Analysis of Factors Affecting Emergency Response Linkage in Coal Mine Gas Explosion Accidents

Abstract

To analyze the influencing factors of the emergency linkage of gas explosion accidents and their causal relationships, a method for analyzing the influencing factors of the emergency linkage of gas explosion accidents is proposed based on a hierarchical holographic model and Bayesian networks. Firstly, based on the hierarchical holographic model to determine the main influencing factors of the accident emergency linkage, we constructed the topological structure model of accident control, secondary disaster, and emergency rescue, and used the triangular fuzzy number to assess the a priori probability and conditional probability of the influencing factors. Next, the most likely factors affecting the accident emergency linkage are quickly identified by combining Bayesian diagnostic reasoning. Finally, sensitivity analysis is conducted to identify the key factors affecting the accident emergency linkage. The results show that the probability of normal operation of gas explosion accident emergency linkage is 78.1%, but when the coal mine environment changes, especially when multiple influencing factors occur simultaneously, the probability of normal operation of accident emergency linkage decreases significantly. Through causal analysis, the degree of influence on the operation of the accident emergency linkage in different situations can be deduced. Through diagnostic analysis, it can be seen that the emergency linkage operation is more sensitive to the two factors of the ventilation and smoke extraction system response and gas over limit, so it is necessary to pay attention to its important role in accident treatment. Meanwhile, the sensitivity analysis shows that the response of the ventilation and smoke extraction system, the accuracy of disaster sharing, the gas over limit, the technical level of the operators, and the team rescue experience are the key factors affecting the emergency response linkage in accidents. This study can provide theoretical guidance for the improvement of the emergency response linkage mechanism of coal mine gas explosion accidents as well as the decision-making of the accidents, minimize the losses of the accidents, and promote the sustainable development of the coal mining industry.

1. Introduction

A gas explosion is a disaster accident formed under the joint action of multiple factors, and it is also one of the major disaster accidents that threaten the safety production of coal mines in China [1]. Especially for major (mega) gas explosion accidents, which very easily lead to mass deaths and injuries, the destruction of the ventilation system, tunnel collapse, etc. [2], relying on a single coal mine (mining group) of a single emergency response force makes it difficult to comprehensively and effectively carry out the emergency rescue, and therefore there is a need to take the government as the lead, fire, public security, medical, and other rescue units and the participation of social forces promptly, with emergency response linkage disposal measures [3]. A gas explosion accident scene emergency linkage disposal of social responsibility and sustainable development are inseparable, and only the combination of the two, in order to better protect the interests of the safety of coal mining enterprises, reduce the damage to the environment and resources [4]. Due to the uncertainty of the impact of sudden gas explosions in coal mines on emergency response, analyzing the factors influencing the emergency response to gas explosion accidents is a difficult task, and a key focus is on enhancing the timeliness and effectiveness of the emergency response. It is also a key factor in ensuring the sustainable development of the coal mining industry.

