Study on Emergency Decision-Making of Mine External Fires Based on Deduction of Precursory Scenarios

Abstract

External mine fires are known for their unpredictability, rapid spread, and difficulty in terms of extinguishment, often resulting in severe casualties and property damage when not managed swiftly. This study examines the progression of coal mine fire incidents through scenario deduction and presents an emergency decision-making model based on precursor scenario analysis. We classify precursor elements according to the causes of coal mine fires, organizing scenario elements into states, precursors, and emergency activities using knowledge meta-theory. A dynamic Bayesian network forms the core of the decision-making model, enabling calculation of scenario node probabilities and the development of expert-driven response strategies for critical scenarios. Additionally, we design a comprehensive evaluation index system, utilizing multi-attribute decision-making to establish decision matrices and attribute weights. An improved entropy-weighting TOPSIS method is used to select the optimal emergency decision scheme. The model’s effectiveness is demonstrated through a case study of the “9–27” fire incident at the Chongqing Songzao Coal Mine, where findings affirm the model’s practicality and accuracy in supporting timely, effective emergency responses to external coal mine fires.

1. Introduction

As the main energy supply in China, coal accounts for more than 2/3 of China’s energy consumption and production structure [1]. Given the unique properties of subterranean environments, the ignition of a coal mine fire can rapidly escalate due to the confined nature of the space and the influx of fresh air, which can exacerbate the blaze. This rapid intensification may quickly lead to uncontrolled conditions and potentially provoke coal dust and gas explosions, thereby causing substantial damage. According to statistics, from 2008 to 2021, 381 accidents occurred in coal mines across the country, and 1441 people died, of which 29 fire accidents caused 203 deaths [2]. Coal mine fire incidents frequently result in significant loss of life, underscoring the necessity for a comprehensive and systematic approach to emergency rescue. Identifying and analyzing the indicators of impending fires is crucial for preventing such incidents and formulating effective emergency responses.

Numerous experts and scholars have extensively studied prevention and mitigation strategies for coal mine fires, encompassing the analysis of coal-related spontaneous combustion [3,4,5], fire detection and monitoring [6], the development of fire prevention and suppression technologies [7,8,9], and emergency responses [10]. Despite this, research on fires ignited by external heat sources remains limited. External fires are often elusive, occur frequently, and escalate quickly, posing a unique challenge compared to those of spontaneous origin [11,12,13]. Unlike spontaneous combustion, which is driven by the internal conditions of the coal, external fires can spread quickly, making them harder to control. This unpredictability significantly increases the risks involved, requiring a multifaceted rescue approach. Timely, well-coordinated rescue strategies are essential in order to minimize damage and loss of life. However, high-stress environments and time constraints complicate decision-making. In such conditions, formulating accurate and effective response plans is a major challenge for decision-makers.

In contemporary emergency management studies, the conventional “prediction-response” model, constrained by its singular analytical approach, often falls short in addressing the complex rescue demands of the modern context. To address this challenge, the academic community has increasingly turned to the adoption of the “scenario-response” framework to guide emergency decision-making. Building on this foundation, many scholars have delved into the evaluation and optimization of emergency decision-making processes based on various theoretical models and algorithms, aiming to significantly enhance response efficiency in complex and dynamic emergency situations. Jing Qu et al. [14] employed a hybrid approach, integrating scenario analysis with a dynamic Bayesian network, to investigate the progression of oil pipeline leakage incidents. Zhe Wang et al. [15] classified the elements of urban flood disaster scenarios as disaster-pregnant environment, disaster-causing factors, disaster-bearing bodies, and emergency management, and established a Bayesian network of urban flood disaster emergency scenarios. Changfeng Yuan et al. [16] summarized the scenario evolution path of oil and gas storage and transportation fire accidents and used the Bayesian network to optimize the scenario path. Xiaoliang Xieh et al. [17] divided the scenario derivation elements into the following categories: the situational state, meteorological factors, emergency activities, decision-maker emotions, and emergency goals. They comprehensively analyzed the coupling relationship between the elements, and studied the influence of these factors on the evolution mechanism of rainstorm disasters. Jinfeng Zhang et al. [18] applied disaster systems theory to analyze the risk evolution dynamics of maritime collision accidents, employing Bayesian network modeling to quantify the associated collision risks for vessels.

Zifu Fan et al. [19] used the method of combining the intuitive fuzzy method and the Topsis method to evaluate the elements of network public opinion emergencies and construct an emergency decision-making model. Zuqin Chen [20] enhanced the efficiency of emergency decision-making by employing processing methods derived from intelligent optimization processes and explored the mechanisms used to generate and refine emergency decision-making strategies. Zhixia Zhang et al. [21] introduced an enhanced emergency decision-making model tailored for natural gas pipeline emergencies, leveraging an improved version of the VIKOR method to optimize the decision-making process. Baode Li et al. [22] introduced a novel dynamic approach to emergency response decision-making, addressing the issue of ambiguity under bounded rationality and enhancing the impact of initial assessments on subsequent decisions throughout the dynamic adjustment phase. Pingping Wang et al. [23] introduced a novel method for large-group emergency decision-making, grounded in Bayesian theory, relative entropy, and Euclidean distance metrics. It accounts for variability among alternatives under identical attributes and contrasts these alternatives with an ideal solution to discern differences.

