A SYSTEM RELIABILITY ANALYSIS METHOD FOR STRUCTURES WITH PROBABILITY AND INTERVAL MIXED UNCERTAINTY
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摘要: 系统可靠性问题中通常存在大量的不确定参数，传统方法一般是基于概率模型对系统进行可靠性分析，但是实际工程中由于数据缺乏或试验条件的限制往往难以得到参数的精确概率分布.本文将结构体系一部分样本信息充足的不确定变量用随机变量进行描述，而另一部分样本缺乏的用区间表示，并提出了一种新的含概率与区间混合不确定性的系统可靠性分析方法.首先，基于一个高效求解方法获得单失效模式下结构的最小可靠度指标；再针对多失效模式下含概率与区间混合不确定性问题建立了系统可靠性分析模型；考虑各失效模式之间的相关性，通过线性相关度计算方法求得相关系数矩阵；最后提出了串联体系和并联体系可靠度求解方法.3个数值算例表明，该方法可以实现含概率与区间混合的多个非线性失效模式下系统可靠度的计算.通过对比传统的概率可靠性分析方法，本文方法只需要少量的不确定信息便可确保系统更加安全，更适合复杂结构系统可靠性的分析和设计.
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关键词:
- 系统可靠性 /
- 概率与区间混合不确定性 /
- 最大失效概率 /
- 失效模式相关性
Abstract: There are a large number of inherently uncertain parameters in the problem of system reliability. Traditional system reliability analysis methods are usually based on the probability model assumption. Probability distribution function of uncertain parameters can be easily obtained with sufficient samples, but in practical engineering problems, it is often difficult to get the precise probability distribution function with limited data or test conditions. In this paper, the uncertain variables of the system based on sufficient information are taken as the random variables, while others with limited information can only be given variation intervals. This paper proposes a new system reliability analysis method for structures with probability and interval mixed uncertainty. Firstly, the minimum reliability index of each failure mode is obtained based on an efficient solution method. Then the system reliability model under multiple failure modes with probability and interval mixed uncertainty is provided. Considering the dependence between different failure modes of systems, a correlation coefficient matrix is obtained by the linear correlation calculated method. Finally, the maximum failure probabilities are calculated for series and parallel system. Three numerical examples show that the present method can effectively deal with the system reliability problems of multiple nonlinear failure modes with probability and interval mixed uncertainty. Compared to the traditional probabilistic reliability analysis method, the presented method can ensure the security of system well and it only needs less uncertain information, and hence it seems suitable for reliability analysis and design of many complex engineering structures or systems. -
表 1 两单元Daniels系统不确定变量分布类型和参数
Table 1. Distribution types and parameter of uncertain variables of the two-component Daniels system
表 2 两单元Daniels系统的可靠性分析结果
Table 2. The reliability analysis results of the two-component Daniels system
表 3 悬臂梁的不确定变量分布类型和参数
Table 3. Distribution types and parameter of uncertain variables of the cantilever beam
表 4 悬臂梁的系统可靠性分析结果
Table 4. The system reliability analysis results of the cantilever beam
表 5 车辆耐撞问题的不确定变量分布类型和参数
Table 5. Distribution types and parameter of uncertain variables of the vehicle crashworthiness problem
表 6 车辆耐撞问题的3个功能函数响应面
Table 6. Response surface for the three performance functions in the vehicle crashworthiness problem
表 7 车辆耐撞问题的系统可靠性分析结果
Table 7. The system reliability analysis results of the vehicle crashworthiness problem
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