﻿ 少故障数据条件下SFEP最终事件发生概率分布确定方法
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 智能系统学报  2020, Vol. 15 Issue (1): 136-143  DOI: 10.11992/tis.201911002 0

引用本文

CUI Tiejun, LI Shasha. Determination method of target event occurrence probability in SFEP under the condition of less fault data[J]. CAAI Transactions on Intelligent Systems, 2020, 15(1): 136-143. DOI: 10.11992/tis.201911002.

文章历史

1. 辽宁工程技术大学，安全科学与工程学院，辽宁 阜新 123000;
2. 大连交通大学 辽宁省隧道与地下结构工程技术研究中心，辽宁 大连 116028;
3. 辽宁工程技术大学 工商管理学院，辽宁 葫芦岛 125105

Determination method of target event occurrence probability in SFEP under the condition of less fault data
CUI Tiejun 1,2, LI Shasha 3
1. College of Safety Science and Engineering, Liaoning Technical University, Fuxin 123000, China;
2. Tunnel & Underground Structure Engineering Center of Liaoning, Dalian Jiaotong University, Dalian 116028 China;
Abstract: To get suitable probability distribution of the target event in the system fault evolution process (SFEP) with less fault data, we propose a calculation method of the probability distribution of the target event occurrence considering the information diffusion and less data. This method uses the information diffusion principle to form a normal distribution in the study area with the factors at the event occurrence as the center. Take the maximum value for many times of occurrence of the same event in the study area, forming the probability distribution of the event occurrence. Thereby, the probability distribution of the edge event occurrence in the SFEP is obtained. The event relationships in SFN are expressed as relationship set and then the relationships are superposed, and the analytic formula of probability distribution of target event occurrence is obtained. The research shows that the results are in good agreement with the original accurate results with much less fault data. This method can be used to study the target event occurrence characteristics of SFEP under the condition of less fault data.
Key words: safety system engineering    space fault network    system fault evolution process    less fault data    information diffusion    target event occurrence probability

1 SFEP和SFN

SFEP描述了系统发生故障的过程。该过程中蕴含了众多事件，也蕴含了这些事件之间的关系。SFEP是在系统层面对系统故障过程进行描述，在系统层面抽象各种类型系统，并予以分析。最终达到对故障演化过程描述、分析、预测和干预的目的。SFEP就研究对象而言大体分为两个方面：一是人工系统；二是自然系统。虽然人工系统和自然系统的目的、发生、发展、结果、预测和控制措施不同，但在系统层面上都可表示为众多事件相互作用的过程。

2 边缘事件发生概率分布确定

 $P({x_1},{x_2}, \cdots ,{x_n}) = \left\{ {\begin{array}{*{20}{l}} {1(100{\text{%}} ),\quad{\text{发生}}}\\ {0,\quad{\text{不发生}}} \end{array}} \right.$ (1)

 $\begin{array}{c} {P_{mj}}({x_1},{x_2}, \cdots ,{x_n})=\\ \exp \Bigg( - \dfrac{{{{\Bigg(\displaystyle\sum\limits_{i = 1}^n {{{({x_i} - {x_{i0}})}^2}} \Bigg)}^{1/2}}}}{{2\tau }}\Bigg),\quad{x_1},{x_2}, \cdots ,{x_n} \in D \end{array}$ (2)

 $\begin{array}{c} {P_M}({x_1},{x_2}, \cdots ,{x_n}) = \\ {\rm{max}}({P_{m_j}}({x_1}, {x_2}, \cdots ,{x_n})) = \\ {\rm{max}}\Bigg(\exp \Bigg( - \dfrac{{{{\Bigg(\displaystyle\sum\limits_{i = 1}^n {{{({x_i} - {x_{i0}})}^2}} \Bigg)}^{1/2}}}}{{2\tau }}\Bigg)\Bigg),\\ {m_j} \in M; j = 1,2, \cdots ;J;{x_1},{x_2}, \cdots ,{x_n} \in D \\ \end{array}$ (3)