This study aims to analyze the precursor events of external fire hazards in coal mines and proposes a “scenario response” emergency decision-making model, along with its associated deduction process. Based on scenario analysis and the extraction of accident precursor characteristics, the study applies knowledge element theory to express these elements and investigates the key components of emergency scenarios. Using Bayesian networks, this paper constructs and deduces an emergency scenario model for coal mine fire accidents. Based on key scenarios, it proposes improved emergency decision-making strategies. The objective is to enhance the prevention level of such fire accidents and provide a solid theoretical foundation and reference for emergency decision-making in this context.

2. Methods

2.1. Analysis of Precursors

A scenario represents the subjective interpretation of an impending environment or situation that individuals confront before taking action. The nature of scenarios evolves with the development stages of potential accidents, making their definition fundamental to the process of scenario deduction [24,25,26]. Through a comprehensive analysis of coal mine fire accident scenarios and the trends in their development, we can understand the situation map of scenario evolution, providing a foundation and basis for emergency decision-making.

The classification of precursor scenario elements for coal mine fires should consider various factors for qualitative analysis. This paper, designed based on the classification method of ignition sources, aims to reflect the nature of the external causes leading to fire accidents. Working according to the classification method of precursory scenarios of coal mine fire accidents, by studying 61 coal mine fire accidents with specific causes from 2005 to 2023, the precursory scenarios of fire accidents outside coal mines are summarized, as shown in

Table 1. Statistical table of precursory scenarios of coal mine fire accidents from 2005 to 2023.

Precursory Scenario	Numbers	Scale
Spontaneous combustion	8	9.09%
Electrical cable fire	11	12.50%
Cable short circuit	11	12.50%
Distribution board overload and sparking	1	1.14%
Coal electric drill short circuit and sparking	2	2.27%
Overloaded cable ignition	1	1.14%
Air compressor malfunction	8	9.09%
Transformer fire	2	2.27%
Unauthorized blasting	3	3.41%
Arson	1	1.14%
Spontaneous ignition of explosives	2	2.27%
Workers carrying open flames	2	2.27%
Open flames for heating	1	1.14%
Conveyor belt ignition	2	2.27%
Friction sparks	4	4.55%
Violation of electric welding regulations	2	2.27%

.

An examination of Table 1 reveals that external fires constitute a significant majority of incidents, representing 90.91%, and substantially exceed the occurrence of internal fire accidents. Regarding external fires, a high likelihood of accidents is attributed to causes such as cable short circuits, electrical cable fires, and air compressor malfunctions. These events are associated with numerous precursory scenarios, including cable short circuits and electrical cable fires.

Working according to the statistics of fire accidents outside coal mines and the summary analysis of accident case information, the scenario elements of fire accidents outside coal mines are summarized and sorted out based on the design of precursory scenarios, and a total of 13 secondary scenario information components are outlined, as shown in Figure 1.

2.2. Evolution Path of Fire Scenarios

A knowledge element can be regarded as the fundamental unit of analysis within an event, objectively representing various conceptual entities [27,28,29]. Utilizing the knowledge meta-model enables a more granular depiction of the progression of coal mine fire incidents. This approach is particularly relevant for the analysis and assessment of emergency decision-making processes during such incidents. The scenario elements have been categorized through the examination and extraction of precursory elements associated with external fire accidents in coal mines. This categorization aligns with the sequence of accident development and includes the scenario state (S), precursory elements (E), and emergency activities (A).

The term ‘scenario state’ primarily denotes the condition of the emergency subject, encompassing both the state of the disaster-initiating and disaster-affected entities. It sequentially incorporates the pre-accident scenario state, the in-accident state, and the post-accident state. The ‘precursory element’ signifies indicators that foreshadow the emergence of each situational state, suggesting an impending event. ‘Emergency response activities’ encompass the array of actions and measures implemented at various coal mine fire accident progression stages. These activities are designed to prevent incidents or mitigate the resulting casualties and property damage.

The knowledge meta-model, denoted as G = [S,E,A], is formulated to categorize the aforementioned scenario elements. The three integral components of this model interact dynamically to constitute a cohesive unit, as illustrated in Figure 2.

The current scenario state, denoted as (S), encompasses both the pre-accident and in-accident conditions. Subject to the influence of the precursory element (E) and the emergency activities (A), the scenario state is transformed, evolving into the subsequent state. This transition represents a comprehensive scenario evolution process, which is a basic unit of the progression of external coal mine fire accident scenarios.

The emergency decision-making entity must accurately apprehend the state of the situation at specific temporal intervals and devise appropriate accident mitigation measures based on the prevailing real-time conditions. The objective is to guide the accident scenario towards resolution and disappearance. When the impact of emergency actions is constructive and steers the scenario along a trajectory that aligns with the decision-makers’ intentions, this transformation is characterized as a positive response. Conversely, the emergency objectives may remain unmet due to factors such as inadequate response resources, and the scenario may diverge onto an undesired path from the decision-makers perspective, leading to an exacerbation of the accident’s impact. In that case, the transformation is deemed a negative response. Accordingly, the potential evolution of external coal mine fire accidents can be bifurcated into two directional outcomes: pessimistic and optimistic trajectories.

