Analysis method for hybrid uncertainty of risk considering distribution parameters dependency
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摘要:
在定量化风险评估中，针对变量分布参数存在依赖时的混合不确定性传播问题，提出一种考虑分布参数完全依赖、部分依赖以及独立传播情形的双层混合不确定性刻画与传播框架，内外层分布参数不确定性分别用概率分布与可能性分布刻画，采用蒙特卡罗模拟法与模糊扩展原则相结合的数值求解方法。针对认知不确定性分布参数依赖性，构建了统一的认知不确定性分布参数依赖性模型，并给出依赖性系数的概念。为实现认知不确定性分布参数独立性采样，设计了基于D-S证据理论与随机集相结合的不确定性传播算法，相比于概率刻画下的双层蒙特卡罗方法，计算代价有效降低。以某型氢氧发动机贮箱共底漏气率为算例，验证本文方法的有效性与可行性。
Abstract:In view of hybrid uncertainty propagation with parameters dependency of variables in quantified risk assessment, a two-level hybrid uncertainty presentation and propagation framework considering parameters total dependency, partial dependency and independency was proposed, in which inner and outer parameters were specified with probability and possibility, and the numerical values were calculated by Monte Carlo simulation and fuzzy extension principle. Based on the epidemic uncertainty parameter dependency, a model with epidemic uncertainty parameters dependency and a dependency coefficient were constructed. An uncertainty propagation algorithm based on the D-S evidence theory and random set theory for parameters sampled independently was built, which, compared with the two-level Monte Carlo method presented with probability, reduced the time costs largely. Leakage rate of the hydrogen and oxygen co-bottom tank was taken as an example, and the effectiveness and feasibility of the proposed method were validated.
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Key words:
- risk assessment /
- hybrid uncertainty /
- Monte Carlo /
- evidence theory /
- fuzzy sets theory
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图 1 D-S证据理论信度区间关系
Figure 1. Relationship between belief intervals of D-S evidence theory
图 2 三角模糊分布对应的α-截集区间
Figure 2. α-cut interval corresponding to triangular fuzzy distribution
图 3 认知不确定性分布参数完全负依赖模型
Figure 3. Total negative dependency model of epistemic uncertainty distribution parameter
图 4 参数非独立时的混合不确定性传播流程
Figure 4. Hybrid uncertainty propagation flowchart under independent distribution parameters
图 5 三角模糊分布函数μ=θj, 1α-截集
Figure 5. α-cut of triangular fuzzy distribution function of μ=θj, 1
图 6 均值为[μα, μα]的Yj的累计分布函数曲线
Figure 6. Curves of cumulative distribution function of Yj between mean value [μα, μα]
图 7 参数独立时的混合不确定性传播流程
Figure 7. Hybrid uncertainty propagation flowchart under dependent distribution parameters
图 8 可能性分布到信度空间的转换
Figure 8. Transformation from possibility distribution to belief space
图 9 液氧液氢贮箱共底结构
Figure 9. Co-bottom tank structure of liquid oxygen and liquid hydrogen
图 10 认知不确定性分布参数独立时混合不确定性传播与双层蒙特卡罗不确定性传播曲线对比
Figure 10. Compared curves of hybrid uncertainty propagation and two-level Monte Carlo uncertainty propagation with epistemic uncertainty distribution parameters independence
图 11 认知不确定性分布参数依赖性、独立性的不确定性传播结果曲线对比
Figure 11. Compared curves of uncertainty propagation with epistemic uncertainty distribution parameters dependency and independency
图 12 认知不确定性分布参数完全正、负依赖时的不确定性传播结果曲线对比
Figure 12. Compared curves of uncertainty propagation of epistemic uncertainty distribution parameters with total dependence and independence
表 1 认知不确定性分布参数
Table 1. Parameter distributions of epistemic uncertainty
参数 数值 μP1 (6 500, 7 000, 7 500) σP1 100 μP2 (3 300, 3 500, 3 400) σP2 100 μV (0.49, 0.50, 0.51) σV (0.004 5, 0.005 0, 0.005 5) μT1 (0, 10, 5) σT1 (0.05, 0, 0.1) μT2 (43 100, 43 200, 43 300) σT2 (0, 100, 200) 
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表 2 认知不确定性分布参数依赖性
Table 2. Dependency of parameter distributions of epistemic uncertainty
参数1 参数2 k μP1 μP2 -0.5 σP1 σP2 0.3 μT1 μT2 -1 σT1 σT2 0.7
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表 3 各种不确定性传播方法计算代价对比
Table 3. Comparison of calculation costs of different uncertainty propagation methods
方法 NL1 NL2 tCPU/s Mpr 3×105 1×105 15.3 Mpo 2×102 1×103 7.5 本文方法 5×101 1×103 3.5
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