3 最终事件发生概率分布确定

 $\begin{array}{l} S = \left\{ {{\rm{CE}} \to {\rm{RE}}|{p_{{\rm{RE}}}} = } \right.\coprod ({q_{{\rm{CE}} \to {\rm{RE}}}}{p_{{\rm{CE}}}})\;{\rm{or}}\\ {{p}_{{\rm RE}}}=\Pi ({{q}_{{\rm CE}\to {\rm RE}}}{{p}_{{\rm CE}}})\;{\rm{and}};\left. {{p}_{{\rm RE}}}=({{q}_{{\rm CE}\to {\rm RE}}}{{p}_{{\rm CE }}})\;{\rm{trans}} \right\} \end{array}$ (4)

S相当于关系字典，记录了原因事件和结果事件之间的逻辑关系。将最终事件作为起点寻找其原因事件，再将该原因事件作为结果事件继续寻找原因事件，直到原因事件为边缘事件时停止。将这些关系从S中提出进行叠加，得到由边缘事件发生概率分布表示的最终事件发生概率分布解析式。

4 实例分析

 $\begin{array}{c} {p_{\rm{U}}} = {q_2}(1 - (1 - {q_4}{q_6}(1 - (1 - {q_8}{q_{13}}(1 - (1 - {q_{20}}{p_{\rm{A}}})(1 - {q_{28}}{q_{21}}(1 - (1 - {q_{24}}{p_{\rm{A}}})(1 - {q_{25}}{p_{\rm{B}}})))){q_{14}}(1 - \\ (1 - {q_{19}}{q_{21}}(1 - (1 - {q_{24}}{p_{\rm{A}}})(1 - {q_{25}}{p_{\rm{B}}})))(1 - {q_{18}}{q_{23}}{p_{\rm{F}}}{q_{22}}(1 - (1 - {q_{26}}{p_{\rm{B}}})(1 - {q_{27}}{p_{\rm{C}}})))(1 - \\ {q_{17}}{p_{\rm{K}}})))(1 - {q_9}{q_{15}}(1 - (1 - {q_{19}}{q_{21}}(1 - (1 - {q_{24}}{p_{\rm{A}}})(1 - {q_{25}}{p_{\rm{B}}})))(1 - {q_{18}}{q_{23}}{p_{\rm{F}}}{q_{22}}(1 - (1 - {q_{26}}{p_{\rm{B}}})(1 - \\ {q_{27}}{p_{\rm{C}}})))(1 - {q_{17}}{p_{\rm{K}}})))))(1 - {q_5}{q_{10}}{q_{15}}(1 - (1 - {q_{19}}{q_{21}}(1 - (1 - {q_{24}}{p_{\rm{A}}})(1 - {q_{25}}{p_{\rm{B}}})))(1 - \\ {q_{18}}{q_{23}}{p_{\rm{F}}}{q_{22}}(1 - (1 - {q_{26}}{p_{\rm{B}}})(1 - {q_{27}}{p_{\rm{C}}})))(1 - {q_{17}}{p_{\rm{K}}})))){q_3}(1 - (1 - {q_{11}}{q_{15}}(1 - (1 - {q_{19}}{q_{21}}(1 - \\ (1 - {q_{24}}{p_{\rm{A}}})(1 - {q_{25}}{p_{\rm{B}}})))(1 - {q_{18}}{q_{23}}{p_{\rm{F}}}{q_{22}}(1 - (1 - {q_{26}}{p_{\rm{B}}})(1 - {q_{27}}{p_{\rm{C}}})))(1 - {q_{17}}{p_{\rm{K}}})))(1 - {q_{12}}{q_{16}}{p_{\rm{K}}})) \end{array}$ (5)
 $\begin{array}{l} {p_{\rm{V}}} = {q_1}{q_7}{q_{13}}(1 - (1 - {q_{20}}{p_{\rm{A}}})(1 - {q_{28}}{q_{21}}(1 - (1 - {q_{24}}{p_{\rm{A}}})(1 - {q_{25}}{p_{\rm{B}}}))))q14(1 - (1 - {q_{19}}{q_{21}}(1 - \\ (1 - {q_{24}}{p_{\rm{A}}})(1 - {q_{25}}{p_{\rm{B}}})))(1 - {q_{18}}{q_{23}}{p_{\rm{F}}}{q_{22}}(1 - (1 - {q_{26}}{p_{\rm{B}}})(1 - {q_{27}}{p_{\rm{C}}})))(1 - {q_{17}}{p_{\rm{K}}})) \end{array}$ (6)