# A Risk Analysis Method of Cable Fire in Utility Tunnel Based on a Bayesian Network

Authors: Hongfu Mi; Xiaomei Zhang; Wenhe Wang; Wenjing Yang; Xinsheng Jiang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Recently, the fire safety of tunnels is attracting more and more attention with the utility tunnel springing up in major cities of China. Faced with challenges from fires in utility tunnels, fire risk analysis is critical and essential to discover the weaknesses of risk. It serves as the foundation of regulatory decision-making on whether to take appropriate measures to reduce risk. This study combines a Bayesian network (BN) model and a bow-tie (BT) method to propose a fire risk analysis method to predict the probability of cable ﬁre in utility tunnels. First, cable ﬁre risk factors and five potential accident scenarios are analyzed by BT method; Second, to avoid the influence of uncertain factors in BT, the optimized BN model is applied to the prediction analysis of cable fire probability, which can consider the actual development of cable fire in utility tunnel. This novel approach can better reveal the causal relationship between events and determine the critical basic events by sensitivity analysis. Finally, the probability of cable fire ignition occurrence and scenarios probabilities are periodically updated using the cumulative information collected during a time interval. The results show that this approach can assist in dealing with the uncertainty problem in utility tunnel and the optimized model is more in line with the reality by comparing the results before model optimization.


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## Body

## 1. Introduction

In the past two centuries, some European cities have adopted underground utility tunnels to avoid repeated excavation of urban roads and congestion of underground pipelines [1, 2]. In recent years, the underground utility tunnel has become a critical infrastructure and lifeline to ensure urban operation with the acceleration of urbanization in China. By 2016, more than 2000 kilometers of utility tunnels had been built in China [3]. However, the utility tunnel brings convenience as well as disaster. For example, on 12 December 2005, a severe fire accident happened in Liaoyuan central hospital. The cause of the accident was that the short circuit of the cable ignited combustible materials, causing 37 deaths, 46 severe injuries, and 49 minor injuries. The burned area was 5714 square meters, and the direct property loss was more than 8.21 million yuan. Meanwhile, as the utility tunnel covers a variety of high-risk pipelines (such as gas, high-voltage cables, sewage, heat, etc.), potential hazards should not be ignored in the utility tunnel, including gas leaks and expansions, water pipes leak and fracture, and cable fires. Among them, cable fire is the most common accident in utility tunnels, and the consequences are extremely serious [4]. However, up to now, there are few fire risk analysis methods suitable for the utility tunnel. Therefore, it is indispensable to explore a method or model to comprehensively analyze the causes and consequences of cable fire accidents and predict the probability of cable fire.Fire risk analysis is a structured method of estimating magnitudes probabilities of the identified fire risk. It provides information through quantitative or qualitative analysis results to decide whether to take steps to reduce the risk [5, 6]. There are mainly four types of fire risk analysis methods: checklist, description, index, and probability method [7]. With the improvement of performance-based fire protection design, some fire risk analysis models and corresponding software have emerged, such as Fire Risk Evaluation and Cost Assessment Model (FiRECAMTM) [8, 9], Fire Evaluation and Risk Assessment system (FiERA system) [10], Centre for Environment Safety and Risk Engineering (CESARE-RISK) [11, 12], and Computation of Risk Indices by Simulation Procedures (Crisp II) [13]. However, these models should depend on strict constraints, such as a large number of input data, specific fire scenarios, and a large amount of calculations [14]. Consequently, researchers are concentrating on developing flexible fire risk analysis tools based on systematic safety theory. For example, Li et al. proposed a fire risk analysis method for high-rise buildings based on the grey risk degree method, analytic hierarchy process (AHP), and fuzzy evaluation method [15]. Hosseini et al. use fault tree (FT) and event tree (ET) to show the path of fire events in processing plants and propose a comprehensive fire risk assessment method for processing plants based on fuzzy logic [16]. Wei et al. use fuzzy mathematics and support vector machine (SVM) algorithm to establish a flexible and operable fire risk evaluation index system [17]. But, the above studies have some weaknesses. For example, these models cannot handle the uncertainty of event relationships well.In order to overcome this limitation, a fire risk analysis method based on BN is proposed, which can well solve the uncertain problems of structure, knowledge, and parameters [18]. Wu [19] proposed a source term estimation (STE) model combining Bayesian inference and slice sampling method to estimate natural gas leakage source parameters in underground utility tunnels. Jafari [20] used computational fluid dynamics (CFD) and BN approaches for dynamic risk assessment. Bayesian inference method shows great application potential to accurately qualify the source term's uncertainties and estimate source term parameters. However, due to the complexity of the BN structure, it is an arduous task to construct a Bayesian model directly [21]. Therefore, some researchers combine the Bayesian network with fault tree [22], event tree [23], and bow-tie analysis [24, 25]. BN is a probabilistic reasoning method under uncertainty, which can relax the limitations of traditional methods. However, few scholars presently consider the cable fire risk of utility tunnels based on BN analysis.In this paper, a fire risk analysis method is proposed for cable compartments in utility tunnels based on BN, which can clarify the evolution process of cable fire ignition accident from cause to consequence and provide strong support for the safety management of utility tunnels. Other parts of this study are organized as follows: a brief description of risk analysis, including BT and BN, is presented in Section2. The cable fire risk analysis framework proposed in this study is shown in Section 3. Section 4 introduces the evolution process of the cable fire ignition accident by the BT method. Section 5 gives the construction and optimization of the BN model and BN’s application in cable fire risk analysis. The conclusion of this paper is shown in Section 6.


## 2. Risk Analysis Techniques

### 2.1. Bow-Tie Model

BT is an excellent graphic method to describe a complete accident scenario, starting from the cause of the accident and ending with the consequence of the accident [26, 27]. While centered on a top event, BT is composed of an FT on the left side, identifying the risk events causing the top event. An ET on the right side shows the potential consequences of the top event based on the failure or success of safety barriers [18]. A generic BT model is shown in Figure 1, where TE, IE, and BE represent the top event, intermediate events, and basic events, respectively. In addition, SB and C represent safety barriers and accident consequences.Figure 1
Generic BT model.The establishment of the BT model helps to understand which combination of basic events and intermediate events are likely to lead to the occurrence of the top event and which failure of different safety barriers will cause specific accident consequences.


### 2.2. Bayesian Network

BN is a graphic technology, which is widely used in risk and safety analysis based on probability and uncertain knowledge [28]. In the BN model structure, nodes represent variables and arcs represent causality among nodes. Nodes and arcs form a directed acyclic graph. Each node in BN has its corresponding conditional probability table (CPT) to show the conditional probability dependence between the variable and the parent node.Based on the chain rule and conditional independence [18], BN is used to describe the joint probability distribution PU of variable U=A1,…,An as(1)PU=∏i=1nPAi|PaAi,where PaAi is the parent set of Ai.


### 2.3. Mapping Algorithm

Due to the limitation of BT model, it cannot solve the uncertainty problems in the cable fire [29]. Therefore, BT can be mapped to BN to relax the limitation of BT and improve it. The mapping process of the BT model to the BN model is mainly divided into two steps. ① The FT analysis part: in the graphical mapping, the basic events, intermediate events, and top event of FT model are represented as root nodes, intermediate nodes, and leaf nodes in BN, respectively, as shown in Figure 2. In the numerical transformation, the occurrence probability of the basic event is regarded as the prior probability of the corresponding root node. ② The ET analysis part: the safety barriers and consequences in the ET model are transformed into corresponding safety nodes and consequence nodes, respectively. In addition, when the probabilities of the consequence nodes are affected by the failure or success of the safety node, the safety node and the consequence node must be connected by an arc.Figure 2
The process of FT mapping to BN.A CPT is assigned to indicate the relationship between parent and child nodes. CPT in BN is determined by the logic gate in fault tree and empirical judgment, as shown in Table1. The logic gate in the fault tree represents the deterministic relationship between events. For example, the AND gate represents that when events X1 and X2 occur at the same time, the top event T occurs. But in fact, even if events X1 and X2 occur successfully at the same time, T may not occur. This scenario can be modeled by the modified CPT, as shown in Table 2. The amending value in CPT can be determined according to historical data or expert feedback.Table 1
CPT corresponding to AND gate in BT.
X1SuccessFailureX2SuccessFailureSuccessFailureTSuccess1000Failure0111Table 2
Amending CPT corresponding to AND gate in BT.
X1SuccessFailureX2SuccessFailureSuccessFailureTSuccess0.980.080.090.01Failure0.020.920.910.99