2.3. Dynamic Bayesian Networks

Dynamic Bayesian networks extend the Bayesian network framework by incorporating the temporal dimension, enabling the modeling of event evolution over time. This approach captures the dynamics and progression patterns of variables within a system [30]. In the context of coal mine fire incidents, the network is constructed by identifying key variables that characterize the accident’s progression, including the intensity of precursor indicators, the extent of fire spread, and the capacity of emergency response forces [31].

The dynamic Bayesian network extends the foundational Bayesian network of sudden accidents by incorporating temporal nodes, thereby accounting for the temporal dimension. This network facilitates temporal situational reasoning, as depicted in Figure 3. By analyzing the evolution patterns of sudden accidents, the interrelationships among node variables are identified. The directed arrows within the network illustrate the interactions between the scenario state (S), precursory elements (E), and emergency activities (A) at various time points. For instance, E₁ comprises E₁₁, E₁₂, E₁₃, etc., A₁ includes A₁₁, A₁₂, A₁₃, etc., and S₁ encompasses S₁₁, S₁₂, S₁₃, etc., with E₁ and A₁ jointly influencing S₁. Specifically, the initial scenario at time t₁ impacts the scenario state at t₂, which in turn affects the state at t₃, and this sequence continues until the scenario state at time t_n either materializes or dissipates.

This study ascertains the probabilities of scenario elements that are without parent nodes by analyzing historical cases, and subsequently deriving their conditional probabilities. Once the node variables are established within the network, it is essential to define their value ranges and possible states. These states must be categorized spatially based on the intrinsic characteristics of each node, encompassing all potential values that the variables can assume.

If A and B be the two fundamental events of E, and P(A) > 0, the Bayesian formula can be expressed as follows:

$$P\left(B_i|A\right)={\displaystyle \frac{P\left(A|B_i\right)\ast P\left(B_i\right)}{{\sum }_{j-1}^{n}P\left(A|B_j\right)\ast P\left(B_j\right)}}$$

(1)

2.4. Emergency Decision-Making Plans

2.4.1. Multi-Attribute Emergency Decision-Making Methods

Based on classification by the number of alternatives, multi-objective decision-making problems also manifest as multi-attribute decision-making issues. Multiple-attribute decision-making (MADM) primarily addresses the task of ranking a finite set of decision schemes based on multiple attributes. Emergency multi-attribute decision-making involves sorting various emergency decision-making plans according to the comparative outcomes of each indicator within an indicator system and a defined evaluation strategy [32]. Solving a multi-attribute decision-making problem typically involves analyzing the decision-making within a constrained set of schemes, identifying the influential decision-making factors, establishing an evaluation index system for these factors, constructing and standardizing the matrix after assigning weights, and comprehensively ranking the decision-making schemes based on the calculated attribute weights [13].

In the context of coal mine fire emergencies, the entropy-weighting TOPSIS method is particularly effective. It dynamically adjusts the weights of decision attributes based on their variability, making it adaptable to the uncertain and evolving nature of emergency situations. Unlike other methods, such as AHP or VIKOR, which rely on fixed weights or subjective judgments, TOPSIS ensures that the decision-making process accounts for the changing importance of each factor in real time. This makes it an ideal choice for coal mine fire emergency decision-making, where rapid, data-driven responses are critical.

This study integrates scenario analysis to construct the emergency decision-making process derived from scenario deduction, as depicted in Figure 4.

2.4.2. Evaluation Indicator System

Following a coal mine fire accident, the severity of the consequences often complicates the execution of emergency rescue operations. Consequently, it is imperative for decision-makers to swiftly make accurate emergency decisions and ascertain the optimal sequence of actions within a constrained timeframe.

At present, each coal mine formulates its own emergency plans based on available resources and response capabilities. While existing research predominantly allocates indicators for assessing the hazards of coal mine fires, there remains a degree of ambiguity in defining the comprehensive evaluation indicators for the emergency decision-making process. This study, in conjunction with the content of general coal mine fire emergency response measures and coal mine fire emergency plans, as well as the International Safety Rating System (ISRS), establishes a comprehensive evaluation index system for emergency countermeasures. The multi-level indicators are refined step by step, ensuring independence among different indicators. It is presented in

Table 2. Comprehensive evaluation index system for emergency countermeasures.

Primary Indicator	Secondary Indicator	Tertiary Indicator
Emergency response	Rescue response	Timeliness of rescue response
		Accuracy of rescue response
Emergency investment	Material input	Quantity of firefighting equipment
		Amount of medical supplies used
	Labor input	Number of enterprise self-rescue personnel
		Number of professional rescue personnel
		Number of medical staff
Personnel safety	Affected employees	Number of rescued employees
		Transfer of affected employees
		Placement of affected employees
Emergency process	Accident site control	Control of accident
Post-incident recovery	Prevention of accident recurrence	Enhancement of disaster resistance

.

2.4.3. The Entropy Weight Method

This study employs the entropy method to calculate the weights of various scenario elements and assign corresponding values to these elements based on the characteristics of external coal mine fire accidents.

