In the vulnerability analysis, correlations among failure modes have significant effects on the estimation of failure probabilities. However, the failure modes were assumed to be independent with each other or only parts of dependencies of failure modes were considered, which might lead to inaccurate results. In the present study, a novel methodology to clarify the entire logical relationship among failure modes and determine system probabilities is developed. Firstly, based on the form-changed limit state equations (LSEs) of failure modes, the LSE surfaces or curves are plotted. Subsequently, the logical relationship among failure modes can be identified with the LSE surfaces or curves. The system consequences are further developed by the logical relationship. Bayesian network (BN) is constructed with the input of logical relationship into arcs. With BN considering logical relationship, the occurrence probabilities of failure modes are calculated and system probabilities are estimated more accurately, which are verified well with Monte Carlo simulation and analytical solution. Furthermore, the detailed compositions of occurrence probabilities of failure modes are specified by the system probabilities. The methodology is illustrated by a case study. This study can be applied to the vulnerability analysis of various hazards or disasters as long as LSEs for corresponding failure modes can be developed.

在脆弱性分析中，故障模式之间的相关性对故障概率的估计有重要影响。但是，假定故障模式彼此独立，或者只考虑了故障模式的部分依赖关系，这可能导致结果不准确。在本研究中，开发了一种新颖的方法来阐明故障模式之间的整个逻辑关系并确定系统概率。首先，基于失效模式的形式变化极限状态方程（LSE），绘制LSE表面或曲线。随后，可以使用LSE曲面或曲线识别故障模式之间的逻辑关系。通过逻辑关系可以进一步发展系统后果。贝叶斯网络（BN）的构建是将逻辑关系输入到弧中。在考虑逻辑关系的BN的情况下，计算故障模式的发生概率并更准确地估计系统概率，并通过蒙特卡洛仿真和解析解进行了很好的验证。此外，故障概率的发生概率的详细组成由系统概率规定。案例研究说明了该方法。只要可以为相应的故障模式开发LSE，该研究就可以应用于各种危害或灾难的脆弱性分析。失效模式的发生概率的详细组成由系统概率规定。案例研究说明了该方法。只要可以为相应的故障模式开发LSE，该研究就可以应用于各种危害或灾难的脆弱性分析。失效模式的发生概率的详细组成由系统概率规定。案例研究说明了该方法。只要可以为相应的故障模式开发LSE，该研究就可以应用于各种危害或灾难的脆弱性分析。