In recent years, many scholars have conducted relevant studies on the propagation law, risk assessment, and emergency response to coal mine gas explosions. Zhang Xuebo et al. [5] proposed the numerical simulation of the shock wave propagation process using a segmented relay and verified the applicability of the simulation by combining it with the Yangchangwan coal mine. They also analyzed the influence of the roadway connection method and length on the shock wave propagation process. Liu Jiajia et al. [6] used Fluent to carry out numerical simulation research on the actual situation of the coal mine working face. They obtained the propagation law of gas explosion shock waves in a Y-type coal mining face. Zhu Yunfei et al. [7] usedFLACS 3D to simulate the gas explosion in the unobstructed straight tunnel of a coal mine to derive the influence law of flame propagation, gas concentration, and space obstruction rate on the explosion pressure. Ye Qing et al. [8,9] studied the propagation law of gas explosions in an in a bifurcating duct by setting up the arrangement of different explosive sources. Jia Zhenzhen et al. [10,11,12] used ANSYS/LS-DYNA to establish the numerical model of gas explosions in different adiabatic pipelines to analyze the propagation process of gas explosions under the influence of the wall thermal effect, and the results showed that the wall thermal effect is inversely proportional to the gas explosion and its propagation. Exploring the propagation and damage characteristics of gas explosions in different structures has guiding significance for the rational design of coal mine gas explosion emergency systems. Pi Zikun et al. [13] combined prospect theory, fuzzy comprehensive evaluation theory, and interval number ordering theory to construct a gas explosion risk assessment model, and verified the model through examples. Zhang Qing [14], based on the disaster system theory, classified the coal mine gas explosion disaster into three subsystems of the pregnant environment, the disaster-causing factor, and the disaster-bearing body, and at the same time, constructed a random forest model for the assessment of the coal mine gas explosion risk. Lu Jintao et al. [15] extracted the influencing factors from classical gas explosion accident cases, constructed a gray-objective element risk assessment model based on the integrated gray system theory, and clarified the action paths between risk factors. Summarizing the risk assessment system of gas explosions constructed by the above scholars and analyzing the causes of gas explosion accidents can help to improve the emergency response mechanism of gas explosion accidents. By integrating multiple heterogeneous optimization measures such as communication software platforms, comprehensive information displays, and security monitoring systems, it is more convenient to obtain information related to mine transportation, ventilation, equipment and facilities, and emergency command [16,17,18,19,20]. Jing Guoxun et al. [21] counted the number of gas explosion accidents occurring from 2015 to 2021, used the HFACS model to study the causation and occurrence law of gas explosion accidents, and proposed that the organizational atmosphere, operator status, management factors, supervisory situation, and operational errors are the prevention and control focuses of the accident and emergency management. Xiong Yachao et al. [22] analyzed coal mine accident cases, laws and regulations, and the relevant literature based on the rooted theory. Currently, underground risks in China are mainly divided into three categories, source risk, derivative risk, and residual risk, and meanwhile accident emergency management measures are put forward to match them. Li Leilei et al. [23], based on explosives and hydrodynamics, combined the research data of gas explosion accidents; the accident process is divided into three stages, and at the same time, according to the characteristics of the accident at each stage, they put forward targeted rescue methods. Based on the law of occurrence of coal mine accidents, Sun Jiping et al. [24] analyzed the deficiencies of existing emergency rescue technology and equipment, and put forward a variety of automatic accident discovery and alarm methods through the research and development of technology and equipment such as disaster identification, emergency communication, personnel positioning, etc., and finally formed a qualitative and quantitative intelligent emergency response system and auxiliary decision-making system. The above scholars have fully considered the influence of coal mine intelligence, management, rescue, and other factors on accident emergency rescue, and provided strong support for emergency decision-making in gas explosion accidents.

In summary, the existing studies have covered the characteristics of gas explosion propagation and damage, risk assessment, and the impact of single or multiple factors on the emergency response to accidents. However, the construction of the emergency linkage influencing factor system for gas explosion accidents is not comprehensive and still needs further improvement. Bayesian networks can be used to determine the process operation state and diagnose the fault propagation path and fault root cause. At present, Bayesian statistical inference methods have also been gradually developed and achieved more successful applications in various fields; for example, Wu Wenjing et al. [25] constructed a Bayesian network model for assessing the smoothness of the road network based on the smoothness and reliability of the road section, and at the same time, analyzed the causal relationship between the road section and the road network, and identified the key road sections. Chen Jiusheng et al. [26] constructed a directed graph of the air conditioning system topology based on the functional behavior and physical structure of the air conditioning system and combined it with the unloop strategy to obtain the optimal Bayesian fault propagation network structure in order to identify the system fault propagation paths under the multi-closed-loop structure. Li Min et al. [27] proposed a coal mine gas explosion risk assessment method based on a fuzzy Bayesian network, assessed the conditional probability of risk indicators based on triangular fuzzy numbers, calculated the probability of occurrence of a gas explosion using a Bayesian network, and deduced and analyzed the accidental causes of a gas explosion. Li et al. [28] carried out a reliability analysis of the early failure of the main drive system of numerical control (CNC) machine tool by establishing a Bayesian network model. Zhao Hongshan et al. [29] proposed a temperature control strategy based on the classified playback of double-delayed Bayesian deep deterministic policy gradients for the accurate model-free control of fuel cells and verified it on a simulation platform.

From the above research, it can be seen that the factor identification method based on Bayesian theory can better consider the uncertainty of the system and has a strong reasoning ability when dealing with complex system problems. Therefore, this article intends to construct the index system of coal mine gas explosion accident emergency response linkage factors from three aspects, accident control, secondary disasters, and emergency rescue, analyze the influence factors of the accident emergency response linkage with the help of Bayesian networks, and explore the causal relationship between the factors. To provide a certain theoretical reference for improving the emergency linkage mechanism and decision-making of coal mine gas explosion accidents, minimizing personnel casualties and economic losses caused by accidents, promoting social harmony and stability, and the sustainable development of the coal mining industry are warranted.

