与传统的概率可靠性分析不同，非概率可靠性分析仅需要知道少量样本信息来确定不确定因素的边界，更适用于小样本、贫信息、可靠性要求高的机械结构。近年来，基于凸集模型的结构非概率可靠性分析方法已成为研究热点之一。本文对结构非概率可靠性分析方法的若干问题进行了有益探索，主要内容包括：

(1)区间模型与椭球模型的非概率可靠性指标对比研究：基于区间模型和椭球模型具备相同中心和方向这一前提，针对区间包络椭球、两者相交但不包含和椭球包络区间三种情况对两种非概率可靠性指标进行了对比研究。探讨了二维情况下两种非概率可靠性指标的大小关系及相应的几何解释，并进一步探讨了高维情况下两者的大小关系。研究结果表明两种非概率可靠性指标的大小关系同时依赖于样本分布和结构本身。

(2)三种串联结构系统非概率可靠性界限法的对比研究：对三种非概率可靠性界限法包括宽界限法、窄界限法和线性规划界限法进行了对比研究。从方法的误差来源、失效模式排序影响、函数调用次数等方面对三种界限法的精度和效率展开对比研究。一个数值算例和两个工程算例的分析结果表明，在精度方面，线性规划界限法最高，窄界限法次之，宽界限法最低；在效率方面，宽界限法最高，线性规划界限法次之，窄界限法最低。

(3)结构非概率可靠性分析软件开发：以非概率可靠性分析中常用的一阶可靠性近似方法、二阶可靠性近似方法、线性规划界限法及蒙特卡洛模拟法为基础，开发了相应的结构非概率可靠性分析软件。通过用Python语言分别对核心算法进行编程，结合模块化设计思想，对软件整体框架进行设计，通过基于Python的第三方库PyQt5构建了交互式图形界面来完成软件的封装。运用四个算例包括两个结构元件算例和两个串联结构系统算例对软件的可行性进行了验证。

Different from the traditional probabilistic reliability analysis, non-probabilistic reliability analysis only needs to know limited sample information to determine the boundary of uncertain parameters, which is more suitable for mechanical structures with small samples, poor information and high reliability requirements. In recent years, the non-probabilistic reliability analysis method of structures based on convex model has become a research hotspot. In this paper, some problems of structural non-probabilistic reliability analysis method are investigated. The main contents include:

(1) Comparative study on the non-probabilistic reliability indexes of the interval model and the ellipsoid model. With the premise that the interval model and the ellipsoid model have the same center and direction, the two non-probabilistic reliability indexes are compared for the three cases, namely the interval envelopes the ellipsoid, there exists the intersection but not the inclusion between two models and the ellipsoid envelopes the interval. For the two-dimensional case, the relationship between the two non-probabilistic reliability indexes and the corresponding geometric interpretation are discussed, and their relationship in the high-dimensional case is further discussed. The results show that the relationship between the two non-probabilistic reliability indexes depends on not only the sample distribution but also the structure.

(2) Comparative study of three non-probabilistic reliability bounds methods for series structural systems. Three non-probabilistic reliability boundary methods including wide boundary method, narrow boundary method and linear programming boundary method are compared and studied. The accuracy and efficiency of three boundary methods are compared from the aspects of the error source, the influence of failure mode sorting and the number of function calls. The results by a numerical example and two engineering examples show that in terms of accuracy, the linear programming boundary method is the highest, followed by the narrow boundary method and then the wide boundary method. The wide boundary method is the highest efficiency, followed by the linear programming boundary method and then the narrow boundary method.

(3) Software development of structural non-probabilistic reliability analysis. Based on the first-order reliability approximation method, the second-order reliability approximation method, the linear programming boundary method and the Monte Carlo simulation method commonly used in the non-probabilistic reliability analysis, the corresponding structural non-probabilistic reliability analysis software is developed. By using Python language to program the core algorithm respectively, combined with the modular design idea, the overall framework of the software is designed, and the interactive graphical interface is constructed by the third-party library PyQt5 based on Python to complete the software package. Four examples including two structural element examples and two series structural system examples are used to verify the feasibility of the software.