Let there be m emergency decision-making schemes, with the set of attribute indicators for the alternative decision schemes denoted as X. Given K assessment indicators X₁, X₂, …, X_k, the data standardization formula is presented as Equation (2). The standardized values for each indicator after data standardization are Y₁, Y₂, …, Y_k.

$$Y_{\mathit{ij}}={\displaystyle \frac{X_{\mathit{ij}}-\mathit{min}\left(X_I\right)}{\mathit{max}\left(X_i\right)-\mathit{min}\left(X_i\right)}}$$

(2)

Following data standardization, the frequency of occurrence for the standardized data, denoted as P_ij, is calculated, as illustrated in Equation (3). Subsequently, the information entropy for each indicator is determined based on Equation (4), which facilitates the assessment of the relative importance and variability of the data across different indicators.

$$P_{\mathit{ij}}={\displaystyle \frac{Y_{\mathit{ij}}}{\sum _{i=1}^n{Y}_{\mathit{ij}}}}$$

(3)

$$H_{\mathit{ij}}=-{\mathit{ln}\left(n\right)}^{-1}{\sum }_{i=1}^n{p}_{\mathit{ij}}$$

(4)

Utilizing the formula for information entropy, the entropy values for each indicator, denoted as H₁, H₂, …, H_k, are computed. Subsequently, the weights of the indicators are calculated based on their respective information entropy values, as demonstrated in Equation (5). This approach ensures that the weights assigned to each indicator reflect their degree of uncertainty and contribution to the decision-making process.

$$W_i={\displaystyle \frac{1-H_i}{k-\sum _{i=1}^n{H}_i}}\left(i=1,2,\dots ,k\right)$$

(5)

2.4.4. The Improved TOPSIS Method

The TOPSIS method evaluates the effectiveness of schemes based on their closeness to the ideal and negative ideal solutions. The ideal solution represents the optimal values of decision attributes, while the negative ideal solution represents the worst values. A scheme closest to the ideal solution and farthest from the negative ideal solution is considered the best; conversely, a scheme not as distant from the negative ideal is deemed less favorable.

Initially, it is essential to construct a weighted standardization matrix V, as depicted in Equation (6).

$$V={\left(W_j{P}_{\mathit{ij}}\right)}_{\mathit{mn}}$$

(6)

It is necessary to identify the positive ideal point and the negative ideal point $L_j^{+}$, $L_j^{-}$.

$${ L}_j^{+}=\left(v_1^{+}, v_2^{+}, \dots v_j^{+}\right),j=1, 2, \dots , j$$

(7)

where $v_j^{+}=\mathit{max}{v}_{ij}$.

$$L_j^{-}=\left(v_1^{-},v_2^{-},\dots v_j^{-}\right),j=1,2,\dots ,j$$

(8)

where $v_j^{-}=\mathit{min}{v}_{ij}$.

It is necessary to calculate the Euclidean distance $d_j^{+}$,$d_j^{-}$:

$$d_j^{+}=\sqrt{{\sum }_{i=1}^n{\left(v_{\mathit{ij}}-v_j^{+}\right)}^2}$$

(9)

$$d_j^{-}=\sqrt{{\sum }_{i=1}^n{\left(v_{\mathit{ij}}-v_j^{-}\right)}^2}$$

(10)

For the ith emergency decision-making scheme, the comprehensive attributes are defined as follows:

$$C_j^{+}={\displaystyle \frac{d_j^{-}}{d_j^{+}+d_j^{-}}},0\le C_j^{+}\le 1$$

(11)

Ultimately, by assessing the comprehensive attributes, this study aims to establish the optimal sequence for emergency decision-making in the event of coal mine fires.

3. Results and Discussion

3.1. Case Study

On 27 September 2020, a catastrophic fire occurred at the Songzao Coal Mine in Chongqing, resulting in 16 fatalities and 42 injuries, with a direct economic loss of CNY 25.01 million. This analysis is based on the scenario delineated in the accident investigation report.

Before the incident, a roller became jammed and eroded, creating a breach. The accumulation of coal gangue beneath the conveyor belt allowed pulverized coal to infiltrate the device and accumulate there, causing the roller to rupture. The substandard safety performance of the belt, coupled with sliding friction against the roller, generated intense heat and sparks, igniting the accumulated coal dust.

During the accident, underground personnel detected abnormal belt friction and promptly alerted the mine’s dispatch room to cease belt operations. Post-emergency shutdown, the belt’s inadequate flame retardancy led to ignition by the burning coal dust. The fire intensified due to the influx of fresh air in the tunnel, resulting in the combined combustion of the belt and coal. The expanding flames caused damage to electrical equipment and impacted ventilation systems.

Post-accident, the toxic and high-temperature smoke produced by the fire rapidly dispersed across the coal mining face, leading to significant casualties.

3.1.1. Scenario Evolution Path

According to the description of the accident, the accident scenario nodes are set as shown in

Table 3. Analysis of scenario elements.

