﻿ 基于UR-MTPGERT网络模型的复杂装备风险传导分析<sup>*</sup>
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Complex equipment risk conduction analysis based on UR-MTPGERT model
SUN Yun, WANG Ying, LI Chao
Equipment Management and UAV Engineering College, Air Force Engineering University, Xi'an 710051, China
Received: 2017-12-25; Accepted: 2018-03-16; Published online: 2018-03-22 17:36
Foundation item: National Natural Science Foundation of China (71601183)
Corresponding author. WANG Ying, E-mail: yingwangkgd@163.com
Abstract: Aimed at the problem of unclear description of the conduction relationship of complex equipment risks, a risk conduction uncertain random multi-transfer parameter graph evaluation and review technique (UR-MTPGERT) model is constructed. First, based on the opportunity theory, the moment function of uncertain random variables is defined, and then a multi-transter parameter UR-MTPGERT network is constructed. Second, to describe the micro-risk information of complex equipment systems, analytic parameters are introduced in the model including the degree of risk, the importance of risk primitives and the degree of relevance of risk paths. Then, when solving the moment function, the Delphi method is used to process the expert empirical data to obtain the empirical uncertainty distribution, and the maximum entropy model is used to process the random data. The probability density function is obtained. The matrix analysis technique is introduced to solve the problem of difficult network topology analysis. On this basis, the network parameters are calculated. Finally, the safety analysis of a certain type of aircraft is carried out. The results show that the model can clearly reflect the relationship between risk elements and provide reference for the risk analysis, prediction and safety control of complex equipment.
Keywords: complex equipment risk     risk conduction     uncertain random multi-transfer parameter graph evaluation and review technique (UR-MTPGERT)     opportunity theory     matrix analysis

1 风险传导UR-MTPGERT网络模型

 图 1 装备服役风险传导网络模型 Fig. 1 Equipment service risk conduction network model
1.1 构建网络模型

 图 2 风险传导UR-MTPGERT基本单元构成示意图 Fig. 2 Schematic of basic unit structure of risk conduction UR-MTPGERT

1.2 构造矩母函数

 (1)

 (2)

1) {Γ}=1；

2) {Λ}+{ΛC}=1；

3)

γ的不确定分布。

ξ的机会分布。

 (3)

 (4)

 (5)
1.3 模型扩展分析

 (6)

2 风险传导UR-MTPGERT网络模型求解 2.1 风险传导强度计算

 (7)

 (8)

2.2 风险度不确定变量矩母函数求解

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

 (15)

 (16)

 (17)

 (18)

 (19)

 (20)

2.3 极大熵法估计风险度概率密度

 (21)

 (22)

 (23)

2.4 GERT网络的矩阵化计算

n阶方程组的向量表示形式为

 (24)

 (25)

3 案例分析

 时段 风险度h1/10-6 1 0.42 2 0.58 3 0.57 4 0.22 5 0.80 6 0.35 7 0.87 8 0.64 9 0.56 10 0.59 11 0.38 12 0.55 13 0.63 14 0.65 15 0.69 16 0.80 17 0.57 18 0.39 19 0.89 20 0.61 21 0.49 22 0.61 23 0.31 24 0.58

 图 3 各算法优化曲线比较 Fig. 3 Comparison of optimization curves of various algorithms

 图 4 某型飞机风险传导UR-MTPGERT网络示意图 Fig. 4 Schematic of risk conduction UR-MTPGERT network of a certain type of aircraft

 代号 子系统 1 环控子系统 2 操纵子系统 3 结构子系统 4 液压子系统 5 供电子系统 6 导航子系统 7 推进子系统

E(HE)可以通过对ME(θ)求导的公式求得，E(hi)可以通过注释3、注释4求得。本文以hi=hi1+hi2+hi3+hi4为例，求解说明该方法的有效性。根据上文求得的不确定随机变量的矩母函数和风险传导强度，可以对该风险传导模型分析如下：

1) 根据定义10，可以得到该型战机的总风险度为HE=3.562×10-8，持续对该型战机的各种风险状况进行评估，可以得到复杂装备总风险度的趋势图，在趋势图中通过设定临界风险点，可对任务的风险度进行预警。

2) 假设Mui(θ)=0，i=2, 3, 4，根据定义11可以解得，I1=0.009, I2=0.313，I3=0.121，I4=0.45，I5=0.482，I6=0.015, I7=0.561。I5>I7>I4>I2>I3>I6>I1表明该型飞机中，供电子系统对飞机安全性的影响最大，推进子系统对飞机安全性的影响较大，液压子系统和操纵子系统对飞机安全性的影响次之，结构子系统、导航子系统和环控系统对飞机安全性的影响相对较小。

3) 由于该实例风险路径比较复杂，本文以路径1(1→4→7→8)和路径2(1→2→5→8)为例，对风险路径的关联度进行分析。路径1和路径2的风险向量假设为{0, 1, 0, 1, 0}、{0, 0, 1, 1, 0}。根据15时段训练数据，以及定义12可得γ1=0.759，γ2=0.549。γ1>γ2说明风险路径1发生的可能性更大，需要加强液压子系统的检查维修，防止飞机降落过程中出现意外情况；同时需要加强推进子系统的检修，翻看检修记录，检查是否达到大修时限。

4 结论

1) 针对复杂装备中存在的非决定现象，基于机会理论，提出不确定随机变量的矩母函数，搭建了多风险因素风险传导分析框架，构建了UR-MTPGERT网络。

2) 引入风险元重要度、风险路径关联度等参数，从微观角度分析风险元对复杂装备整体风险度的影响，有利于找到复杂装备的脆弱点，对下一步安全控制提供指导。

3) 运用德尔菲法求解经验不确定分布；运用极大熵模型求解任意随机变量的概率分布；引入矩阵分析技术，解决了模型传递参数求解困难的问题，为下一步利用计算机编程处理复杂装备风险问题做好铺垫。

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#### 文章信息

SUN Yun, WANG Ying, LI Chao

Complex equipment risk conduction analysis based on UR-MTPGERT model

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(8): 1587-1595
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0800