2. Method

2.1. Hierarchical Holographic Modeling

The hierarchical holographic model (HHM) was proposed by Haimes et al., which starts from various levels of the system, comprehensively, and from multiple perspectives to understand the essence and inherent characteristics of complex systems [30]. The hierarchical holographic modeling approach assumes that the actual existing system is difficult to reasonably represent by a single model and that a model can only represent a certain aspect of the system, just as a photograph can only represent a two-dimensional plane, in which a lot of hidden information cannot be captured, whereas a perspective view can represent a three-dimensional structure. The HHM’s aim is to decompose the system into several subsystems, where each of the subsystems can be represented by a different model and then can be continuously decomposed so that each subsystem is a particular perspective structure of the complete system. HMM modeling determines the structure of all the factors through an iterative approach, which is a continuous cyclic process, and the rationality of the framework can be further refined using this process [31].

2.2. Bayesian Theory

A Bayesian network is a directed acyclic graph based on probability theory and is expressed graphically, in which each node represents a random variable, and the strength of association between nodes can be expressed by conditional probability [32]. The mathematical formulation is as follows: if the domain $X=\left\{X_1,X_2,\cdots ,X_n\right\}$, where $X_1,X_2,\cdots ,X_n$ are variables in the network, the joint probability can be expressed as

$$P\left(U\right)=p\left(X_1,X_2,\cdots ,X_n\right)=\prod _{i=1}^{n}p\left(\left.X_i\right|\pi \left(X_i\right)\right)$$

(1)

where $\pi \left(X_i\right)$ denotes the set of $X_i$ parent nodes.

Each node in a Bayesian network is assigned a probability distribution, and the root node $X$ is assigned an edge distribution, and the edge probability of $X_i$ is denoted as

$$P\left(X_i\right)=\sum _{1.2,\dots ,i-1}P\left(U\right)$$

(2)

Instead, the non-root nodes are assigned a conditional probability distribution $P\left(\left.X\right|\pi \left(X\right)\right)$. Suppose that given known evidence $\theta$, the probability of an event occurring is expressed as

$$P\left(\left.U\right|\theta \right)={\displaystyle \frac{P\left(U,\theta \right)}{P\left(\theta \right)}}={\displaystyle \frac{P\left(U,\theta \right)}{\sum _{U}P\left(U,\theta \right)}}$$

(3)

3. Indicator System Construction

3.1. Identification of Emergency Linkage Influences

For the coal mine gas explosion accident system, the HHM can be used to model the risk factors of multiple subsystems, while analyzing the impact of each subsystem on the whole. Based on the HHM, the organic linkage of each subsystem is established to achieve a more complete tracking analysis of the emergency linkage influencing factors of coal mine gas explosion accidents. Therefore, in the identification of emergency linkage influencing factors of gas explosion accidents, an identification framework is established from the three levels of accident control, secondary disasters, and emergency rescue (as shown in Figure 1), which lays the foundation for the establishment of the index system of emergency linkage influencing factors of coal mine gas explosion accidents.

3.2. Expert Authority Calculation

Since different educational backgrounds, industry experience, etc., have an impact on the results of expert assessment, the degree of expert authority is introduced into the expert research when synthesizing the experts’ opinions, to construct a more complete indicator system of the factors influencing the accident and emergency response linkage. The degree of expert authority is expressed by the coefficient of expert authority ($C_r$), which is composed of the basis of the judgment made by the expert in the research process ($C_a$) and the degree of familiarity with the research field or issue ($C_s$), and the specific assigned values are shown in

Table 1. A quantification of the basis for judgment and the extent of its impact.

Basis of Judgement	Degree of Impact
	Large	Medium	Small
Practical experience	0.5	0.4	0.3
Theoretical analysis	0.3	0.2	0.1
Domestic and international literature	0.1	0.1	0.05
Intuitive perception	0.1	0.1	0.05

and

Table 2. Table of expert familiarity factors.