### 2.4. Sensitivity Analysis

In the BN model, the slight change of the prior probability of each basic event (root node) may lead to the change of the fire probability of the cable in the utility tunnel. In order to quantify the degree of change in the BN model result caused by the basic event probability and identify in the critical basic events nodes of the BN model, the sensitivity analysis method is adopted to find out these critical basic events nodes [30]. In general, sensitivity analysis methods include Birnbaum importance measure (BIM), ratio of variation (RoV), and risk reduction worth (RRW) [31]. The RoV method based on prior and posterior probabilities is better for determining the root node sensitivity. The RoV method could be calculated as follows:(2)RoVXi=ϕXi−φXiφXi.Herein,φXi represents the prior probability of the Xi node and ϕXi represents the posterior probability of the Xi node.


### 2.5. Bayesian Network Analysis

Probability updating is an essential application of BN. Probabilistic updating is a diagnostic reasoning function based on BN. When a new observation or evidenceE appears, the BN uses the Bayesian theory to update the probability [32, 33].(3)PU|E=PU,EPE=PU,E∑UPU,E.Probability adaptation, also known as sequence learning, is another important application of BN. The probability adaptation of BN is to update the probability based on the collected new information accumulated over time as a priori probability. The new information represents the frequency of some basic events occurring within a certain time interval (such as one year) as evidence. The probability P updated by the new information can be obtained by (4) [30].(4)P=a+sn+s.where s represents the number of critical basic events and a and n represent the experience value and total experience value of critical basic events, respectively.


## 2.1. Bow-Tie Model

BT is an excellent graphic method to describe a complete accident scenario, starting from the cause of the accident and ending with the consequence of the accident [26, 27]. While centered on a top event, BT is composed of an FT on the left side, identifying the risk events causing the top event. An ET on the right side shows the potential consequences of the top event based on the failure or success of safety barriers [18]. A generic BT model is shown in Figure 1, where TE, IE, and BE represent the top event, intermediate events, and basic events, respectively. In addition, SB and C represent safety barriers and accident consequences.Figure 1
Generic BT model.The establishment of the BT model helps to understand which combination of basic events and intermediate events are likely to lead to the occurrence of the top event and which failure of different safety barriers will cause specific accident consequences.


## 2.2. Bayesian Network

BN is a graphic technology, which is widely used in risk and safety analysis based on probability and uncertain knowledge [28]. In the BN model structure, nodes represent variables and arcs represent causality among nodes. Nodes and arcs form a directed acyclic graph. Each node in BN has its corresponding conditional probability table (CPT) to show the conditional probability dependence between the variable and the parent node.Based on the chain rule and conditional independence [18], BN is used to describe the joint probability distribution PU of variable U=A1,…,An as(1)PU=∏i=1nPAi|PaAi,where PaAi is the parent set of Ai.


## 2.3. Mapping Algorithm

Due to the limitation of BT model, it cannot solve the uncertainty problems in the cable fire [29]. Therefore, BT can be mapped to BN to relax the limitation of BT and improve it. The mapping process of the BT model to the BN model is mainly divided into two steps. ① The FT analysis part: in the graphical mapping, the basic events, intermediate events, and top event of FT model are represented as root nodes, intermediate nodes, and leaf nodes in BN, respectively, as shown in Figure 2. In the numerical transformation, the occurrence probability of the basic event is regarded as the prior probability of the corresponding root node. ② The ET analysis part: the safety barriers and consequences in the ET model are transformed into corresponding safety nodes and consequence nodes, respectively. In addition, when the probabilities of the consequence nodes are affected by the failure or success of the safety node, the safety node and the consequence node must be connected by an arc.Figure 2
The process of FT mapping to BN.A CPT is assigned to indicate the relationship between parent and child nodes. CPT in BN is determined by the logic gate in fault tree and empirical judgment, as shown in Table1. The logic gate in the fault tree represents the deterministic relationship between events. For example, the AND gate represents that when events X1 and X2 occur at the same time, the top event T occurs. But in fact, even if events X1 and X2 occur successfully at the same time, T may not occur. This scenario can be modeled by the modified CPT, as shown in Table 2. The amending value in CPT can be determined according to historical data or expert feedback.Table 1
CPT corresponding to AND gate in BT.
X1SuccessFailureX2SuccessFailureSuccessFailureTSuccess1000Failure0111Table 2
Amending CPT corresponding to AND gate in BT.
X1SuccessFailureX2SuccessFailureSuccessFailureTSuccess0.980.080.090.01Failure0.020.920.910.99


## 2.4. Sensitivity Analysis

In the BN model, the slight change of the prior probability of each basic event (root node) may lead to the change of the fire probability of the cable in the utility tunnel. In order to quantify the degree of change in the BN model result caused by the basic event probability and identify in the critical basic events nodes of the BN model, the sensitivity analysis method is adopted to find out these critical basic events nodes [30]. In general, sensitivity analysis methods include Birnbaum importance measure (BIM), ratio of variation (RoV), and risk reduction worth (RRW) [31]. The RoV method based on prior and posterior probabilities is better for determining the root node sensitivity. The RoV method could be calculated as follows:(2)RoVXi=ϕXi−φXiφXi.Herein,φXi represents the prior probability of the Xi node and ϕXi represents the posterior probability of the Xi node.


## 2.5. Bayesian Network Analysis

Probability updating is an essential application of BN. Probabilistic updating is a diagnostic reasoning function based on BN. When a new observation or evidenceE appears, the BN uses the Bayesian theory to update the probability [32, 33].(3)PU|E=PU,EPE=PU,E∑UPU,E.Probability adaptation, also known as sequence learning, is another important application of BN. The probability adaptation of BN is to update the probability based on the collected new information accumulated over time as a priori probability. The new information represents the frequency of some basic events occurring within a certain time interval (such as one year) as evidence. The probability P updated by the new information can be obtained by (4) [30].(4)P=a+sn+s.where s represents the number of critical basic events and a and n represent the experience value and total experience value of critical basic events, respectively.


## 3. Proposed the Framework of Cable Fire Risk Analysis Method

As shown in Figure3, the framework of the fire risk analysis method for cable compartment proposed in this paper mainly includes the following eight steps. (1) definition of the target utility tunnel: this step is to obtain the relevant information of the target utility tunnel. The necessary information related to the utility tunnel includes the size, location, types of the included pipeline, the fire protection system, the possible status of duty staff, and the information of the fire department, etc. (2) Hazard identification of cable fire ignition:, the potential hazards may lead to a cable fire ignition occurrence are identified using FT analysis. (3) Design of fire scenario: the accident scenarios after ignition occurrence are composed of a series of fire events linked together by the success or failure of fire protection measures or actions. Then, combined with step (2), a BT model is established to show a complete accident evolution process. (4) Mapping and optimization of BN model: in order to overcome the limitation of the BT model, the BN of cable fire ignition in utility tunnel is developed using the GeNIe software. In order to make the BN model more reasonable and feasible, the BN model is optimized according to the actual situation of accident development and the dependence between safety barriers. (5) Probability updating: this step uses the optimized BN model for diagnostic reasoning to get the posterior probabilities of basic events. In addition, the critical basic events were selected by sensitivity analysis. (6) Probability adaptation: the cumulative information collected in a time interval is used to provide new evidence for the BN model and update the probability. Observe the changing trend of accident consequences probabilities with time in a period to achieve the purpose of risk prediction. (7) Model validation: in order to verify the feasibility and reliability of the optimized model, the calculation results before optimization are compared with those after optimization. (8) Suggestion on risk control: the above calculation data and analysis can provide references and suggestions for effectively controlling the cable fire risk.Figure 3
Flow chart of proposed cable fire risk analysis.


