模糊随机可靠性分析的统一模型

针对基本变量和状态变量的不确定性可能既有随机性又有模糊性的情况，通过 引入规一化因子和模糊变量隶属函数的等效概率密度函数转换，建立了同时考虑随机和模糊 两种不确定性因素的统一可靠性模型. 由于该模型将模糊变量等价转换成了随机变量，并且 这种等价变换没有改变模糊变量的可能性分布，因而随机可靠性模型的所有方法均可用于统 一模型，并且其可靠度和失效概率的计算将是准确的. 所提模型不仅适用于只有应力和强度 两个基本变量的情况，而且也适用于多个变量的情况. 用算例对所提模型与前人的采 用截集并在截集中引入人为分布的模型进行了对比，结果表明该方法更适于工程应用.

Unified reliability model for fuzziness and randomness of the basic variables and state variables in structure

Based on the randomness and fuzziness of the basic variables and state variables, a unified reliability model is presented for the fuzzy random structure. In the unified reliability model, a factor is introduced to formulate the safe measure for the fuzzy random structure as the same one for the random structure. After the membership function of the fuzzy variable is replaced by the equivalent probability density function from the mathematical transition in the unified reliability model, the conventional reliability methods for random structure can be extended for the fuzzy random structure directly. Due to the unchangeable possibility distribution of the fuzzy variable in the equivalent mathematic transition, the failure probability can be calculated precisely for the fuzzy random structure. And the unified reliability model for random fuzzy structure can be extended to the structure with multiple variables from strength-stress two variables. Comparison in the illustrations shows that the presented method is more suitable for engineering application than the existed methods in the references.