考虑状态与基本变量随机模糊性的广义响应面可靠性分析

针对复杂结构、机构可靠性分析中的隐式极限状态方程，建立了可以同时考虑基本变量和失效一安全状态随机模糊双重不确定性因素的广义响应面可靠性分析方法。该方法采用模糊基本变量的等效随机化变换，在不改变基本变量模糊分布的情况下，建立了基于有限元分析的复杂结构、机构多个随机一模糊基本变量情况下的广义响应面法，利用广义响应面函数和模糊随机事件概率的计算公式，定义了复杂结构、机构广义失效概率的计算公式，并给出了多个模式情况下体系同时考虑状态和基本变量随机模糊性的广义失效概率计算公式。在弹性连杆机构强度刚度多模式广义可靠性分析的应用算例说明了所提方法的合理性。

General Response Surface Reliability Analysis for Fuzzy-Random Uncertainty both in Basic Variables and in State Variables

A general response surface(RS) method is presented for reliability analysis of complex structure/mechanism with fuzzy-random uncertainty both in basic variables and in failure state variables. On the basis of equivalent transformation from fuzzy basic variable to random basic variable, the fuzziness and randomness in the basic variables are considered simultaneously in the presented general RS method. Once the fuzzy basic variables are transformed into the random basic variables, the conventional RS method is employed to establish the general RS for the complex structure/mechanism with implicit limit state equation by finite element numerical simulation. Furthermore, the general failure probability is defined according to the probability formula for fuzzy-random event by taking the fuzziness and randomness in the failure-safety state into consideration, and an appropriate fuzzy operator is adopted to calculate the general failure probability for the complex structure/mechanism with multiple implicit failure modes. Finally, a general reliability analysis of an elastic linkage mechanism is introduced to illustrate the present method.