## 4. Accident Evolution Process of Cable Fire Modeling with BT

### 4.1. Definition of the Target Utility Tunnel (Step 1)

Take the utility tunnel of Xuesong Road in Xiangjiang New Area of Changsha, Hunan Province, as an example [3]. The tunnel consists of two compartments, the north is a cable compartment, including six 110 kV high-voltage cables and three 220 kV high-voltage cables. The south side is an integrated compartment, including medium voltage cables, water supply, and reclaimed water. The cable compartment discussed in this paper has a cross section size of 2.7 m × 2.75 m, including six layers of 110 kV cables laid on the left cable tray and three layers of 220 kV cables on the right, as shown in Figure 4.Figure 4
Cross-section diagram of the cable compartment.


### 4.2. Hazard Identification of Fire Ignition (Step 2)

An FT technique was employed to identify the potential hazards that may cause cable fire ignition. The cable fire accident in the utility tunnel occurs due to either cable spontaneous combustion or external fire source. The factors of spontaneous cable combustion include poor connection, overheating of cable core, and insulation breakdown. In contrast, external fire source factors include combustibles entering, fire spreading, and hot work near cables [30, 34]. The overheated cable core is the leading risk factor of spontaneous cable combustion [35]. The causes of overheated cable core include poor heat dissipation, cable overload, and cable short circuit. Insulation breakdown is also a significant risk factor of spontaneous cable combustion. It can be caused by insulation layer aging, insufficient insulation thickness, damage of cable, and low dielectric strength [36]. Furthermore, if the cable joint corrosion, poor installation quality, or cable joint explosion will lead to poor connection, in this case, cable spontaneous combustion may also occur. In addition to the combustibles entering and hot work near cables, the fire spreading is also an important factor to cause external fire sources. Fire spreading may happen because of unblocked holes, unpainted fireproof coating, and unclosed fire door.


### 4.3. Design of Fire Scenarios (Step 3)

In order to illustrate the process of fire after ignition, ET analysis is a graphical method for identifying all possible accident scenarios following the initial event [26]. Fire safety barriers play a very significant role in scenarios design. ET analysis lists possible fire scenarios considering automatic detection system, manual fire suppression, sprinkler suppression, and fire brigade suppression. In fact, there are a great number of elements affecting the development of fire, such as fuel load, the geometry of tunnel of fire origin, ventilation condition, and lining materials of wall and ceiling. However, this research mainly focuses on fire protection measures and personnel or fire brigade response to simplify the BT model.Using the FT and ET technique employed above, the BT model was developed and is shown in Figure5.Figure 5
BT (FT and ET) model of cable fire.


## 4.1. Definition of the Target Utility Tunnel (Step 1)

Take the utility tunnel of Xuesong Road in Xiangjiang New Area of Changsha, Hunan Province, as an example [3]. The tunnel consists of two compartments, the north is a cable compartment, including six 110 kV high-voltage cables and three 220 kV high-voltage cables. The south side is an integrated compartment, including medium voltage cables, water supply, and reclaimed water. The cable compartment discussed in this paper has a cross section size of 2.7 m × 2.75 m, including six layers of 110 kV cables laid on the left cable tray and three layers of 220 kV cables on the right, as shown in Figure 4.Figure 4
Cross-section diagram of the cable compartment.


## 4.2. Hazard Identification of Fire Ignition (Step 2)

An FT technique was employed to identify the potential hazards that may cause cable fire ignition. The cable fire accident in the utility tunnel occurs due to either cable spontaneous combustion or external fire source. The factors of spontaneous cable combustion include poor connection, overheating of cable core, and insulation breakdown. In contrast, external fire source factors include combustibles entering, fire spreading, and hot work near cables [30, 34]. The overheated cable core is the leading risk factor of spontaneous cable combustion [35]. The causes of overheated cable core include poor heat dissipation, cable overload, and cable short circuit. Insulation breakdown is also a significant risk factor of spontaneous cable combustion. It can be caused by insulation layer aging, insufficient insulation thickness, damage of cable, and low dielectric strength [36]. Furthermore, if the cable joint corrosion, poor installation quality, or cable joint explosion will lead to poor connection, in this case, cable spontaneous combustion may also occur. In addition to the combustibles entering and hot work near cables, the fire spreading is also an important factor to cause external fire sources. Fire spreading may happen because of unblocked holes, unpainted fireproof coating, and unclosed fire door.


## 4.3. Design of Fire Scenarios (Step 3)

In order to illustrate the process of fire after ignition, ET analysis is a graphical method for identifying all possible accident scenarios following the initial event [26]. Fire safety barriers play a very significant role in scenarios design. ET analysis lists possible fire scenarios considering automatic detection system, manual fire suppression, sprinkler suppression, and fire brigade suppression. In fact, there are a great number of elements affecting the development of fire, such as fuel load, the geometry of tunnel of fire origin, ventilation condition, and lining materials of wall and ceiling. However, this research mainly focuses on fire protection measures and personnel or fire brigade response to simplify the BT model.Using the FT and ET technique employed above, the BT model was developed and is shown in Figure5.Figure 5
BT (FT and ET) model of cable fire.


## 5. Cable Fire Risk Analysis Based on Bayesian Networks

### 5.1. Mapping and Optimization of BN Model (Step 4)

In order to overcome the limitations of BT model, a BN model is developed, as shown in Figure6 , through mapping from the BT model, as shown in Figure 5, and the mapping algorithm in Section 2.3 is adopted. However, there is still a big gap between the fire consequence scenario in the BN model and the actual fire scenario. Therefore, it is necessary to optimize the BN model. The details are as follows:(1)
In the BN model mapped from BT, each safety barrier node is assumed to be independent. Still, in fact, the manual fire suppression, sprinkler suppression, and fire brigade suppression are based on the premise of successful automatic detection, so a directed arc is added between nodeD and nodes E, F, and G.(2)
In addition, before optimization, each consequence node represents a possible alternative event (safe barrier) sequence, which falls short of displaying the temporal sequence of cable fire development from ignition to outcome. Therefore, according to the order of safety barriers intervention and the actual situation of fire development, three stages (Phase I, Phase II, Phase III) are introduced to represent different consequence nodes in the optimization model. Each node has two states of 0 and 1, which indicate whether the accident can be controlled in this stage. Phase I shows that once the cable fire is not effectively controlled by the safe barrier event (manual suppression) after the cable is ignited and before the automatic sprinkler is active, the fire develops into Phase I; Phase II demonstrates that after the cable fire develops to Phase I, once the safe barrier event (sprinkler suppression) does not effectively control the further development of the cable fire, the fire develops to Phase II; Phase III demonstrates that after the cable fire develops to Phase II, once the safe barrier event (fire brigade suppression) does not effectively control the further development of the cable fire, the fire completely loses control and develops to Phase III.(3)
Before the BN model is optimized, the sprinkler suppression (F) activation means that the fire is under control, which is obviously not in line with reality. Due to uncertain factors, even if the sprinkler system starts, the cable fire may still be uncontrolled. Therefore, the conditional probability of node F can be set to reflect reality, as shown in Figure7.Figure 6
BN model of cable fire.Figure 7
CPT of consequence nodes.Use the mapping algorithm mentioned above and the optimization method to transform the BT model into a BN model, as shown in Figure7.


