﻿ 空间故障网络的柔性逻辑描述
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 智能系统学报  2021, Vol. 16 Issue (3): 552-559  DOI: 10.11992/tis.202003029 0

### 引用本文

CUI Tiejun, LI Shasha. Flexible logic description of space fault network[J]. CAAI Transactions on Intelligent Systems, 2021, 16(3): 552-559. DOI: 10.11992/tis.202003029.

### 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

Flexible logic description of space fault network
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;
3. School of Business Administration, Liaoning Technical University, Huludao 125105, China
Abstract: Flexible logic is proposed in this paper to describe and transform the space fault network (SFN) and to describe the system fault evolution process (SFEP) with information uncertainty and evolution characteristics to overcome the factors, data, and evolution uncertainty. The present report discusses the problems of SFN and the possibility of using flexible logic to solve these problems. The use of flexible logic to describe SFN should be based on the basic unit, event occurrence relationship, and SFN structure. Flexible logical representations of the and, or and transfer relationship in SFN are given. Further, under the condition of flexible logic, the relationship set of SFN is given, and the flexible logic representation of the target event state of SFN is obtained. The results show the flexible logical relationship and uncertainty among events, factors, and evolution processes in SFEP and provide a new methodology and theoretical basis for the intelligent research of SFEP.
Key words: intelligent science    safety science    safety system engineering    space fault network    flexible logic    system fault evolution process    factor influence    uncertainty

SFEP[1-7]存在于各行各业，无论是自然系统灾害还是人工系统故障都是系统功能性下降或故障性升高的结果。SFEP中蕴含了一系列事件，受到多种因素影响，事件间也存在不同的逻辑关系，因此SFEP的事先分析极其困难。因为SFEP中各种事件和它们之间的逻辑关系，加之不同因素的影响，使得SFEP存在多样性。事先分析只能得到各种SFEP的可能性，只有发生后才能确定是哪一种SFEP。那么如何智能化地事先分析SFEP成为关键问题。

1 空间故障网络

SFN是空间故障树理论[1-7,35-46](space fault tree, SFT)的第三研究阶段。SFT包括SFT基础理论[35-39]、智能化SFT[40-46]、SFN[1-7]、系统运动空间与系统映射论。SFN用于描述SFEP。SFEP代表了系统性能变化过程中各种事件、各种逻辑关系和各种因素的联系。SFN通过网络拓扑形式表示SFEP。

SFN由点和线组成。点表示SFEP的事件，线表示SFEP的演化途径。在SFEP中多个原因事件可能存在不同逻辑关系导致结果事件，最典型的是同时发生的与关系和之一发生的或关系。在理论上使用SFN描述SFEP是适合的，但在实际过程中存在问题。其中最重要的就是不确定性和演化特征。

2 柔性逻辑

3 柔性逻辑描述

SFN描述SFEP，SFEP中的事件、传递概率和事件发生关系分别对应SFN中的节点、连接和因果逻辑。但为了说明方便，在论述SFN时也使用事件、传递概率和事件发生关系。SFN的柔性逻辑描述要从几个方面来讨论，包括：SFN最基本单元的柔性逻辑描述、事件发生关系的柔性逻辑描述、SFN结构的柔性逻辑描述。

3.1 SFN最基本单元的柔性逻辑描述

SFN的基本单元：原因事件→传递概率→结果事件，将结果事件作为下一个单元的原因事件继续通过传递概率指向下一个结果事件，如图1(a)所示。整个过程起始于边缘事件(导致SFEP的最基本事件)，终止于最终事件(SFEP结束的事件或过程中关心的事件)。将基本单元进一步分解，原因事件与传递概率组成SFN柔性逻辑基本单元。所得结果作为原因事件与下一个传递概率形成柔性逻辑基本单元，如图1(b)所示。因此SFN的基本单元从原来的三元组变为两元组。该变化原因在于柔性逻辑的逻辑运算完整簇形式[29-30]。柔性逻辑运算完整簇被规定为一个二元算子，两个输入一个输出，是为了简化逻辑表达，也因为任何逻辑运算都可拆分为二元运算。

 Download: 图 1 SFN的基本单元 Fig. 1 Basic unit of SFN

 \begin{aligned} &{T_{et_p}}({e_p},t{p_q},k,h,\beta ) = \\ &{(\max (0,2\beta {e_p^{nm}} + 2(1 - \beta )t{p_q^{nm}} - 1))^{\frac{1}{{nm}}}} \end{aligned} (1)

3.2 事件发生关系的柔性逻辑描述

 Download: 图 2 柔性逻辑表示的SFN事件发生关系 Fig. 2 SFN event occurrence relationship represented by flexible logic

 \left\{ {\begin{aligned} {T_{et_{p} + 1}}= T(T( \cdots (T({T_{et_{p_1}}},{T_{et_{p_2}}}),{T_{et_{p_3}}}) \cdots ),{T_{et_{p_A}}})\\ \quad T({T_{et_{p_1}}},{T_{et_{p_2}}}) = T({T_{et_{p_1}}},{T_{et_{p_2}}},k,h,\beta ) =\quad\;\;\\ {(\max (0,2\beta {T_{et_{p_1}}}^{nm} + 2(1 - \beta ){T_{et_{p_2}}}^{nm} - 1))^{\frac{1}{{nm}}}}\;\;\; \end{aligned}} \right. (2)

