the fuzzy distribution parameter. The second is using the characteristic of F-MPP to derive the analytical solution of the partial derivative of F-MPP. The third is establishing an efficient method to estimate F-MPP for completing LS-FP, where new learning function and stopping criterion are proposed to improve the computational efficiency. The proposed algorithm has no limitation on the nonlinearity of performance function and can be applied in any fuzzy membership distribution form of the fuzzy input. Several examples are used to validate the wide applicability, the accuracy, and the efficiency of the proposed algorithm to solve LS-FP.



中文翻译:

故障可能性的局部敏感性分析及其通用解的模糊仿真

在存在模糊不确定性的情况下,失效可能性(FP)被广泛用于测量结构的安全程度,但是很少研究如何量化模糊分布参数对FP的影响。为了寻找FP的重要参数并指导基于FP的设计优化,本文首先通过FP相对于模糊分布参数的偏导数来定义FP的局部灵敏度。然后,导出特殊情况下的LS-FP的解析解。提出了一种利用模糊仿真求解LS-FP的通用算法。提出的通用算法包括三个创新步骤。第一个方法是使用模糊仿真,将FP明确表示为模糊最可能失效点(F-MPP)上模糊输入的联合隶属函数,相对于模糊分布参数,LS-FP可以等效地转换为F-MPP的偏导数。二是利用F-MPP的特性推导F-MPP偏导数的解析解。第三是建立一种用于估计完成LS-FP的F-MPP的有效方法,其中提出了新的学习功能和停止准则以提高计算效率。该算法对性能函数的非线性没有限制,可以应用于模糊输入的任何模糊隶属度分布形式。使用几个例子来验证所提出算法解决LS-FP的广泛适用性,准确性和效率。二是利用F-MPP的特性推导F-MPP偏导数的解析解。第三是建立一种用于估计完成LS-FP的F-MPP的有效方法,其中提出了新的学习功能和停止准则以提高计算效率。该算法对性能函数的非线性没有限制,可以应用于模糊输入的任何模糊隶属度分布形式。使用几个例子来验证所提出算法解决LS-FP的广泛适用性,准确性和效率。二是利用F-MPP的特性推导F-MPP偏导数的解析解。第三是建立一种用于估计完成LS-FP的F-MPP的有效方法,其中提出了新的学习功能和停止准则以提高计算效率。该算法对性能函数的非线性没有限制,可以应用于模糊输入的任何模糊隶属度分布形式。使用几个例子来验证所提出算法解决LS-FP的广泛适用性,准确性和效率。提出了新的学习功能和停止准则,以提高计算效率。该算法对性能函数的非线性没有限制,可以应用于模糊输入的任何模糊隶属度分布形式。使用几个例子来验证所提出算法解决LS-FP的广泛适用性,准确性和效率。提出了新的学习功能和停止准则,以提高计算效率。该算法对性能函数的非线性没有限制,可以应用于模糊输入的任何模糊隶属度分布形式。使用几个例子来验证所提出算法解决LS-FP的广泛适用性,准确性和效率。

更新日期:2021-04-11
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