### 5.2. Cable Fire Probability Updating (Step 5)

#### 5.2.1. Posterior Probability Estimation

Bidirectional reasoning is an effectual measure for BN to update probability, which can be used for prediction analysis and diagnostic analysis [37]. In the predictive analysis, the occurrence probability of cable fire ignition was calculated to be 7.056 × 10−3 according to the prior probability of all root nodes and their conditional dependencies. The probability of cable fire developing to Phase I is 5.020 × 10−3, the Phase II is 3.062 × 10−3, and the Phase III is 2.065 × 10−4. It can also be implied that the probability of cable fire developing to Phase I is the highest. Therefore, in order to effectively reduce the consequences of cable fire, it is necessary to prevent the occurrence of Phase I. The prior probabilities of root nodes were derived from the estimation of probabilities presented in literature and historical data or safety expert feedback [30]. In diagnostic analysis, the most common evidence used in probability updating is the knowledge about the top event. In this paper, the top event (cable fire ignition) is used as the evidence to estimate the posterior probability of the root node, and the posterior probabilities are listed in Table 3.Table 3
Basic events of cable fire ignition occurrence.
CodenameDescriptionPriori probabilityPosterior probabilityX1Joint corrosion1.302E − 041.845E − 02X2Inadequate maintenance management5.948E − 048.430E − 02X3Insufficient technical training8.358E − 041.185E − 01X4Poor workmanship1.848E − 031.848E − 03X5Long-term overload1.945E − 042.756E − 02X6Ventilation failure1.116E − 031.158E − 03X7Small cable spacing2.762E − 022.766E − 02X8Unreasonable cable compartment design9.766E − 039.808E − 03X9Breaker failure9.600E − 041.361E − 01X10Overvoltage1.876E − 042.659E − 02X11Stray current3.153E − 044.469E − 02X12Insulation layer aging1.938E − 042.757E − 02X13Cables overlapping1.222E − 041.732E − 02X14Humid environment3.121E − 044.423E − 02X15Insufficient insulation thickness1.948E-042.761E − 02X16Damaged installation8.954E − 041.269E − 01X17Animal destruction1.008E − 041.429E − 02X18Low dielectric strength2.703E − 043.831E − 02X19Combustibles entering1.208E − 041.179E − 01X20Unblocked holes2.130E − 042.130E − 05X21Unpainted fireproof coating1.224E − 031.224E − 03X22Unclosed fire door1.938E − 041.938E − 04X23Hot work near cables9.380E − 041.329E − 01


#### 5.2.2. Strength of Influence Analysis

BN inference can find the probable evolution paths through implementing the strength of influence. By clicking the tool named “Strength of Influence” in Genie 2.0, the dependence strength between nodes in the BN model is calculated to obtain the evolution paths of the cable fire accident. As shown in Figure8, the strength of the dependency between nodes is distinguished by different arc thicknesses. Obviously, spontaneous cable combustion (A1) is the main contributor to cable fire ignition accident, and it is more influenced by overheating of cable core (B2). Further, B2 is affected more by cable overload (C4). Besides, C4 is more affected by breaker failure (X9). Therefore, the most probable evolution path of cable ignition accident is breaker failure (X9)⟶cable overload (C4)⟶overheating of cable core (B2)⟶spontaneous cable combustion (A1)⟶cable fire ignition (T). The system's most efficient safety monitoring chain is obtained when the most probable path of the accident is obtained.Figure 8
Strength of influence analysis of BN.


#### 5.2.3. Sensitivity Analysis Based on BN

In order to improve the effectiveness of safety management and the accuracy of decision-making, it is essential to identify the most critical basic events causing cable fire ignition. The critical basic events have high posterior probability and high increasing probability, which will provide helpful information for utility tunnel managers to implement safety measures and preventive measures to avoid accidents. Critical basic events can be identified by comparing the ratio of variation in probabilities of all basic events. RoVs are calculated according to the prior and posterior probabilities in Table1, and the results are shown in Figure 9. It can be observed that the RoVs of X1-X3, X5, X9-X19, and X23 are significantly higher than other root nodes, which indicates that these nodes play a critical role in contributing to the ignition of cable fire. All these critical basic events should be paid more attention to the fire safety management of utility tunnels.Figure 9
Ratio of variation in probabilities.


### 5.3. Probability Adaptation (Step 6)

Probability adaptation, which uses previous experience to perform probability updating, and adjusts the conditional probability distribution by taking the accumulated information collected during the time interval (e.g., one year) as evidence [38, 39]. As the probabilities of accidents and consequences can be updated over time, it is used in risk analysis to monitor the fire risk of the system and help managers take appropriate safety measures before the risk becomes unacceptable.


#### 5.3.1. Critical Basic Events Probabilities Changed

There are 23 basic events that can be updated given their occurrence in the constructed BN model of cable fire ignition. However, it is very difficult for the monitoring system to monitor all basic events and cannot achieve the maximum utilization of limited resources. Therefore, this paper selects the critical basic events analyzed above as the fire risk analysis events of cable compartment.In the present work, the cumulative occurrence number of critical basic events has been observed and recorded according to the statistics over ten years [40, 41], as shown in Table 4. The probabilities can be changed based on new information by collecting the number of these critical basic events over ten years. The changed possibilities are shown in Table 5.Table 4
Records of critical basic events over ten years.
Critical basic events codeYears2007200820092010201120122013201420152016X10100010120X20111010120X30111010120X51102032251X90000000111X100000000110X110000000110X121102002231X131003001230X141002001230X150100000110X160000000111X170001000111X180000000110X190001000000X231001000000Table 5
The changed probabilities of critical basic events.
Critical basic events codeYears20072008200920102011X11.302 × 10−42.302 × 10−42.302 × 10−42.302 × 10−42.302 × 10−4X25.948 × 10−46.947 × 10−47.946 × 10−48.945 × 10−48.945 × 10−4X38.358 × 10−49.357 × 10−41.036 × 10−31.135 × 10−31.135 × 10−3X52.945 × 10−43.944 × 10−43.944 × 10−45.943 × 10−45.943 × 10−4X99.600 × 10−49.600 × 10−49.600 × 10−49.600 × 10−49.600 × 10−4X101.876 × 10−41.876 × 10−41.876 × 10−41.876 × 10−41.876 × 10−4X113.153 × 10−43.153 × 10−43.153 × 10−43.153 × 10−43.153 × 10−4X122.938 × 10−43.937 × 10−43.937 × 10−45.936 × 10−46.935 × 10−4X132.222 × 10−42.222 × 10−42.222 × 10−45.220 × 10−45.220 × 10−4X144.121 × 10−44.121 × 10−44.121 × 10−46.119 × 10−46.119 × 10−4X151.948 × 10−42.948 × 10−42.948 × 10−42.948 × 10−42.948 × 10−4X168.954 × 10−48.954 × 10−48.954 × 10−48.954 × 10−48.954 × 10−4X171.008 × 10−41.008 × 10−41.008 × 10−42.008 × 10−42.008 × 10−4X182.703 × 10−42.703 × 10−42.703 × 10−42.703 × 10−42.703 × 10−4X191.208 × 10−41.208 × 10−41.208 × 10−42.208 × 10−42.208 × 10−4X231.038 × 10−31.038 × 10−31.038 × 10−31.138 × 10−31.138 × 10−3Critical basic events codeYears20122013201420152016X13.301 × 10−43.301 × 10−44.301 × 10−46.299 × 10−46.299 × 10−4X29.944 × 10−49.944 × 10−41.094 × 10−31.294 × 10−31.294 × 10−3X31.235 × 10−31.235 × 10−31.335 × 10−31.535 × 10−31.535 × 10−3X57.940 × 10−49.937 × 10−41.193 × 10−31.692 × 10−31.792×10X99.600 × 10−49.600 × 10−41.060 × 10−31.160 × 10−31.260 × 10−3X101.876 × 10−41.876 × 10−42.876 × 10−43.875 × 10−43.875 × 10−4X113.153 × 10−43.153 × 10−44.153 × 10−45.152 × 10−45.152 × 10−4X126.935 × 10−48.932 × 10−41.093 × 10−31.392 × 10−31.492 × 10−3X135.220 × 10−46.219 × 10−48.216 × 10−41.121 × 10−31.121 × 10−3X146.119 × 10−47.118 × 10−49.116 × 10−41.211 × 10−31.211 × 10−3X152.948 × 10−42.948 × 10−43.947 × 10−44.947 × 10−44.947 × 10−4X168.954 × 10−48.954 × 10−49.953 × 10−41.095 × 10−31.195 × 10−3X172.008 × 10−42.008 × 10−43.007 × 10−44.007 × 10−45.006 × 10−4X182.703 × 10−42.703 × 10−43.703 × 10−44.702 × 10−44.702 × 10−4X192.208 × 10−42.208 × 10−42.208 × 10−42.208 × 10−42.208 × 10−4X231.138 × 10−31.138 × 10−31.138 × 10−31.138 × 10−31.138 × 10−3


