System reliability sensitivity analysis method based on sequential compounding method
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摘要: 岩土工程一般是由多个失效模式组成的复杂系统，且参数的不确定性对岩土工程的失效模式及可靠指标具有重要影响。为了分析参数不确定性对系统可靠度的影响，提出基于顺序组件法的系统可靠度敏感性分析方法(SCMSA)。SCMSA利用SCM组合元件的原理，在计算两元件并联和串联的简单系统可靠度及敏感性的基础上，进一步计算两元件组成的组合元件与系统内其他剩余元件间的等效相关系数，从而达到将两个元件进行组合，简化复杂系统的目的。SCMSA的优点是在系统可靠度分析的同时，融入相对敏感性指标的计算，使得敏感性分析作为可靠度分析的副产品一起算出，且该方法可适用于非正态相关变量的系统可靠度敏感性分析。最后通过简单的数值算例说明SCMSA的计算过程、计算精度及计算优势，并将其应用于半重力式挡土墙的系统可靠度敏感性分析，说明SCMSA可为岩土工程的风险分析与防治提供理论基础。Abstract: To analyze the influences of parameter uncertainty on system reliability, a system reliability sensitivity analysis method based on the sequential compounding method (SCMSA) is proposed. The SCMSA makes use of the principle of SCM combination element, and further calculates the equivalent correlation coefficient between the two components and other remaining components in the system on the basis of calculating the reliability and sensitivity of a simple system with two components in parallel or in series, so as to achieve the purpose of combining the two components and simplifying the complex system. The advantage of SCMSA is that it integrates the calculation of the relative sensitivity index into the system reliability analysis, so that the sensitivity analysis can be calculated together as a byproduct of the reliability analysis, and this method can be applied to the system reliability sensitivity analysis of the relative non-normal variables. Finally, a simple numerical example is used to illustrate the calculation process, calculation accuracy and calculation advantage of SCMSA, and it is applied to the sensitivity analysis of a system reliability of semi-gravity retaining wall, indicating that the SCMSA can provide a theoretical basis for the risk analysis and prevention of geotechnical engineering.
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图 4 五元件混联系统组合过程中的相关系数矩阵
Figure 4. Correlation coefficient matrix in combination process of five-component hybrid system
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图 5 SCMSA、CSP以及FDM的系统相对敏感性指标
Figure 5. Relative sensitivity indexes of SCMSA, CSP and FDM systems
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图 7 半重力式挡土墙的元件功能函数及其逻辑关系示意图
Figure 7. Schematic diagram of component performance functions and their logic relationship of semi-gravity retaining wall
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图 8 半重力式挡土墙的系统相对敏感性指标
Figure 8. System relative sensitivity indexes for semi-gravity retaining wall
表 1 元件(组合元件)的可靠指标、相对敏感性指标
Table 1 Reliability and relative sensitivity indexes of components (combination components)
元件(组合元件) A B C D E 
β(name) 1.556 0.466 1.405 1.118 0.979 0.979 0.944 1.158 
Sμ(name)(1) 0.707 0.380 0.986 0.447 0.213 0.218 0.672 0.413 Sμ(name)(2) 0.707 0.925 0.169 0.894 0.977 0.956 0.677 0.850 Sσ(name)(1) −0.778 −0.067 −1.364 −0.224 −0.044 −0.045 −0.659 −0.305 Sσ(name)(2) −0.778 −0.398 −0.040 −0.894 −0.935 −0.887 −0.629 −0.789 注：虚线圈为组合元件；实线圈为系统可靠指标及相对敏感性指标计算结果。 
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表 2 随机变量的概率分布
Table 2 Probability distribution of random variables
变量(单位) csoil/kPa φsoil/(°) γsoil/(kN·m-3) γwall/(kN·m-3) 均值 14 30 21 18.5 变异系数 0.3 0.1 0.1 0.05 标准差 4.2 3 2.1 0.925 分布类型 LN LN LN LN 注：LN表示对数正态分布。
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