Scenario State (S)	Precursory Elements (E)	Emergency Activities (A)
Friction on the conveyor belt generates intense heat and sparks (S1)	The belt’s friction leads to excessive heat and ignition sources (E1)	Implement dust suppression and cooling measures
Accumulated coal dust ignites (S2)	The accumulation of coal dust creates an explosive environment (E2)	Activate water sprinkling systems to extinguish the fire
The incident is mitigated (S3)
The belt catches fire due to substandard quality (S4)	The belt’s inadequate flame retardancy is compromised (E4)	Utilize water cannons for targeted cooling and fire suppression
The incident is mitigated (S5)
The belt and coal undergo mixed combustion (S6)	The belt’s surface is contaminated with combustible dust (E6)	Deploy deluge systems to intercept and extinguish the fire
The incident is mitigated (S7)
Adjacent equipment and facilities catch fire (S8)	A short circuit occurs in the electrical system (E8)	Initiate power shutdown and use dry powder extinguishers to combat the fire
The incident is mitigated (S9)

.

After identifying the node variables within the accident network, causal relationships between these variables are delineated with arrows in order to form a directed acyclic graph (DAG). This DAG represents the scenario states of the Songzao coal mine fire accident, providing a more intuitive and clear illustration of the interconnections between scenarios, as depicted in Figure 5.

The evolution path diagram of the fire accident scenario at the Songzao Coal Mine illustrates that the horizontal positive evolution path depicts the optimal progression of the fire: S₁→S₂→S₃. Conversely, the vertical negative evolution path is represented by S₁→S₆→S₈.

3.1.2. Calculation of Scenario Node Probabilities

Referencing the evolution network depicted in Figure 6 and leveraging historical empirical data, the prior probabilities for nodes without antecedents are established, as illustrated in

Table 4. Prior probabilities of network node variables.

Node Computing	Prior Probabilities
P(S1)	P(E1 = T) = 0.7	P(E1 = F) = 0.3
	P(A1 = T) = 0.9	P(A1 = F) = 0.1
P(S2)	P(E2 = T) = 0.75	P(E2 = F) = 0.25
	P(A2 = T) = 0.96	P(A2 = F) = 0.04
P(S4)	P(E4 = T) = 0.87	P(E4 = F) = 0.13
	P(A4 = T) = 0.95	P(A4 = F) = 0.05
P(S6)	P(E6 = T) = 0.73	P(E6 = F) = 0.27
	P(A6 = T) = 0.92	P(A6 = F) = 0.08
P(S8)	P(E8 = T) = 0.8	P(E8 = F) = 0.2
	P(A8 = T) = 0.9	P(A8 = F) = 0.1

. For nodes with parent nodes within the network, conditional probabilities are ascertained through a synthesis of data analysis and expert judgment, as detailed in

Table 5. Conditional probability distribution of network node variables.

Node Computing	Prior Probabilities
P(S1)	P(S1 = T|E1 = T, A1 = T) = 0.94
	P(S1 = T|E1 = T, A1 = F) = 0.80
	P(S1 = T|E1 = F, A1 = T) = 0.75
	P(S1 = T|E1 = F, A1 = F) = 0.40
P(S2)	P(S2 = T|E2 = T, A2 = T,S1 = T) = 0.87
	P(S2 = T|E2 = T, A2 = T,S1 = F) = 0.75
	P(S2 = T|E2 = T, A2 = F,S1 = T) = 0.70
	P(S2 = T|E2 = T, A2 = F,S1 = F) = 0.55
	P(S2 = T|E2 = F, A2 = T,S1 = T) = 0.50
	P(S2 = T|E2 = F, A2 = T,S1 = F) = 0.45
	P(S2 = T|E2 = F, A2 = F,S1 = T) = 0.40
	P(S2 = T|E2 = F, A2 = F,S1 = F) = 0.30
P(S4)	P(S4 = T|E4 = T, A4 = T,S2 = T) = 0.9
	P(S4 = T|E4 = T, A4 = T,S2 = F) = 0.88
	P(S4 = T|E4 = T, A4 = F,S2 = T) = 0.74
	P(S4 = T|E4 = T, A4 = F,S2 = F) = 0.70
	P(S4 = T|E4 = F, A4 = T,S2 = T) = 0.65
	P(S4 = T|E4 = F, A4 = T,S2 = F) = 0.50
	P(S4 = T|E4 = F, A4 = F,S2 = T) = 0.44
	P(S4 = T|E4 = F,A4 = F,S2 = F) = 0.40
P(S6)	P(S6 = T|E6 = T, A6 = T,S1 = T) = 0.88
	P(S6 = T|E6 = T, A6 = T,S1 = F) = 0.75
	P(S6 = T|E6 = T, A6 = F,S1 = T) = 0.70
	P(S6 = T|E6 = T, A6 = F,S1 = F) = 0.64
	P(S6 = T|E6 = F, A6 = T,S1 = T) = 0.58
	P(S6 = T|E6 = F, A6 = T,S1 = F) = 0.51
	P(S6 = T|E6 = F, A6 = F,S1 = T) = 0.45
	P(S6 = T|E6 = F, A6 = F,S1 = F) = 0.36
P(S8)	P(S8 = T|E8 = T, A8 = T,S6 = T) = 0.85
	P(S8 = T|E8 = T, A8 = T,S6 = F) = 0.70
	P(S8 = T|E8 = T, A8 = F,S6 = T) = 0.63
	P(S8 = T|E8 = T, A8 = F,S6 = F) = 0.54
	P(S8 = T|E8 = F, A8 = T,S6 = T) = 0.50
	P(S8 = T|E8 = F, A8 = T,S6 = F) = 0.46
	P(S8 = T|E8 = F, A8 = F,S6 = T) = 0.40
	P(S8 = T|E8 = F, A8 = F,S6 = F) = 0.35

.

