含广义三角模糊数的机械结构可靠度计算方法

Reliability calculation method for mechanical structures with generalized triangular fuzzy number

针对可靠性度量时机械结构中存在广义三角模糊数的不确定性问题，提出一种基于证据理论的离散化机械结构可靠度计算方法．为合理地构建不确定性变量的基本概率分配，首先基于证据变量基本概率分配的离散特性，改进了熵等效法在广义三角模糊数去模糊化时的不足，并在改进熵等效法的基础上提出一种广义密度法对其进行去模糊化处理．然后利用离散化方法将随机变量和广义三角模糊数进行证据结构表征，并将离散的连续焦元序列（子区间）作为其证据体，进而构造其基本概率分配．最后利用证据融合法则对证据体进行融合，以实现信任度和似真度的数值计算．将所提出的方法运用于曲柄滑块机构的可靠度计算，并结合蒙特卡罗模拟法验证了该方法的可行性．

Aiming at the problem that the uncertainty of generalized triangular fuzzy numbers （GTFN） exists in the mechanical structures for the reliability measurement, a discretization reliability calculation method based on evidence theory is proposed. Firstly, to properly construct the basic probability assign- ment （BPA） for uncertain variables, based on the discrete property of the BPA of the evidence variables, the deficiency of entropy equivalent method （EEM） is improved when the generalized triangular fuzzy number is defuzzified. On the basis of the improved entropy equivalent method （IEEM）, a more simple defuzzification method, generalized density method （GDM）, is proposed. Secondly, the evidence structure characterization of the random variables and GTFN are realized by the discretization method, the discrete continuous focal element sequences （or subintervals） are used as their evidence bodies, and then the BPA is constructed. Finally, the fusion rule of evidence theory is used to fuse the evidence bodies, in order to achieve the numerical calculation of the belief and plausibility. Combined with the Monte Carlo simula- tion （MCS） method, the feasibility of proposed approach is verified by taking the reliability calculation of crank-slider mechanism for example.