#### 5.3.2. Update on the Probability of Accident Consequences

Using the changed probabilities of critical basic events during one period (one year) combined with the reliabilities of safety nodes shown in Table6 [42, 43], the probabilities of cable compartment safe state (S0) and different consequences (PhaseI, PhaseII, and PhaseIII) are updated. As shown in Table 7, it is apparent that the probability of S0 decreased from 0.9932 to 0.9848, indicating a downward trend year by year. This could be ascribed to the aging of equipment, devices, and materials with the increase of service life of utility tunnels. Therefore, it is necessary to carry out preventive maintenance, daily maintenance checks, periodic inspection, and experiment in order to provide safe and efficient service for utility tunnels.Table 6
Safety barriers and their reliabilities.
Code nameSafety barriersReliabilityDAutomatic detection system0.78EManual fire suppression0.37FSprinkler suppression0.92GFire brigade suppression0.51Table 7
The posterior probabilities of cable compartment safe state and consequences.
Consequences of the accidentYears20072008200920102011PhaseI4.870 × 10−35.294 × 10−35.435 × 10−36.422 × 10−36.492 × 10−3PhaseII1.899 × 10−32.064 × 10−32.119 × 10−32.504 × 10−32.532 × 10−3PhaseIII1.699 × 10−31.846 × 10−31.896 × 10−32.240 × 10−32.264 × 10−3S09.932 × 10−19.926 × 10−19.924 × 10−19.910 × 10−19.909 × 10−1Consequences of the accidentYears20122013201420152016PhaseI6.845 × 10−37.267 × 10−38.533 × 10−31.043 × 10−21.078 × 10−2PhaseII2.669 × 10−32.834 × 10−33.327 × 10−34.066 × 10−34.203 × 10−3PhaseIII2.387 × 10−32.535 × 10−32.976 × 10−33.637 × 10−33.759 × 10−3S09.904 × 10−19.898 × 10−19.880 × 10−19.853 × 10−19.848 × 10−1In BN adaptation, by analyzing the trends of probability changes, as shown in Figure10, it could be concluded that the probabilities of consequences (PhaseI, PhaseII, and PhaseIII) have the same change trend, which increases with time from the year 2007 to the year 2016. The ascending trend represents the deterioration of the operating conditions of the cable compartment. Meanwhile, it can also be seen that the probability of Phase I is significantly higher than that of PhaseII and PhaseIII, this is because the occurrence of PhaseI is an essential prerequisite of the occurrence of PhaseII and PhaseIII. Therefore, preventing the evolution of PhaseI plays a decisive role in controlling the cable fire of the utility tunnel. In addition, it can be observed that the probabilities of PhaseII and PhaseIII are very close. This could be attributed that it is difficult of the fire brigade to enter and extinguish the fire for the narrow and long confined space characteristics of the utility tunnel.Figure 10
Probability change trend of each phase.


### 5.4. Model Validation (Step 7)

In order to verify the superiority of the optimized BN model in dealing with uncertainty problems, this paper compared the occurrence probability of scenario 5 (before optimization) in Figure5 and Phase III (after optimization) in Figure 7 through Bayesian inference from 2007 to 2016, since scenario 5 (before optimization) represents that all safety barriers fail and the fire is out of control, which is consistent with Phase III (after optimization). As shown in Figure 11, it can be clearly seen that the probability of Phase III (after optimization) is higher than that in scenario 5 (before optimization), this is due to the error caused by uncertainty factors, such as dependencies between barrier events, and time-series relationship between consequence nodes is not considered before model optimization. In other words, the uncertainty of these factors has a relatively significant influence on the disturbance of the fire risk analysis, and the BN model after optimization reflects the actual cable fire situation more reasonably. Meanwhile, the results are in accordance with a previous study [44].Figure 11
Comparison of failure probability of all safety barriers before and after optimization.


## 5.1. Mapping and Optimization of BN Model (Step 4)

In order to overcome the limitations of BT model, a BN model is developed, as shown in Figure6 , through mapping from the BT model, as shown in Figure 5, and the mapping algorithm in Section 2.3 is adopted. However, there is still a big gap between the fire consequence scenario in the BN model and the actual fire scenario. Therefore, it is necessary to optimize the BN model. The details are as follows:(1)
In the BN model mapped from BT, each safety barrier node is assumed to be independent. Still, in fact, the manual fire suppression, sprinkler suppression, and fire brigade suppression are based on the premise of successful automatic detection, so a directed arc is added between nodeD and nodes E, F, and G.(2)
In addition, before optimization, each consequence node represents a possible alternative event (safe barrier) sequence, which falls short of displaying the temporal sequence of cable fire development from ignition to outcome. Therefore, according to the order of safety barriers intervention and the actual situation of fire development, three stages (Phase I, Phase II, Phase III) are introduced to represent different consequence nodes in the optimization model. Each node has two states of 0 and 1, which indicate whether the accident can be controlled in this stage. Phase I shows that once the cable fire is not effectively controlled by the safe barrier event (manual suppression) after the cable is ignited and before the automatic sprinkler is active, the fire develops into Phase I; Phase II demonstrates that after the cable fire develops to Phase I, once the safe barrier event (sprinkler suppression) does not effectively control the further development of the cable fire, the fire develops to Phase II; Phase III demonstrates that after the cable fire develops to Phase II, once the safe barrier event (fire brigade suppression) does not effectively control the further development of the cable fire, the fire completely loses control and develops to Phase III.(3)
Before the BN model is optimized, the sprinkler suppression (F) activation means that the fire is under control, which is obviously not in line with reality. Due to uncertain factors, even if the sprinkler system starts, the cable fire may still be uncontrolled. Therefore, the conditional probability of node F can be set to reflect reality, as shown in Figure7.Figure 6
BN model of cable fire.Figure 7
CPT of consequence nodes.Use the mapping algorithm mentioned above and the optimization method to transform the BT model into a BN model, as shown in Figure7.


## 5.2. Cable Fire Probability Updating (Step 5)

### 5.2.1. Posterior Probability Estimation

Bidirectional reasoning is an effectual measure for BN to update probability, which can be used for prediction analysis and diagnostic analysis [37]. In the predictive analysis, the occurrence probability of cable fire ignition was calculated to be 7.056 × 10−3 according to the prior probability of all root nodes and their conditional dependencies. The probability of cable fire developing to Phase I is 5.020 × 10−3, the Phase II is 3.062 × 10−3, and the Phase III is 2.065 × 10−4. It can also be implied that the probability of cable fire developing to Phase I is the highest. Therefore, in order to effectively reduce the consequences of cable fire, it is necessary to prevent the occurrence of Phase I. The prior probabilities of root nodes were derived from the estimation of probabilities presented in literature and historical data or safety expert feedback [30]. In diagnostic analysis, the most common evidence used in probability updating is the knowledge about the top event. In this paper, the top event (cable fire ignition) is used as the evidence to estimate the posterior probability of the root node, and the posterior probabilities are listed in Table 3.Table 3
Basic events of cable fire ignition occurrence.
CodenameDescriptionPriori probabilityPosterior probabilityX1Joint corrosion1.302E − 041.845E − 02X2Inadequate maintenance management5.948E − 048.430E − 02X3Insufficient technical training8.358E − 041.185E − 01X4Poor workmanship1.848E − 031.848E − 03X5Long-term overload1.945E − 042.756E − 02X6Ventilation failure1.116E − 031.158E − 03X7Small cable spacing2.762E − 022.766E − 02X8Unreasonable cable compartment design9.766E − 039.808E − 03X9Breaker failure9.600E − 041.361E − 01X10Overvoltage1.876E − 042.659E − 02X11Stray current3.153E − 044.469E − 02X12Insulation layer aging1.938E − 042.757E − 02X13Cables overlapping1.222E − 041.732E − 02X14Humid environment3.121E − 044.423E − 02X15Insufficient insulation thickness1.948E-042.761E − 02X16Damaged installation8.954E − 041.269E − 01X17Animal destruction1.008E − 041.429E − 02X18Low dielectric strength2.703E − 043.831E − 02X19Combustibles entering1.208E − 041.179E − 01X20Unblocked holes2.130E − 042.130E − 05X21Unpainted fireproof coating1.224E − 031.224E − 03X22Unclosed fire door1.938E − 041.938E − 04X23Hot work near cables9.380E − 041.329E − 01