Familiarity	Very Familiar	More Familiar	Fairly Familiar	Not Very Familiar	Unfamiliar
$C_s$	1.0	0.8	0.6	0.4	0.2

. The degree of expert authority has a considerable impact on the reliability of the research results, and the larger the coefficient, the higher the degree of authority of the expert, and the greater the reference of the rating. It is usually considered that the degree of expert authority is recognized when the expert authority coefficient $C_r$ > 0.7 [33], which is calculated as follows:

$$C_r=(C_a+C_s)/2$$

(4)

Based on the weight statistics method, the expert authority coefficient weight $W_j$ is calculated, and then the mean value $E_j$ of each indicator as well as the coefficient of variation $CV$ are calculated as follows:

$$E_j=\sum W_j\times Q_{i,j}$$

(5)

$$CV={\delta }_j/E_j$$

(6)

where $Q_{i,j}$ denotes the rating of the $j$th influence factor by the $i$th expert; and ${\delta }_j$ denotes the standard deviation of each expert’s rating of the $j$th influence factor. The larger the mean value, the higher the importance of the corresponding influencing factor; the smaller the coefficient of variation, the higher the degree of concentration of the experts’ opinions ($CV$ < 0.25, the reliability of the indicator is considered to be up to standard).

3.3. Establishment of HHM-Based Indicator System for Influencing Factors

This study invited 16 experts, including coal mine managers, rescuers, and university professors, to conduct the research, and the mean, standard deviation, and coefficient of variation of each influence indicator were calculated by the above formula. Limited to space, only some parameters of the indicators are given, as shown in

Table 3. Parameters of selected indicators of impact factors for emergency linkages.

Indicators	${\mathit{E}}_{\mathit{j}}$	${\mathit{\delta }}_{\mathit{j}}$	$\mathit{C}\mathit{V}$
Accident control	4.432	0.496	0.112
Personnel quality	4.069	0.658	0.161
Equipment response	4.128	0.599	0.145
Evacuation capacity	3.971	0.707	0.178
Technical level of operators	3.886	0.781	0.201
Literacy level of operators	3.867	0.857	0.222
Awareness of operator safety responsibilities	3.689	0.768	0.208
Automatic alarm system response	3.997	0.612	0.153
Automatic sprinkler system response	2.687	0.682	0.254
Ventilation and smoke extraction system response	4.178	0.634	0.152
Emergency lighting system response	2.373	0.599	0.253
Ease of evacuation underground	4.009	0.866	0.216
Level of protective equipment	3.687	0.696	0.180
Self-evacuation by operators	3.822	0.808	0.211
Managers organize evacuation	3.883	0.696	0.179

. In the process of establishing the indicators, the experts agreed on most of the indicators, but the coefficients of variation of the indicators of the automatic sprinkler system response and emergency lighting system response were greater than 0.25, which were deleted based on the principles of indicator selection and the results of repeated discussions among the experts.

Based on the identification framework of emergency linkage influencing factors of the HHM, combined with the calculation results of the indicators by the degree of authority of experts, and reasonable screening, we finally obtain the index system of the emergency linkage influencing factors of coal mine gas explosion accidents which contains 3 first-level indicators, 10 second-level indicators, and 24 third-level indicators as shown in

Table 4. Indicator system of factors affecting emergency response to coal mine gas explosion accidents.

Target Variable	First-Level Indicators	Second-Level Indicators	Third-Level Indicators
Emergency re-sponse linkage operation for coal mine gas explosion acci-dents $F$	Accident control $M1$	Personnel quality $S1$	Technical level of operators $B1$
			Literacy level of operators $B2$
			Awareness of operator safety responsibilities $B3$
		Equipment response $S2$	Automatic alarm system response $B4$
			Ventilation and smoke extraction system re-sponse $B5$
		Evacuation capacity S3	Ease of evacuation underground $B6$
			Level of protective equipment $B7$
			Self-evacuation by operators $B8$
			Managers organize evacuation $B9$
	Secondary disaster $M2$	Secondary explosion $S4$	Gas over limit $B10$
			Oxygen content $B11$
		Fire $S5$	Combustible substance $B12$
			High temperature $B13$
		Collapse $S6$	Destruction of the roadway structure $B14$
			Shockwave intensity $B15$
		Toxicity $S7$	Toxic and hazardous gas concentrations $B16$
	Emergency rescue $M3$	Rescue team $S8$	Team rescue experience $B17$
			Team rescue equipment $B18$
			Technical support for team rescue $B19$
		Rescue system $S9$	Reasonableness of rescue program $B20$
			Uniformity of rescue standards $B21$
		Information sharing $S10$	Communications equipment coverage $B22$
			Timeliness of disaster sharing $B23$
			Accuracy of disaster sharing $B24$

, which is reliable and referential to a certain extent.

