模糊可靠性模型的收敛性及改进的截集分布

基于截集法的结构模糊可靠性基本模型已被用于各种可靠性工程问题中，形成了应力-强度模糊可靠性干涉模型、结构疲劳寿命模糊可靠性模型和结构抗共振模糊可靠性模型等具体模型.提出了常用截集分布下模糊可靠性模型的收敛性定理，并予以理论证明，进而针对单侧无限安全域和双侧无限安全域这两类模型，分别给出了相应推论.定理表明，当截集逐渐变长时，采用常用截集分布所得的可靠性分析结果趋于某一固定值，而与具体的结构无关，因此是不合理的.为了避免这种不足，提出了一种新的截集分布——修正的截尾正态分布.并通过3个具体例子验证，采用文中所给的截集分布，模糊可靠性模型收敛于相应的随机可靠性模型，表明其具有良好的收敛性和更好的适用性.

Convergence of fuzzy reliability models and an improved cut-set distribution

The basic fuzzy reliability model of mechanical structures based on cut-set method has been applied to various engineering problems, and some specific models have been formed, such as stress-strength interference model, fatigue life model and avoid-resonance model. A convergence theorem of the model with commonly used cut-set distributions was proposed and proved, and then two corresponding inferences were obtained for the models with unilateral-infinite and bilateral-infinite safety domains respectively. The theorem indicates that when the cut-set becomes longer gradually, the reliability assessments of the fuzzy models with these commonly used cut-set distributions converge to a fixed value which has nothing to do with the specific mechanical structures and thus is unreasonable. In order to avoid this deficiency, a new cut-set distribution called modified truncated normal distribution was proposed. Meanwhile, three specific examples were carried out to verify that the fuzzy reliability model with the proposed cut-set distribution converges well to the corresponding random reliability model, which indicates it is of better convergence and wider applicability.