机械结构中大量存在着与载荷、材料特性、装配误差和测量误差等相关的不确定性。传统的概率模型是处理不确定性的有效方法，但其样本信息获取成本较大，而非概率凸集模型仅需获知样本的界限或边界信息即可对结构进行安全评估，因此受到研究者的广泛关注。本文对基于凸集模型机械结构非概率可靠性分析问题进行研究。主要内容包括： (1)提出一种多边凸集模型非概率可靠性指标，用结构功能函数的均值与离差之比度量机械结构的安全可靠程度，揭示了多边凸集模型可靠性指标的不一致性问题。并就传统规则凸集模型几何可靠性指标对多边凸集模型的适用性问题进行探讨。采用一个数值算例和三个工程实例对多边凸集、普通区间模型和主成分分析区间模型的非概率可靠性指标进行比较，验证了所提非概率可靠性指标的有效性。 (2)针对谢凌所提出的距离比非概率可靠性指标的不完备性进行了补充，给出了改进版本；将本文所提出的多边凸集模型非概率可靠性指标和改进后的距离比非概率可靠性指标进行比较研究，从定义和不一致性问题两个方面对两种非概率可靠性指标进行了对比，并通过三个高度非线性数值算例和两个工程实例对两种指标进行定量比较。采用一个三杆桁架实例对基于两种非概率可靠性指标的优化设计进行了比较，表明两种指标均能考虑不确定变量的多种影响。 针对复杂机械结构可靠性分析中面临的隐式功能函数和小样本问题，提出一种粒子群优化和Kriging模型相结合的结构非概率可靠性分析方法。采用多维椭球描述结构不确定参数，运用粒子群优化对模型相关参数进行求解，并构建隐式功能函数的Kriging模型进行非概率可靠性分析。通过三个算例结果表明所提方法有效可行，精度和效率均优于基于Kriging模型的非概率可靠性分析方法。

There are many uncertainties related to load, material characteristics, assembly errors and measurement errors in mechanical structures. The traditional probability model is an effective method for dealing with uncertainty, but its sample information acquisition cost is large. The non-probabilistic convex set model only needs to know the boundary or boundary information of the sample to evaluate the safety of the structure, and therefore it is widely concerned by researchers. In this paper, the non-probabilistic reliability analysis of mechanical structure based on convex set model is studied. The main contents include : (1)A non-probabilistic reliability index of polygonal convex set model is proposed, in which the ratio of mean of structural function function to its deviation is used to measure the safety degree of mechanical structures. The invariance problem in the above-mentioned reliability index is then revealed. The applicability of geometric reliability index of traditional regular convex set model to polygonal convex set model is also discussed. A numerical example and three engineering examples are used to illustrate the effectiveness of the proposed non-probabilistic reliability index by comparing the results obtained by polygonal convex set model, interval model and principal component analysis interval model. (2)The incompleteness of distance ratio non-probabilistic reliability index proposed by Xie Ling is supplemented and an improved version is given. The non-probabilistic reliability index of the polygonal convex set model proposed in this paper and the improved non-probabilistic reliability index of the distance ratio are compared and studied. The two non-probabilistic reliability indexes are compared from two aspects of definition and inconsistency. The two indexes are quantitatively compared through three highly nonlinear numerical examples and two engineering examples. A three-bar truss example is used to compare the optimization design based on two kinds of non-probabilistic reliability indexes. The results show that both indexes can consider the influence of uncertain variables. (3)Non-probabilistic reliability analysis of structures integrating PSO and Kriging model: In view of the problems with implicit performance functions and limited experimental data in the reliability analysis of complex structures, a non-probabilistic reliability method combining particle swarm optimization(PSO) with Kriging model is presented. A multidimensional ellipsoid is first used to characterize the uncertain parameters of structures. The Kriging model is then constructed for a implicit performance function, wherein its optimal relative parameters is determined by the PSO. Based on the proposed model the reliability analysis is explicitly conducted. The results by three numerical show that the proposed method is effectiveness and feasibility, and has a higher accuracy and efficiency than the one based on traditional Kriging model.

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