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摘要:
针对现有动态故障树分析方法存在的状态空间爆炸、计算效率低、适用范围有限等缺点，提出一种基于顺序二元决策图的动态故障树分析方法。在将动态逻辑门转化为含顺序事件的逻辑门的基础上，给出了顺序二元决策图的模型以及含有顺序事件的布尔运算规则，利用顺序二元决策图和扩展的布尔运算获取动态故障树的失效路径，并给出多单元顺序事件的发生概率。以某弹药为实例，考虑不完全覆盖问题，针对指数分布与非指数分布2种情形进行了动态故障树分析，结果表明该方法具有计算高效、精度高、适用性广泛等优点，为复杂动态系统的可靠性分析提供了理论基础。
Abstract:In order to solve the problem of the existing dynamic fault tree analysis method, such as state space explosion, low computational efficiency and limited application range, a method for dynamic fault tree analysis based on sequential binary decision diagram is proposed. First, dynamic logic gates are transformed into logic gates with sequential events. Next, sequential binary decision diagram model and Boolean operation with sequential events are presented. Then, failure paths of dynamic fault tree are obtained by sequential binary decision diagram and extensional Boolean operation. Finally, probability calculations for sequential events with multi-unit are deduced. With a certain ammunition as an example, considering the imperfect coverage problem, the dynamic fault tree is analyzed under the situations of exponential and non-exponential distribution. The results show that this method has the advantages of high efficiency, high accuracy and wide applicability, which provides a theoretical basis for the reliability analysis of complex dynamic systems.
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图 5 考虑不完全覆盖的温备份门转化
Figure 5. Conversion of warm spare gates considering imperfect coverage
图 11 部件指数分布情形系统可靠度随时间变化曲线
Figure 11. System reliability curves changes over time with elements obeying exponential distribution
图 12 部件非指数分布情形系统可靠度随时间变化曲线
Figure 12. System reliability curves changes over time with elements obeying non-exponential distribution
表 1 本文方法与基于马尔可夫模型方法的系统可靠度
Table 1. Reliability of the system by proposedmethod and Markov-based method
t/h R(t) 本文方法 马尔可夫模型方法 5 000 0.951 0 0.951 0 10 000 0.903 7 0.903 7 30 000 0.729 6 0.729 6 50 000 0.577 8 0.577 8 100 000 0.321 6 0.321 6 
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表 2 本文方法与基于蒙特卡罗仿真方法的系统可靠度
Table 2. Reliability of the system by proposedmethod and Monte Carlo simulation method
t/h R(t) 相对误差/% 本文方法 蒙特卡罗仿真方法 5 000 0.963 4 0.963 4 0 10 000 0.927 2 0.927 2 0 30 000 0.784 3 0.784 4 0.01 50 000 0.647 2 0.647 4 0.03 100 000 0.357 2 0.357 5 0.08
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表 3 本文方法与基于蒙特卡罗仿真方法的运算时间
Table 3. Computation time by proposed method andMonte Carlo simulation method
方法 本文方法 蒙特卡罗仿真方法 运算时间/s 24.894 0 48.093 7
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