Utilizing Equation (3), the probability of the scenario state node S1 is calculated as follows:

$$\begin{array}{c}P\left(S_1=T\right)=P\left(E_1=T\right)P\left(A_1=T\right)P\left(S_1=T|E_1=T,A_1=T\right)+P\left(E_1=T\right)P\left(A_1=F\right)P\left(S_1=T|E_1=T,A_1=F\right)+\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}P\left(E_1=F\right)P\left(A_1=T\right)P\left(S_1=T|E_1=F,A_1=T\right)+P\left(E_1=F\right)P\left(A_1=F\right)P\left(S_1=T|E_1=F,A_1=F\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} =0.592+0.056+0.203+0.012=0.863\end{array}$$

It can be seen from this that $P\left(S_1=T\right)=0.137$.

By extension, the probabilities of the remaining node variables can be determined similarly. Figure 6 illustrates the outcomes of the scenario state probability calculations, facilitated by the Netica5.18 (32 bit) software.

The fire accident at the Songzao Coal Mine was characterized by two primary events: the high temperature and sparks from tape friction S₁, and the ignition of the tape S₄. The respective probabilities of these scenario states were 86.3% and 81.6%. These events led to the mixed combustion of the tape and coal S₆, with a scenario probability of 77.1%. The spread of fire further escalated to involve adjacent equipment and facilities S₈, with a probability of 73.2%. Timely attention to the performance qualification and maintenance of a conveyor belt is crucial in order to prevent excessive friction and sparks resulting from belt heating. Controlling the negative evolution of these precursors can mitigate the risk of accidents. The actual progression of the fire validated the model, as the belt’s substandard flame retardancy led to ignition by burning coal dust, causing a sudden increase in fire intensity. The model’s calculation results align well with field observations, confirming the scientific validity and practical feasibility of the Bayesian network model for use in scenario evolution.

3.1.3. Determination of Weights for Evaluation Criteria

Three analogous cases were identified using the indices of the fire accident scenario evolution path from the Songzao coal mine and statistical data from coal mine fire accidents. The emergency responses for these cases are detailed in

Table 6. Emergency decision-making plans.

Emergency Response Plan	Specific Measures
M1	Evacuate personnel immediately
	Disconnect power sources from electrical equipment
	Use water cannons to extinguish the fire and contain the flames
	Transfer materials in the vicinity to prevent further damage
	Construct firebreaks and water screens to isolate and extinguish the fire
M2	Evacuate personnel immediately
	Deploy 18 squads and 130 rescue personnel to the site
	Utilize fire extinguishers and sprinkler systems to combat the fire
	Extinguish the fire on the intake air side and set up water screens
	Disconnect power sources promptly
	Enhance ventilation in the tunnels to disperse smoke and fumes
	Protect and process residual materials
M3	Evacuate underground personnel promptly
	Seal off the area for isolation and extinguish the fire
	Use fire extinguishers to put out the fire
	Transfer materials in the vicinity and clean up the accident scene

, denoted as M = {M₁, M₂, M₃}. Ten experts assessed the emergency countermeasures based on a comprehensive evaluation index system designed for the three-tiered response to coal mine fires. The scoring was binary, with criteria being met scored as 1 and criteria remaining unmet being scored as 0, reflecting the fulfillment of the index requirements. The compiled evaluation scores for the emergency decision-making are presented in

Table 7. Expert scoring table for scenario emergency decision-making.

No.	Evaluation Criterion
1	Timeliness of rescue response	4	5	8
2	Accuracy of rescue response	5	7	9
3	Quantity of firefighting equipment used	9	4	6
4	Quantity of medical supplies used	7	6	2
5	Number of people engaging in self-rescue	3	8	6
6	Number of medical personnel	5	9	4
7	Number of professional rescue personnel	2	8	3
8	Number of employees rescued	6	3	8
9	Number of people evacuated	4	2	5
10	Number of people relocated for safety	3	7	4
11	Hazard mitigation	4	8	5
12	Enhancement of disaster resistance capacity	8	4	9
		M1	M2	M3

.

