基于T-S模糊故障树和贝叶斯网络的隧道坍塌易发性评价

doi:10.16183/j.cnki.jsjtu.2020.99.011

摘要/Abstract

摘要：

坍塌是钻爆法隧道施工过程中常见的灾害事故之一.为了有效预防坍塌事故,为隧道施工安全风险分析和管理提供决策依据,将T-S模糊故障树和贝叶斯网络进行互补融合,提出了一种基于两者的钻爆法施工隧道坍塌可能性评价方法.根据T-S模糊故障树向贝叶斯网络转化的方法来确定贝叶斯网络模型和条件概率表;利用模糊数和模糊子集分别描述节点的故障状态和故障概率;运用贝叶斯网络双向推理算法进行计算.该方法可以利用根节点的故障概率模糊子集和施工中实际故障状态两种不同的正向推理方式计算隧道坍塌可能性,并且可以依据根节点的重要度分析结果排查故障,同时可以通过反向推理计算根节点的后验概率诊断故障.两个工程实例的应用结果表明,该方法能够科学、合理地评价隧道坍塌的可能性并确定关键致险因子,可作为隧道施工安全保障和管理的决策工具.

关键词: 钻爆法施工隧道, 坍塌可能性, T-S模糊故障树, 贝叶斯网络, 模糊数, 模糊子集, 重要度

Abstract:

Collapse is one of the common disasters in the process of drilling and blasting tunnel construction. In order to effectively prevent the collapse accident and provide decision-making basis for safety risk analysis and management of tunnel construction, the T-S fuzzy fault tree and Bayesian network were combined, and an evaluation method based on both of them was proposed to calculate tunnel collapse possibility. According to the transformation of T-S fuzzy fault tree to Bayesian network, the Bayesian network model and conditional probability table were determined. In addition, fuzzy number and fuzzy subset were used to describe the fault state and probability of nodes respectively, and the bidirectional reasoning algorithm of Bayesian network was used to calculate. This method can use two different forward inferences to calculate the possibility of tunnel collapse, including the fuzzy subset of root node fault probability and the actual fault state in construction. At the same time, it can check the fault according to the result of importance analysis of root nodes, and can calculate the posterior probability of fault diagnosis of root nodes by back inference. Finally, the application of two engineering examples shows that the method can scientifically evaluate the possibility of tunnel collapse and determine key risk factors. This method can be used as a decision-making tool for tunnel construction safety assurance and management.

Key words: construction tunnel by drilling and blasting, collapse possibility, T-S fuzzy fault tree, Bayesian network, fuzzy number, fuzzy subset, importance

中图分类号:

U458

陈舞, 王浩, 张国华, 王成汤, 钟国强. 基于T-S模糊故障树和贝叶斯网络的隧道坍塌易发性评价[J]. 上海交通大学学报, 2020, 54(8): 820-830.

CHEN Wu, WANG Hao, ZHANG Guohua, WANG Chengtang, ZHONG Guoqiang. Evaluation of Tunnel Collapse Susceptibility Based on T-S Fuzzy Fault Tree and Bayesian Network[J]. Journal of Shanghai Jiaotong University, 2020, 54(8): 820-830.

图/表 17

图1

图2

图3

图4

图5

图6

图7

图8

图9

表1

表2

表3

表4

表5

根节点模糊重要度

根节点	模糊重要度		根节点	模糊重要度
根节点	$I 0.5 F u$ (x_i)	$I 1 F u$ (x_i)	根节点	$I 0.5 F u$ (x_i)	$I 1 F u$ (x_i)
x₁	—	0.12994	x₁₄	—	0.10102
x₂	—	0.14835	x₁₅	—	0.13685
x₃	—	0.13271	x₁₆	—	0.13995
x₄	—	0.13061	x₁₇	—	0.06813
x₅	—	0.13125	x₁₈	—	0.13049
x₆	—	0.13639	x₁₉	—	0.12948
x₇	—	0.13728	x₂₀	0.00192	0.09198
x₈	—	0.13015	x₂₁	0.00309	0.11141
x₉	—	0.12881	x₂₂	0.00183	0.07501
x₁₀	—	0.12881	x₂₃	0.00149	0.06457
x₁₁	—	0.12276	x₂₄	—	0.34127
x₁₂	—	0.13837	x₂₅	0.00886	0.07658
x₁₃	—	0.13401	x₂₆	—	0.08089

表5

图10

表6

根节点当前故障状态的隶属度

根节点	当前故障状态	隶属度
根节点	当前故障状态	$μ x ~ i a i$ (x'_i)=0	$μ x ~ i a i$ (x'_i)=0.5	$μ x ~ i a i$ (x'_i)=1
x₁₁	x₁₁=0.15	5/6	1/6	0
x₁₂	x₁₂=0.13	9/10	1/10	0
x₁₅	x₁₅=0.20	2/3	1/3	0
x₁₉	x₁₉=0.20	2/3	1/3	0
x₂₀	x₂₀=0.20	2/3	1/3	0
x₂₂	x₂₂=0.50	0	1	0
x₂₃	x₂₃=0.50	0	1	0
x₂₄	x₂₄=0.32	4/15	11/15	0
其他	0	1	0	0

表6

表7

根节点状态重要度

根节点	状态重要度
根节点	$I 0.5 D e$ (x'_i)	$I 1 D e$ (x'_i)
x₁₁	0	0.00767
x₁₂	0	0.00644
x₁₅	0	0.02559
x₁₉	0	0.02113
x₂₀	0	0.02465
x₂₂	0	0.27841
x₂₃	0	0.27841
x₂₄	0	0.25554
其他	0	0

表7

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中间节点	中间事件名称	中间节点	中间事件名称
y₁	支护措施不当	y₁₀	不良地形地貌
y₂	施工人员操作不当	y₁₁	工程设计不合理
y₃	初支背后空洞	y₁₂	施工组织管理不当
y₄	开挖方法选择不合理	y₁₃	施工质量不满足要求
y₅	衬砌支护参数和方式不合理	y₁₄	不利水文地质
y₆	施工作业不合理	y₁₅	不良工程地质
y₇	支护作用减弱	y₁₆	人为因素不利影响
y₈	辅助措施不到位	y₁₇	自然条件差
y₉	不良地质构造	—	—

等级	可能性	概率
I	频繁的	[0.1,1]
II	可能的	[0.01,0.1)
III	偶尔的	[0.001,0.01)
IV	罕见的	[0.0001,0.001)
V	不可能的	[0,0.0001)