4. Bayesian Network Modeling of Emergency Linkage Influencing Factors

4.1. Model Construction

Based on the advantages of the Bayesian network, the coal mine gas explosion accident emergency linkage impact indicator system is mapped to form a gas explosion emergency linkage network (Figure 2).

4.2. Fuzzy Probability Calculation

When describing problems, people tend to use vague language to define them. For example, when describing the good or bad of a problem, they often use “very good”, “good”, “general”, “bad”, or “very bad”; when describing the importance of a problem, there are commonly used phrases such as “particularly important”, “very important”, “generally important”, “unimportant”, etc. [34]. Given this, this article introduces seven language variables as domain experts to describe the probability of node variables occurring. The corresponding relationship between language variables and triangular fuzzy numbers is shown in

Table 5. Forms of linguistic probability description.

Serial Number	Language Variable	Triangular Fuzzy Number
1	Very high	(0.85, 0.925, 1)
2	High	(0.75, 0.8, 0.85)
3	Slightly high	(0.55, 0.65, 0.75)
4	Medium	(0.45, 0.5, 0.55)
5	Slightly low	(0.25, 0.35, 0.45)
6	Low	(0.05, 0.15, 0.25)
7	Very low	(0, 0.025, 0.05)

.

(1)

Averaging, which removes the effect of extreme values and makes the results obtained more objective and reasonable, is given by the following formula:

$${\overline{P}}_i={\displaystyle \frac{P_1+P_2+\cdots +P_n}{n}}=\left(\overline{l},\overline{m},\overline{u}\right)$$

(7)

where ${\overline{P}}_i$ denotes the fuzzy probability means; $P_n$ denotes the triangular fuzzy number of the $n$th expert’s score; and $n$ denotes the total number of experts.

(2)

Probability calculation, using the mean area method to convert triangular fuzzy probability into deblurring values, the formula is

$$P_i^{\prime }={\displaystyle \frac{\overline{l}+2\overline{m}+\overline{u}}{4}}$$

(8)

(3)

Normalization, the resulting probabilities are normalized to obtain the standard probabilities, with the formula

$$P_{ij}={\displaystyle \frac{P_{ij}^{\prime }}{\sum _{i=1}^n{P}_{ij}^{\prime }}}$$

(9)

where $P_{ij}$ denotes the probability that the $i$th node is in the $j$th state after normalization; and $P_{ij}^{\prime }$ denotes the probability that the $i$th node is in the $j$th state before normalization.

4.3. Bayesian Reasoning

(1)

Causal reasoning. Also known as forward reasoning, this means that the state of a node has been determined based on a certain cause event, and according to the conditional probability of the distribution between each node, the probability of the event occurring can be calculated. The probability of the event occurring is represented by $P\left(T\right)$, and the calculation formula is

$$p\left(T=S_t\right)=P\left(X_i=x_{\dot{J}}\right)\times P\left(T=\left.S_t\right|X_i=x_j\right)$$

(10)

where $S_t$ is the t-state of the event $(t=\mathrm{1,2},\cdots ,k)$, $P\left(X_i=x_{\dot{J}}\right)$ is the joint probability of the node, $X_i$ denotes the $i$th node, $x_j$ denotes the $j$th state of the node, and $P\left(T=S_t|X_i=x_j\right)$ denotes the conditional probability of Bayesian transmission.

(2)

Diagnostic inference. Under the condition that the event has occurred, the posterior probability of each node can be calculated through the conditional probability distribution between the nodes according to the Bayesian inverse inference technique. The specific formula is

$$P\left(X_i=\left.x_j\right|T=S_t\right)={\displaystyle \frac{P\left(X_i=x_j\right)P\left(T=\left.S_t\right|X_i=x_j\right)}{P\left(T=S_t\right)}}$$

(11)

(3)

Sensitivity analysis. Sensitivity analysis is the main basis for risk analysis and risk decision-making, which can identify accident-causing factors more accurately and quickly. Therefore, this article identifies the key factors affecting the emergency response to coal mine gas explosion accidents through three indicators: Risk Achievement Worth (RAW), Risk Reduction Worth (RRW), and Birnbaum Measure (BM). The larger value of the index indicates higher sensitivity, which is calculated by the following formula:

$$RAW(X_i)={\displaystyle \frac{MAX\left\{P\left(T=S_t|X_i=x_j\right)-P(T=S_t)\right\}}{P\left(T=S_t\right)}}$$