Using the expert evaluation table of emergency decision-making in different scenarios, the evaluation matrix X was constructed.

$$X=\left[\begin{array}{cccccccccccc}4& 5& 9& 7& 3& 5& 2& 6& 4& 3& 4& 8\\ 5& 7& 4& 6& 8& 9& 8& 3& 2& 7& 8& 4\\ 8& 9& 6& 2& 6& 4& 3& 8& 5& 4& 5& 9\end{array}\right]$$

By applying Equation (2), the matrix X is normalized to yield Matrix Y.

$$Y=\left[\begin{array}{cccccccccccc}0& 0& 1& 1& 0& 0.2& 0& 0.6& 0.67& 0& 0& 0.8\\ 0.25& 0.5& 0& 0.8& 1& 1& 1& 0& 0& 1& 1& 0\\ 1& 1& 0.4& 0& 0.6& 0& 0.17& 1& 1& 0.25& 0.25& 1\end{array}\right]$$

$$P=\left[\begin{array}{cccccccccccc}0& 0& 0.71& 0.56& 0& 0.17& 0& 0.375& 0.4& 0& 0& 0.44\\ 0.2& 0.33& 0& 0.44& 0.63& 0.83& 0.85& 0& 0& 0.8& 0.8& 0\\ 0.8& 0.67& 0.29& 0& 0.37& 0& 0.15& 0.625& 0.6& 0.2& 0.2& 0.56\end{array}\right]$$

Following normalization, the attribute values of the indicators are confined to the range of [0, 1]. Subsequently, we calculate the information entropy and the corresponding weights.

Utilizing Equation (4), the entropy values are computed as follows:

$${\mathrm{h}}_1=-{\displaystyle \frac{1}{\ln 3}}\left(0.2\ln 0.2+0.8\ln 0.8\right)=0.455$$

The same method was applied to the following data:

$$H_i=\left\{\begin{array}{c}{\mathrm{h}}_1=0.455,{\mathrm{h}}_2=0.577,{\mathrm{h}}_3=0.546,{\mathrm{h}}_4=0.619,{\mathrm{h}}_5=0.601,{\mathrm{h}}_6=0.410,\\ {\mathrm{h}}_7=0.385,{\mathrm{h}}_8=0.602,{\mathrm{h}}_9=0.612,{\mathrm{h}}_{10}=0.455,{\mathrm{h}}_{11}=0.455,{\mathrm{h}}_{12}=0.619\end{array}\right\}$$

where${\sum }_{\mathrm{i}=1}^{12}{\mathrm{h}}_{\mathrm{i}}=6.336$.

By applying Equation (5), it can be seen that

$$W_i=\left\{\begin{array}{c}{\mathrm{w}}_1=0.0962,{\mathrm{w}}_2=0.0747,{\mathrm{w}}_3=0.0802,{\mathrm{w}}_4=0.0673,{\mathrm{w}}_5=0.0703,{\mathrm{w}}_6=0.1042,\\ {\mathrm{w}}_7=0.1086,{\mathrm{w}}_8=0.0703,{\mathrm{w}}_9=0.0685,{\mathrm{w}}_{10}=0.0962,{\mathrm{w}}_{11}=0.0962,{\mathrm{w}}_{12}=0.0673\end{array}\right\}$$

The number of professional rescue personnel has the highest weight, indicating that the equipping of professional rescue forces is the most critical factor in emergency decision-making. The reasonable allocation of professional rescue personnel can significantly improve the efficiency and effectiveness of rescue, which is the core component of the rationality of decision-making; the importance of the number of medical personnel ranked second, indicating that in the emergency response process, the medical support for the rescue of the affected persons as well as the ability to follow up the treatment is very critical; the timeliness of the rescue response, the resettlement of the number of people, and the elimination of dangerous situations of the weight of the three indicators tied for the third, which reflects that the time efficiency of the response, the ability to resettle the affected persons, and the elimination of dangerous situations have an important impact on decision-making. The timeliness of rescue response is the third most important indicator, reflecting the time efficiency of the emergency response and the ability to resettle the affected people. The elimination of dangerous situations has an important impact on the decision-making process.

3.1.4. TOPSIS Method

Utilizing Equation (6), the weighted standardized decision matrix V is derived as follows:

$$V=\left[\begin{array}{cccccccccccc}0& 0& 0.0569& 0.0377& 0& 0.0024& 0& 0.0264& 0.0274& 0& 0& 0.0296\\ 0.0192& 0.0247& 0& 0.0296& 0.0444& 0.0865& 0.0923& 0& 0& 0.0770& 0.0770& 0\\ 0.0770& 0.0500& 0.0233& 0& 0.0260& 0& 0.0163& 0.0439& 0.0411& 0.0192& 0.0192& 0.0377\end{array}\right]$$

Equations (7) and (8) are applied to determine the positive and negative ideal points, respectively.

$$L_j^{+}= \{0.0770, 0.0500, 0.0569,0.0377,0.0444, 0.0865,0.0923,0.0439,0.0411,0.0770,0.0770,0.0377\}$$

$$L_j^{-}= \{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0\}$$

Using Equations (9) and (10), the Euclidean distances $d_j^{+}$, $d_j^{-}$.

$${ d}_j^{+}=\{0.0384, 0.0123, 0.0228 \}$$

$${ d}_j^{-}=\{0.0070, 0.0317, 0.0157\}$$

Using Equation (11), the relative closeness index for each alternative is determined.

$$C_j^{+}=\{0.1542, 0.7205, 0.4078\}$$

Comprehensive evaluation utilizing the TOPSIS method yielded the following results: M₂ exhibits the greatest proximity to the optimal solution vector, while M₁ aligns most closely with the worst solution vector. The schemes are ordered based on the magnitude of their comprehensive attribute values (C_j), with the sequence being M₂ > M₃ > M₁. Specifically, M₂ possesses the highest comprehensive attribute value of 0.7205, signifying its superiority in terms of emergency response effectiveness and identifying it as the optimal strategy. In contrast, M₁ demonstrates relatively inferior performance. Decision-makers can utilize these insights to inform their choices accordingly.