### 5.2.2. Strength of Influence Analysis

BN inference can find the probable evolution paths through implementing the strength of influence. By clicking the tool named “Strength of Influence” in Genie 2.0, the dependence strength between nodes in the BN model is calculated to obtain the evolution paths of the cable fire accident. As shown in Figure8, the strength of the dependency between nodes is distinguished by different arc thicknesses. Obviously, spontaneous cable combustion (A1) is the main contributor to cable fire ignition accident, and it is more influenced by overheating of cable core (B2). Further, B2 is affected more by cable overload (C4). Besides, C4 is more affected by breaker failure (X9). Therefore, the most probable evolution path of cable ignition accident is breaker failure (X9)⟶cable overload (C4)⟶overheating of cable core (B2)⟶spontaneous cable combustion (A1)⟶cable fire ignition (T). The system's most efficient safety monitoring chain is obtained when the most probable path of the accident is obtained.Figure 8
Strength of influence analysis of BN.


### 5.2.3. Sensitivity Analysis Based on BN

In order to improve the effectiveness of safety management and the accuracy of decision-making, it is essential to identify the most critical basic events causing cable fire ignition. The critical basic events have high posterior probability and high increasing probability, which will provide helpful information for utility tunnel managers to implement safety measures and preventive measures to avoid accidents. Critical basic events can be identified by comparing the ratio of variation in probabilities of all basic events. RoVs are calculated according to the prior and posterior probabilities in Table1, and the results are shown in Figure 9. It can be observed that the RoVs of X1-X3, X5, X9-X19, and X23 are significantly higher than other root nodes, which indicates that these nodes play a critical role in contributing to the ignition of cable fire. All these critical basic events should be paid more attention to the fire safety management of utility tunnels.Figure 9
Ratio of variation in probabilities.


## 5.2.1. Posterior Probability Estimation

Bidirectional reasoning is an effectual measure for BN to update probability, which can be used for prediction analysis and diagnostic analysis [37]. In the predictive analysis, the occurrence probability of cable fire ignition was calculated to be 7.056 × 10−3 according to the prior probability of all root nodes and their conditional dependencies. The probability of cable fire developing to Phase I is 5.020 × 10−3, the Phase II is 3.062 × 10−3, and the Phase III is 2.065 × 10−4. It can also be implied that the probability of cable fire developing to Phase I is the highest. Therefore, in order to effectively reduce the consequences of cable fire, it is necessary to prevent the occurrence of Phase I. The prior probabilities of root nodes were derived from the estimation of probabilities presented in literature and historical data or safety expert feedback [30]. In diagnostic analysis, the most common evidence used in probability updating is the knowledge about the top event. In this paper, the top event (cable fire ignition) is used as the evidence to estimate the posterior probability of the root node, and the posterior probabilities are listed in Table 3.Table 3
Basic events of cable fire ignition occurrence.
CodenameDescriptionPriori probabilityPosterior probabilityX1Joint corrosion1.302E − 041.845E − 02X2Inadequate maintenance management5.948E − 048.430E − 02X3Insufficient technical training8.358E − 041.185E − 01X4Poor workmanship1.848E − 031.848E − 03X5Long-term overload1.945E − 042.756E − 02X6Ventilation failure1.116E − 031.158E − 03X7Small cable spacing2.762E − 022.766E − 02X8Unreasonable cable compartment design9.766E − 039.808E − 03X9Breaker failure9.600E − 041.361E − 01X10Overvoltage1.876E − 042.659E − 02X11Stray current3.153E − 044.469E − 02X12Insulation layer aging1.938E − 042.757E − 02X13Cables overlapping1.222E − 041.732E − 02X14Humid environment3.121E − 044.423E − 02X15Insufficient insulation thickness1.948E-042.761E − 02X16Damaged installation8.954E − 041.269E − 01X17Animal destruction1.008E − 041.429E − 02X18Low dielectric strength2.703E − 043.831E − 02X19Combustibles entering1.208E − 041.179E − 01X20Unblocked holes2.130E − 042.130E − 05X21Unpainted fireproof coating1.224E − 031.224E − 03X22Unclosed fire door1.938E − 041.938E − 04X23Hot work near cables9.380E − 041.329E − 01


## 5.2.2. Strength of Influence Analysis

BN inference can find the probable evolution paths through implementing the strength of influence. By clicking the tool named “Strength of Influence” in Genie 2.0, the dependence strength between nodes in the BN model is calculated to obtain the evolution paths of the cable fire accident. As shown in Figure8, the strength of the dependency between nodes is distinguished by different arc thicknesses. Obviously, spontaneous cable combustion (A1) is the main contributor to cable fire ignition accident, and it is more influenced by overheating of cable core (B2). Further, B2 is affected more by cable overload (C4). Besides, C4 is more affected by breaker failure (X9). Therefore, the most probable evolution path of cable ignition accident is breaker failure (X9)⟶cable overload (C4)⟶overheating of cable core (B2)⟶spontaneous cable combustion (A1)⟶cable fire ignition (T). The system's most efficient safety monitoring chain is obtained when the most probable path of the accident is obtained.Figure 8
Strength of influence analysis of BN.


## 5.2.3. Sensitivity Analysis Based on BN

In order to improve the effectiveness of safety management and the accuracy of decision-making, it is essential to identify the most critical basic events causing cable fire ignition. The critical basic events have high posterior probability and high increasing probability, which will provide helpful information for utility tunnel managers to implement safety measures and preventive measures to avoid accidents. Critical basic events can be identified by comparing the ratio of variation in probabilities of all basic events. RoVs are calculated according to the prior and posterior probabilities in Table1, and the results are shown in Figure 9. It can be observed that the RoVs of X1-X3, X5, X9-X19, and X23 are significantly higher than other root nodes, which indicates that these nodes play a critical role in contributing to the ignition of cable fire. All these critical basic events should be paid more attention to the fire safety management of utility tunnels.Figure 9
Ratio of variation in probabilities.


## 5.3. Probability Adaptation (Step 6)

Probability adaptation, which uses previous experience to perform probability updating, and adjusts the conditional probability distribution by taking the accumulated information collected during the time interval (e.g., one year) as evidence [38, 39]. As the probabilities of accidents and consequences can be updated over time, it is used in risk analysis to monitor the fire risk of the system and help managers take appropriate safety measures before the risk becomes unacceptable.