(12)

$$RRW(X_i)={\displaystyle \frac{P\left(T=S_t\right)-MIN\left\{P\left(T=S_t|X_i=x_j\right)\right\}}{P\left(T=S_t\right)}}$$

(13)

$$BM={\displaystyle \frac{RAW\left(X_i\right)+RRW\left(X_i\right)}{2}}$$

(14)

5. Emergency Linkage Network Modeling Analysis

Combining the relevant literature on gas explosions, historical data, and experts’ experience, the interrelationship of each factor is determined, so as to infer the influence of different factors on the operation of emergency response linkage in gas explosion accidents according to the Bayesian network. The data acquisition includes “a particularly serious gas explosion accident at Sunjiawan Coal Mine in Fuxin, Liaoning Province on 14 February 2005”, “a gas explosion accident at Xinxing Coal Mine in Hegang City, Heilongjiang Province on 21 November 2009”, “a vicious gas explosion accident at Soma Coal Mine in Türkiye on 13 May 2014”, “a gas explosion accident at Zachadko Coal Mine in Donetsk State, eastern Ukraine on 4 March 2015”, “a major gas explosion accident at Xintai Coal Mine in Yan’an County, Shaanxi Province on 25 August 2023”, “a coal mine explosion accident at Bakiskan balochistan Province on 19 March 2024”, and 40 other domestic and international cases of gas explosion accidents that have had a large impact on society. Since the unstructured accident data are not convenient for direct calculation, eight experts in the field were invited to make fuzzy language descriptions of the constructed indicator system of emergency linkage influencing factors and the relationship between the factors, which were transformed into structured data according to Equations (7)–(9).

Space limitation intercepts the sub-model personnel quality $S1$ under accident control $P1$ for a detailed description. The root node prior probabilities corresponding to personnel quality $S1$ are shown in

Table 6. Node prior probabilities.

Root node	P (State = High)	P (State = Low)
$B1$	0.84	0.16
$B2$	0.71	0.29
$B3$	0.82	0.18

, and the conditional probabilities are shown in

Table 7. Nodal conditional probabilities.

Root Node			$\mathit{S}1$
$B1$	$B2$	$B3$	High	Low
High	High	High	0.95	0.05
		Low	0.84	0.16
	Low	High	0.72	0.28
		Low	0.39	0.61
Low	High	High	0.65	0.35
		Low	0.29	0.71
	Low	High	0.21	0.79
		Low	0	1

.

The prior probabilities and conditional probabilities of all nodes are input into the GeNIe Academic 4.1 software to obtain the probability distribution graph of the factors affecting the emergency linkage of coal mine gas explosion accidents, as shown in Figure 3.

5.1. Causal Analysis

Coal mine gas explosion belongs to a dynamic process of continuous change, and reasoning and analyzing the factors affecting the accidental emergency linkage can help coal mine managers take necessary measures in time to improve the level of emergency linkage operations. Under normal conditions, i.e., each variable obeys the distribution initially described by the domain experts, the probability of a normal operation of accident and emergency linkage is calculated as 0.781, and the probability of abnormal operation is 0.219 according to Equation (10), and the probability of occurrence of the event in different situations can be quickly inferred from the BN when there is other evidence input. Taking the “worst state” of each root node as an example, under the condition of obeying the initial description of the experts, the a priori probability of each node is adjusted upward by 10% and 20%, and the rate of change of its impact on the emergency response linkage is shown in Figure 4. As can be seen from the figure, when there is a small change in the prior probability of the root node, the impact on the normal operation of the accident emergency linkage is very small. However, when the gas severely exceeds the limit and the ventilation system malfunctions, i.e., when $P\left(B5\right)=1$ and $P\left(B10\right)=1$, the impact on the accident emergency linkage can be deduced using Bayesian networks, and the established inference model is shown in Figure 5. At this time, the probability of accidental emergency linkage non-normal operation is 0.304, and the probability of emergency linkage non-normal operation increases by 38.81% compared with the normal situation. It can be seen that when the coal mine environment changes, through the established accidental emergency linkage Bayesian network, the degree of influence on the operation of the accidental emergency linkage in different situations can be deduced.

