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针对同时存在随机基本变量和模糊基本变量的结构,提出了一种模糊可靠度隶属函数求解的迭代线抽样方法。所提方法首先求得给定隶属度水平下模糊基本变量的取值域。然后通过优化建模和迭代策略,求得使功能函数取最值的模糊基本变量取值点,并求得对应的缩减后的随机变量空间内功能函数的设计点。最后基于功能函数最值对应的模糊基本变量取值点及其相应的设计点,运用线抽样法求得给定隶属水平下可靠度值的上界、下界,进而得到模糊可靠度的隶属函数。对于每个给定隶属度水平对应的模糊变量取值域,所提方法通过寻找功能函数的最值代替寻找可靠度最值的策略,大大降低了计算量。另外,所提方法通过迭代过程保证功能函数最值对应的设计点收敛于可靠度最值对应的设计点,并通过线抽样方法来求解相应的可靠度,可以保证算法具有较高的精度。该文算例将对所提算法的优越性进行验证。
Aiming at the structure of random basic variables and fuzzy basic variables, an iterative line sampling method for solving fuzzy membership function is proposed. The proposed method first obtains the value range of the fuzzy basic variables for a given membership level. Then, through the optimization modeling and iteration strategy, we get the fuzzy basic variables which make the function function take the most value, and get the design point of the corresponding reduced function function in the random variable space. Finally, the upper and lower bounds of the reliability values for a given membership level are obtained by using the line sampling method based on the fuzzy basic variables’ value points and their corresponding design points corresponding to the most value of the functional function, and the membership functions of the fuzzy reliability are obtained. For each fuzzy variable value range corresponding to a given membership level, the proposed method can greatly reduce the computational cost by finding the most value of the function instead of finding the most reliable value. In addition, the proposed method ensures that the design points corresponding to the maximum value of the functional function converge to the design points corresponding to the maximum reliability value through the iterative process, and the corresponding reliability is solved by the line sampling method to ensure the algorithm with higher accuracy. This example will verify the superiority of the proposed algorithm.