### 5.3.1. Critical Basic Events Probabilities Changed

There are 23 basic events that can be updated given their occurrence in the constructed BN model of cable fire ignition. However, it is very difficult for the monitoring system to monitor all basic events and cannot achieve the maximum utilization of limited resources. Therefore, this paper selects the critical basic events analyzed above as the fire risk analysis events of cable compartment.In the present work, the cumulative occurrence number of critical basic events has been observed and recorded according to the statistics over ten years [40, 41], as shown in Table 4. The probabilities can be changed based on new information by collecting the number of these critical basic events over ten years. The changed possibilities are shown in Table 5.Table 4
Records of critical basic events over ten years.
Critical basic events codeYears2007200820092010201120122013201420152016X10100010120X20111010120X30111010120X51102032251X90000000111X100000000110X110000000110X121102002231X131003001230X141002001230X150100000110X160000000111X170001000111X180000000110X190001000000X231001000000Table 5
The changed probabilities of critical basic events.
Critical basic events codeYears20072008200920102011X11.302 × 10−42.302 × 10−42.302 × 10−42.302 × 10−42.302 × 10−4X25.948 × 10−46.947 × 10−47.946 × 10−48.945 × 10−48.945 × 10−4X38.358 × 10−49.357 × 10−41.036 × 10−31.135 × 10−31.135 × 10−3X52.945 × 10−43.944 × 10−43.944 × 10−45.943 × 10−45.943 × 10−4X99.600 × 10−49.600 × 10−49.600 × 10−49.600 × 10−49.600 × 10−4X101.876 × 10−41.876 × 10−41.876 × 10−41.876 × 10−41.876 × 10−4X113.153 × 10−43.153 × 10−43.153 × 10−43.153 × 10−43.153 × 10−4X122.938 × 10−43.937 × 10−43.937 × 10−45.936 × 10−46.935 × 10−4X132.222 × 10−42.222 × 10−42.222 × 10−45.220 × 10−45.220 × 10−4X144.121 × 10−44.121 × 10−44.121 × 10−46.119 × 10−46.119 × 10−4X151.948 × 10−42.948 × 10−42.948 × 10−42.948 × 10−42.948 × 10−4X168.954 × 10−48.954 × 10−48.954 × 10−48.954 × 10−48.954 × 10−4X171.008 × 10−41.008 × 10−41.008 × 10−42.008 × 10−42.008 × 10−4X182.703 × 10−42.703 × 10−42.703 × 10−42.703 × 10−42.703 × 10−4X191.208 × 10−41.208 × 10−41.208 × 10−42.208 × 10−42.208 × 10−4X231.038 × 10−31.038 × 10−31.038 × 10−31.138 × 10−31.138 × 10−3Critical basic events codeYears20122013201420152016X13.301 × 10−43.301 × 10−44.301 × 10−46.299 × 10−46.299 × 10−4X29.944 × 10−49.944 × 10−41.094 × 10−31.294 × 10−31.294 × 10−3X31.235 × 10−31.235 × 10−31.335 × 10−31.535 × 10−31.535 × 10−3X57.940 × 10−49.937 × 10−41.193 × 10−31.692 × 10−31.792×10X99.600 × 10−49.600 × 10−41.060 × 10−31.160 × 10−31.260 × 10−3X101.876 × 10−41.876 × 10−42.876 × 10−43.875 × 10−43.875 × 10−4X113.153 × 10−43.153 × 10−44.153 × 10−45.152 × 10−45.152 × 10−4X126.935 × 10−48.932 × 10−41.093 × 10−31.392 × 10−31.492 × 10−3X135.220 × 10−46.219 × 10−48.216 × 10−41.121 × 10−31.121 × 10−3X146.119 × 10−47.118 × 10−49.116 × 10−41.211 × 10−31.211 × 10−3X152.948 × 10−42.948 × 10−43.947 × 10−44.947 × 10−44.947 × 10−4X168.954 × 10−48.954 × 10−49.953 × 10−41.095 × 10−31.195 × 10−3X172.008 × 10−42.008 × 10−43.007 × 10−44.007 × 10−45.006 × 10−4X182.703 × 10−42.703 × 10−43.703 × 10−44.702 × 10−44.702 × 10−4X192.208 × 10−42.208 × 10−42.208 × 10−42.208 × 10−42.208 × 10−4X231.138 × 10−31.138 × 10−31.138 × 10−31.138 × 10−31.138 × 10−3


### 5.3.2. Update on the Probability of Accident Consequences

Using the changed probabilities of critical basic events during one period (one year) combined with the reliabilities of safety nodes shown in Table6 [42, 43], the probabilities of cable compartment safe state (S0) and different consequences (PhaseI, PhaseII, and PhaseIII) are updated. As shown in Table 7, it is apparent that the probability of S0 decreased from 0.9932 to 0.9848, indicating a downward trend year by year. This could be ascribed to the aging of equipment, devices, and materials with the increase of service life of utility tunnels. Therefore, it is necessary to carry out preventive maintenance, daily maintenance checks, periodic inspection, and experiment in order to provide safe and efficient service for utility tunnels.Table 6
Safety barriers and their reliabilities.
Code nameSafety barriersReliabilityDAutomatic detection system0.78EManual fire suppression0.37FSprinkler suppression0.92GFire brigade suppression0.51Table 7
The posterior probabilities of cable compartment safe state and consequences.
Consequences of the accidentYears20072008200920102011PhaseI4.870 × 10−35.294 × 10−35.435 × 10−36.422 × 10−36.492 × 10−3PhaseII1.899 × 10−32.064 × 10−32.119 × 10−32.504 × 10−32.532 × 10−3PhaseIII1.699 × 10−31.846 × 10−31.896 × 10−32.240 × 10−32.264 × 10−3S09.932 × 10−19.926 × 10−19.924 × 10−19.910 × 10−19.909 × 10−1Consequences of the accidentYears20122013201420152016PhaseI6.845 × 10−37.267 × 10−38.533 × 10−31.043 × 10−21.078 × 10−2PhaseII2.669 × 10−32.834 × 10−33.327 × 10−34.066 × 10−34.203 × 10−3PhaseIII2.387 × 10−32.535 × 10−32.976 × 10−33.637 × 10−33.759 × 10−3S09.904 × 10−19.898 × 10−19.880 × 10−19.853 × 10−19.848 × 10−1In BN adaptation, by analyzing the trends of probability changes, as shown in Figure10, it could be concluded that the probabilities of consequences (PhaseI, PhaseII, and PhaseIII) have the same change trend, which increases with time from the year 2007 to the year 2016. The ascending trend represents the deterioration of the operating conditions of the cable compartment. Meanwhile, it can also be seen that the probability of Phase I is significantly higher than that of PhaseII and PhaseIII, this is because the occurrence of PhaseI is an essential prerequisite of the occurrence of PhaseII and PhaseIII. Therefore, preventing the evolution of PhaseI plays a decisive role in controlling the cable fire of the utility tunnel. In addition, it can be observed that the probabilities of PhaseII and PhaseIII are very close. This could be attributed that it is difficult of the fire brigade to enter and extinguish the fire for the narrow and long confined space characteristics of the utility tunnel.Figure 10
Probability change trend of each phase.