5.2. Diagnostic Analysis

The ratio of posterior probability and a priori probability can measure the relationship between the root node and the leaf node, and the larger the ratio of the two, the greater the influence of the root node on the leaf node [35]. Setting the accident emergency linkage operation as an unacceptable range, the ratio of the posterior probability to the prior probability of each root node is shown in Figure 6. It can be seen that the growth rate of the posterior probability of $B5$, $B10$, and $B15$ is larger, which indicates that these factors are more likely to lead to the abnormal operation of the accident emergency linkage. The main reason is that when the accident occurs, under the influence of the violent drive of the chemical reaction of the gas explosion and the obstacles in the coal mine roadway, the explosion shock wave is transformed from the deflagration state to the explosive bombardment state [36], which makes the shock wave cause serious damage to the coal mine roadway in the space, and in the horizontal direction, it pushes and squeezes the electromechanical transport equipment and so on in the roadway, leading to the deformation damage of the equipment and so on; in the vertical direction, it produces huge impact damage to the supporting roof plate, forming a large area of collapse. At the same time, the flame front accompanying the propagation process of the shock wave will make the gas and wood in the roadway very easy to ignite, thus inducing a fire. Influenced by the fluid effect, the gas and toxic and harmful gases quickly disperse in all directions, forming a dynamically changing environment in the disaster area [37,38]. When the ventilation and smoke extraction equipment fail, the disaster area environment is in a state of no wind or light wind, and the gas migration in the collapsed area is hindered due to shock wave damage. A large amount of gas and toxic and harmful gases accumulate, which is very likely to cause serious secondary disasters such as secondary explosions, poisoning, and suffocation.

5.3. Sensitivity Analysis

Based on the established Bayesian network model, taking the “worst state” of each node as an example, the RAW, RRW, and BM index values of each node are calculated according to Equations (12)–(14), and the results are shown in Figure 7. Combined with the results of the three importance degrees, it can be concluded that the factors that rank higher in importance at the root node include the ventilation and smoke extraction system response, the accuracy of disaster sharing, gas over limit, the technical level of the operators, team rescue experience, and so on, which are the key factors affecting the emergency response to gas explosion accidents in coal mines. Therefore, coal mining enterprises should pay attention to the daily management of the ventilation and smoke extraction system, to maximize the guarantee that it can respond normally in accidents; once the ventilation system suffers damage, the gas and other harmful gases cannot be effectively discharged, and in the process of an emergency response linkage, you need to be careful to dispose of the gas-containing gas reservoirs formed by collapsed objects caused by the explosion. At the same time, the construction of sharing information on gas explosion accidents is continuously strengthened. In the event of an accident, the rescue team should take effective measures to control the amount of gas gushing out the first time to avoid more serious secondary disasters. It is necessary to attach great importance to the technical level of the operators and the rescue experience of the team and strengthen the daily training so that the level of emergency response to gas explosion accidents in coal mines is constantly improved.

6. Conclusions

(1)

For the problem of a coal mine gas explosion emergency linkage, the influencing factors are complicated, and this paper proposes a gas explosion emergency linkage influencing factors analysis method based on the HHM and Bayesian networks. The HHM is based on systematic thinking, which can sort out the accident emergency linkage influencing factors more comprehensively. At the same time, based on the knowledge and experience of the experts in various fields, the indicator system established has a certain degree of scientific validity and reliability.

(2)

Through Bayesian causal inference, the probability of normal operation of the coal mine gas explosion emergency response linkage is 78.1%. When the coal mine environment changes, especially when multiple influencing factors occur simultaneously, the level of emergency response linkage operation decreases greatly. Through Bayesian diagnostic analysis, the most likely influencing factors of the accidental emergency linkage can be quickly identified by using Bayesian networks when the gas explosion accident occurs, accordingly reducing the blindness of the accidental diagnosis. Three importance indicators, RAW, RRW, and BM, are introduced to measure the degree of influence of each factor on the emergency linkage, and the results show that the ventilation and smoke extraction system response, the accuracy of disaster sharing, gas over limit, the technical level of the operators, and team rescue experience are the key factors influencing the emergency linkage of the accident.

(3)

In this paper, the acquisition of data contains the gas explosion-related literature, historical data, expert experience, etc., and the future can be integrated with more gas explosion data for analysis, and constantly improve the universality of the analysis method; in addition, the method can also be applied to the coal mine non-gas explosion emergency response linkage factors in the process of analysis and comparison with the results of this paper, in order to more accurately grasp the factors of the emergency response to the gas explosion accident linkage.