The highest attribute value for M₂ indicates that emergency decision-making should focus on measures covering evacuation, rescue, firefighting, the protection of materials, and ventilation to ensure that all aspects are coordinated and linked. The adequate allocation of rescue personnel and equipment contributes more than other factors to the rationality of the overall response. Strengthening the input of professional rescue forces, especially in the initial stage in order to ensure that the number of ambulance personnel is sufficient and equipment is in place, can significantly improve the effectiveness of emergency decision-making. In order to achieve a more efficient and reasonable emergency response in complex environments, future emergency decision-making should focus on the optimal allocation of integrated resources and the comprehensive control of risks. At the same time, it is necessary to increase the input of professional rescue forces, strengthen the isolation and protection measures in key areas, and formulate a systematic and flexible emergency response programme, so as to comprehensively improve the level of emergency management.

3.2. Discussion

By analyzing the characteristics and classification of coal mine fire accidents, this study applies the foundational theories of scenario analysis to investigate the extraction of critical scenarios and the methods of precursor scenario deduction. Furthermore, it integrates dynamic Bayesian theory to account for temporal factors and probabilities, thereby enhancing the emergency decision-making process with a combination of qualitative and quantitative analysis. This approach not only enriches the application of precursor scenario deduction methods in emergency decision-making for such incidents but also advances identification techniques and research into precursor scenarios for coal mine fire accidents. It contributes to the body of emergency decision-making theories, offering theoretical guidance and methodological references for emergency decision-making in coal mine fires.

This study pioneers a novel perspective in the realm of emergency decision-making for coal mine fire accidents. Its findings have the potential to enrich the theoretical framework of precursor scenario deduction and offer substantial practical benefits for enhancing emergency response capabilities in China. By pinpointing and examining key precursor scenarios, this research enables the timely assessment of coal mine fire accident scenarios. It facilitates subsequent scenario deduction and provides innovative guidance for the design of response strategies during actual incidents. This approach is expected to popularize the emergency decision-making model grounded in precursor scenario deduction, thereby increasing the efficiency of emergency decisions and elevating the overall prevention and mitigation strategies against such accidents. This will ultimately improve the emergency management level of coal mine fire accidents in China, reduce the incidence of accident precursors, and mitigate the resulting losses and injuries, underscoring its profound practical significance.

While scholars worldwide have delved into scenario-based emergency decision-making, elucidating its evolution mechanisms [33,34,35,36] and scenario connotations [37], there remains a need for further in-depth exploration of situation deduction and decision-making mechanisms. Traditional model scenario deduction is characterized by static analysis, which fails to account for the dynamic nature of scenarios over time, relying solely on static analyses to make emergency decisions. In contrast, the “scenario response” model incorporates dynamic analysis within its steps and processes [38,39]. Yet, it is often confined to qualitative assessments and lacks robust evidential support for emergency decision-making, indicating an area ripe for further research.

In the field of sudden accident emergency decision-making, various index systems are proposed and evaluated through scenario analysis, leading to the construction of tailored emergency decision-making models. These models reflect the specific scenarios that different emergencies present. Although experts have achieved considerable success in researching the theory and technology of emergency decision-making under diverse scenario modes, the evolving complexity of coal mine fires necessitates the ongoing exploration and enhancement of existing emergency decision-making technologies and theories.

4. Conclusions

Traditional approaches to emergency decision-making have been reactive and insufficient in terms of the proactive management of modern emergency response scenarios. This study addresses these limitations by introducing scenario deduction theory, grounded in the analysis of accident precursors. Through historical case analysis, the study extracts elements of precursor scenarios and investigates the patterns and pathways of scenario evolution. Utilizing the dynamic Bayesian network, an emergency decision-making model based on precursor scenario deduction is constructed. This model is enhanced through the entropy weight method and an improved TOPSIS method to facilitate more optimized decision-making processes. The model’s efficacy is demonstrated through analysis and validation with real-world coal mine fire accident cases. The key findings of the study are as follows:

• The accident evolution process is decomposed into three critical components: scenario states (S), emergency activities (A), and precursory elements (E). By analyzing these elements, a scenario evolution law is established, enabling the visualization of fire accident scenarios outside coal mines.
• This study constructs an initial Bayesian network structure to serve as a foundation for subsequent analysis. Utilizing dynamic Bayesian network methodologies, we calculate the probabilities of accidents and predict their potential future trajectories. Furthermore, we employ the Netica to facilitate the quantitative computation of scenario probabilities, culminating in the development of an emergency decision-making model.
• We employ the entropy weight method and an improved TOPSIS method for the quantification and weighting of emergency decision-making schemes. The establishment of a three-tiered emergency decision-making evaluation index system enhances the targeted nature of emergency decision-making. This contributes to the efficiency and accuracy of responses to external coal mine fires and expands the application of scenario deduction theory within the domain of coal mine fire accidents.