## 5.3.1. Critical Basic Events Probabilities Changed

There are 23 basic events that can be updated given their occurrence in the constructed BN model of cable fire ignition. However, it is very difficult for the monitoring system to monitor all basic events and cannot achieve the maximum utilization of limited resources. Therefore, this paper selects the critical basic events analyzed above as the fire risk analysis events of cable compartment.In the present work, the cumulative occurrence number of critical basic events has been observed and recorded according to the statistics over ten years [40, 41], as shown in Table 4. The probabilities can be changed based on new information by collecting the number of these critical basic events over ten years. The changed possibilities are shown in Table 5.Table 4
Records of critical basic events over ten years.
Critical basic events codeYears2007200820092010201120122013201420152016X10100010120X20111010120X30111010120X51102032251X90000000111X100000000110X110000000110X121102002231X131003001230X141002001230X150100000110X160000000111X170001000111X180000000110X190001000000X231001000000Table 5
The changed probabilities of critical basic events.
Critical basic events codeYears20072008200920102011X11.302 × 10−42.302 × 10−42.302 × 10−42.302 × 10−42.302 × 10−4X25.948 × 10−46.947 × 10−47.946 × 10−48.945 × 10−48.945 × 10−4X38.358 × 10−49.357 × 10−41.036 × 10−31.135 × 10−31.135 × 10−3X52.945 × 10−43.944 × 10−43.944 × 10−45.943 × 10−45.943 × 10−4X99.600 × 10−49.600 × 10−49.600 × 10−49.600 × 10−49.600 × 10−4X101.876 × 10−41.876 × 10−41.876 × 10−41.876 × 10−41.876 × 10−4X113.153 × 10−43.153 × 10−43.153 × 10−43.153 × 10−43.153 × 10−4X122.938 × 10−43.937 × 10−43.937 × 10−45.936 × 10−46.935 × 10−4X132.222 × 10−42.222 × 10−42.222 × 10−45.220 × 10−45.220 × 10−4X144.121 × 10−44.121 × 10−44.121 × 10−46.119 × 10−46.119 × 10−4X151.948 × 10−42.948 × 10−42.948 × 10−42.948 × 10−42.948 × 10−4X168.954 × 10−48.954 × 10−48.954 × 10−48.954 × 10−48.954 × 10−4X171.008 × 10−41.008 × 10−41.008 × 10−42.008 × 10−42.008 × 10−4X182.703 × 10−42.703 × 10−42.703 × 10−42.703 × 10−42.703 × 10−4X191.208 × 10−41.208 × 10−41.208 × 10−42.208 × 10−42.208 × 10−4X231.038 × 10−31.038 × 10−31.038 × 10−31.138 × 10−31.138 × 10−3Critical basic events codeYears20122013201420152016X13.301 × 10−43.301 × 10−44.301 × 10−46.299 × 10−46.299 × 10−4X29.944 × 10−49.944 × 10−41.094 × 10−31.294 × 10−31.294 × 10−3X31.235 × 10−31.235 × 10−31.335 × 10−31.535 × 10−31.535 × 10−3X57.940 × 10−49.937 × 10−41.193 × 10−31.692 × 10−31.792×10X99.600 × 10−49.600 × 10−41.060 × 10−31.160 × 10−31.260 × 10−3X101.876 × 10−41.876 × 10−42.876 × 10−43.875 × 10−43.875 × 10−4X113.153 × 10−43.153 × 10−44.153 × 10−45.152 × 10−45.152 × 10−4X126.935 × 10−48.932 × 10−41.093 × 10−31.392 × 10−31.492 × 10−3X135.220 × 10−46.219 × 10−48.216 × 10−41.121 × 10−31.121 × 10−3X146.119 × 10−47.118 × 10−49.116 × 10−41.211 × 10−31.211 × 10−3X152.948 × 10−42.948 × 10−43.947 × 10−44.947 × 10−44.947 × 10−4X168.954 × 10−48.954 × 10−49.953 × 10−41.095 × 10−31.195 × 10−3X172.008 × 10−42.008 × 10−43.007 × 10−44.007 × 10−45.006 × 10−4X182.703 × 10−42.703 × 10−43.703 × 10−44.702 × 10−44.702 × 10−4X192.208 × 10−42.208 × 10−42.208 × 10−42.208 × 10−42.208 × 10−4X231.138 × 10−31.138 × 10−31.138 × 10−31.138 × 10−31.138 × 10−3


## 5.3.2. Update on the Probability of Accident Consequences

Using the changed probabilities of critical basic events during one period (one year) combined with the reliabilities of safety nodes shown in Table6 [42, 43], the probabilities of cable compartment safe state (S0) and different consequences (PhaseI, PhaseII, and PhaseIII) are updated. As shown in Table 7, it is apparent that the probability of S0 decreased from 0.9932 to 0.9848, indicating a downward trend year by year. This could be ascribed to the aging of equipment, devices, and materials with the increase of service life of utility tunnels. Therefore, it is necessary to carry out preventive maintenance, daily maintenance checks, periodic inspection, and experiment in order to provide safe and efficient service for utility tunnels.Table 6
Safety barriers and their reliabilities.
Code nameSafety barriersReliabilityDAutomatic detection system0.78EManual fire suppression0.37FSprinkler suppression0.92GFire brigade suppression0.51Table 7
The posterior probabilities of cable compartment safe state and consequences.
Consequences of the accidentYears20072008200920102011PhaseI4.870 × 10−35.294 × 10−35.435 × 10−36.422 × 10−36.492 × 10−3PhaseII1.899 × 10−32.064 × 10−32.119 × 10−32.504 × 10−32.532 × 10−3PhaseIII1.699 × 10−31.846 × 10−31.896 × 10−32.240 × 10−32.264 × 10−3S09.932 × 10−19.926 × 10−19.924 × 10−19.910 × 10−19.909 × 10−1Consequences of the accidentYears20122013201420152016PhaseI6.845 × 10−37.267 × 10−38.533 × 10−31.043 × 10−21.078 × 10−2PhaseII2.669 × 10−32.834 × 10−33.327 × 10−34.066 × 10−34.203 × 10−3PhaseIII2.387 × 10−32.535 × 10−32.976 × 10−33.637 × 10−33.759 × 10−3S09.904 × 10−19.898 × 10−19.880 × 10−19.853 × 10−19.848 × 10−1In BN adaptation, by analyzing the trends of probability changes, as shown in Figure10, it could be concluded that the probabilities of consequences (PhaseI, PhaseII, and PhaseIII) have the same change trend, which increases with time from the year 2007 to the year 2016. The ascending trend represents the deterioration of the operating conditions of the cable compartment. Meanwhile, it can also be seen that the probability of Phase I is significantly higher than that of PhaseII and PhaseIII, this is because the occurrence of PhaseI is an essential prerequisite of the occurrence of PhaseII and PhaseIII. Therefore, preventing the evolution of PhaseI plays a decisive role in controlling the cable fire of the utility tunnel. In addition, it can be observed that the probabilities of PhaseII and PhaseIII are very close. This could be attributed that it is difficult of the fire brigade to enter and extinguish the fire for the narrow and long confined space characteristics of the utility tunnel.Figure 10
Probability change trend of each phase.


## 5.4. Model Validation (Step 7)

In order to verify the superiority of the optimized BN model in dealing with uncertainty problems, this paper compared the occurrence probability of scenario 5 (before optimization) in Figure5 and Phase III (after optimization) in Figure 7 through Bayesian inference from 2007 to 2016, since scenario 5 (before optimization) represents that all safety barriers fail and the fire is out of control, which is consistent with Phase III (after optimization). As shown in Figure 11, it can be clearly seen that the probability of Phase III (after optimization) is higher than that in scenario 5 (before optimization), this is due to the error caused by uncertainty factors, such as dependencies between barrier events, and time-series relationship between consequence nodes is not considered before model optimization. In other words, the uncertainty of these factors has a relatively significant influence on the disturbance of the fire risk analysis, and the BN model after optimization reflects the actual cable fire situation more reasonably. Meanwhile, the results are in accordance with a previous study [44].Figure 11
Comparison of failure probability of all safety barriers before and after optimization.


## 6. Summary and Conclusions

This paper proposes a novel model that combines the Bayesian network and bow-tie technique for analyzing the fire risk of a utility tunnel. The cable fire's hazard identification and accident evolution process were modeled by the bow-tie technique. In order to overcome the limitation of bow-tie in conditional dependencies and temporal sequences of events, an optimized BN model is adopted. In the process of fire risk analysis, sensitivity analysis was implemented based on bidirectional reasoning. In addition, a probability adaptation was also conducted with historical accident data, and probabilities trend of critical basic events and consequences were obtained through this method.In the present study, for verifying the advantages of the optimized BN model, the comparison between not optimization model and optimization model was carried out, which illustrated that the results of the optimized model are more reliable and close to the actual fire situation. In BN analysis, probability updating has been successfully applied to predict the probability of cable fire ignition and find out the most probable explanations leading to the accident or a specific consequence. In addition, by means of sensitivity analysis, “insulation layer aging,” “long-term overload,” “overvoltage,” and“stray current” et al. are identified as critical factors for leading to cable fire ignition and should attract great attention. By observing critical events occurring during an interval, this paper implements probability adaptation. Based on these results, there are suggestions for preventing cable fire: (1) it is essential to control the fire inPhaseI. In order to detect fire in time, new detection equipment such as intelligent inspection robots can be adopted and (2) the existing equipment of the fire brigade has a poor fire extinguishing effect on the utility tunnel. It is more practical to improve the reliability of the automatic fire extinguishing system in a utility tunnel.The present study demonstrated that the Bayesian network is an efficient tool in risk analysis on cable fire for utility tunnels, the estimating outcome of probability updating and probability adapting could provide strong support for risk decision-making and preventive measures implementation. Furthermore, the study could provide a technical guidance for fire risk analysis of other underground space and cable equipment.



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*Source: 1952263-2022-07-12.xml*