 \left\{{\begin{aligned} &{S_{et_{p} + 1}} = S(S( \cdots (S({T_{et_{p_1}}},{T_{et{p_2}}}),{T_{et_{p_3}}}) \cdots ),{T_{et_{p_A}}})\\ &S({T_{et_{p_1}}},{T_{et_{p_2}}}) = S({T_{et_{p_1}}},{T_{et_{p_2}}},k,h,\beta ) =\\ & \quad\quad(1 - (\max (0,2\beta {(1 - {T_{et_{p_1}}^n})^m} + \quad\quad \\ &\quad\quad2(1 - \beta ){(1 - {T_{et_{p_2}}^n})^m} - 1))^{\frac{1}{m}})^{\frac{1}{n}} \quad \quad\\ \end{aligned}} \right. (3)

 \left\{ {\begin{aligned} &{{T_{et_{p} + 1}} = {T_{et_{p_1}}}} \\ &{T_{et_p}}({e_p},t_{p_q},k,h,\beta ) = \\ &\quad{(\max (0,2{\beta_{{e_p}}^{nm}} + 2(1 - \beta )t{p_q^{nm}} - 1))}^{\frac{1}{nm}} \end{aligned}} \right. (4)
3.3 SFN结构的柔性逻辑描述

 $\begin{array}{l} {\rm{RS}} = \{ {e_{{\rm{CE}}}} \to {e_{{\rm{RE}}}}|{e_{{\rm{RE}}}} = {S_{et_{p} + 1}}{\rm{,or}};{e_{{\rm{RE}}}} = {T_{et_{p} + 1}}{\rm{,and;}} \\ {e_{{\rm{RE}}}} = {T_{et_{p_1}}}{\rm{,trans;}}{e_{{\rm{CE}}}}{\rm{, }}{e_{{\rm{RE}}}} \in {\rm{\{ 0,1\} }}\} \\ \end{array}$ (5)

4 SFN的柔性逻辑描述举例

 Download: 图 3 空间故障网络 Fig. 3 Space fault network(SFN)

 $\begin{split} {e_v} =& {T_{et_{p}}}({T_{et_{p}}}({T_{et_{p}}}({T_{et_{p}}}({S_{et_{p}}}({T_{et_{p}}}({e_{\rm{A}}},{q_{20}}),\\ &{T_{et_{p}}}({T_{et_{p}}}({S_{et_{p}}}({T_{et_{p}}}({e_{\rm{A}}},{q_{24}}),{T_{et_{p}}}({e_{\rm{B}}},{q_{25}})),{q_{21}}),{q_{28}})),{q_{13}}),\\ &{T_{et_{p}}}({S_{et_{p}}}({S_{et_{p}}}({T_{et_{p}}}({T_{et_{p}}}({S_{et_{p}}}({T_{et_{p}}}({e_{\rm{A}}},{q_{24}}),\\ &{T_{et_{p}}}({e_{\rm{B}}},{q_{25}})),{q_{21}}),{q_{19}}),{T_{et_{p}}}({T_{et_{p}}}({T_{et_{p}}}({S_{et_{p}}}({T_{et_{p}}}({e_{\rm{B}}},{q_{26}}),\\ &{T_{et_{p}}}({e_{\rm{C}}},{q_{27}})),{q_{22}}),{T_{et_{p}}}({e_{\rm{F}}},{q_{23}})),{q_{18}})),\\ &{T_{et_{p}}}({e_{\rm{K}}},{q_{17}})),{q_{14}})),{q_7}),{q_1}) \end{split}$ (6)

5 结束语

1)论述了使用SFN描述和研究SFEP存在的问题。由于SFEP自身特点，对其进行描述和研究存在的问题主要包括因素的不确定性、数据的不确定性和SFEP本身的逻辑关系，及它们出现的原因。

2)论述了柔性逻辑情况。给出了泛逻辑学的基本目的和基本形式，论述了使用柔性逻辑描述和研究SFEP的优势，从而对SFN进行了柔性逻辑表示。

3)论述了SFN的柔性逻辑具体描述方法。根据SFEP和SFN特征，给出了柔性逻辑描述方法，包括SFN最基本单元描述、事件发生关系描述、SFN结构描述。研究了SFN中与、或和传递关系转化为柔性逻辑关系的方式。将原因事件和传递概率设置为SFN柔性逻辑基本单元，其结果作为本次结果事件状态和下次原因事件状态。再结合SFN柔性逻辑关系组，即可得到SFN最终事件状态。柔性逻辑的20种形式都可进行类似转化，在丰富SFN事件发生逻辑关系的同时，也使SFN具备了使用泛逻辑方法论的基础。

4)使用实例SFN得到了柔性逻辑最终事件状态表达式。这种表达式可以表达SFEP中各事件、各因素和演化过程之间的柔性逻辑关系，并表示它们的不确定性。

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