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Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39232059
71004
10.1038/s41598-024-71004-2
Article
Research on coal mine safety risk evolution and key hidden dangers under the perspective of complex network
Su Guorui horyhu@126.com

Hu Eryi
Information Research Institute of the Ministry of Emergency Management, Chaoyang, Beijing, 100029 China
4 9 2024
4 9 2024
2024
14 2062425 9 2023
23 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
In order to find out the main causes of coal mine safety accidents and improve the pertinence of coal mine safety risk management and control, the identification and analysis of coal mine safety risks and hidden dangers are carried out based on the analysis of coal mine accident reports. Combing the complex network theory, a complex network model for the evolution of coal mine safety risks is constructed. The key elements that affect coal mine safety risk accidents are obtained through quantitative research on the characteristic indicators of the complex network model of coal mine safety risks. And the key nodes of coal mine safety risk spread network are obtained through network interference to the overall efficiency. The research results show that the complex network of coal mine safety risks illustrate the characteristics of a small-world network, and the spread of a certain risk is likely to cause coal mine safety accidents. Strengthening the risk management and control of hidden dangers with higher intermediate centrality can isolate the spread of coal mine safety risks and reduce the possibility of coal mine accidents.

Keywords

Coal mine safety risk
Complex network
Risk evolution
Risk control
Subject terms

Energy science and technology
Engineering
S&T Innovation and Development Project of Information Institution of Ministry of Emergency Management2024507 Su Guorui http://dx.doi.org/10.13039/501100001809 National Natural Science Foundation of China 52274159 Hu Eryi issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

The identification of major safety hazards in the evolution process of safety risks is of great significance for management and control of industrial safety risks and coal mine safety risks (CSR)1–3. Scholars have conducted extensive research on industrial safety risks analysis from two aspects. First, regarding research on risk control based on risk evolution mechanisms, in 2014, Li4 analyzed industrial safety risks by utilizing risk mechanisms and established the “six-ization” risk control system, which was applied to coal enterprises later. In 2017, Deng et al.5 constructed a complex network model of industrial safety risks and analyzed the evolution characteristics of mine accidents based on the evolution of safety risks. He et al.6 established a CSR model known as the safety management mechanism model by exploring risk evolution mechanisms. In this model, 18 types of causal processes that led to changes in effectiveness of safety management were analyzed. Wei7 explored the evolution mechanisms of mine accidents and discussed the application effect of dual-prevention mechanism in coal enterprises. Zhang8 investigated the hierarchical control of potential hazards in coal mines based on the risk-hazard-accident evolutionary logic. Second, with respect to identification and analysis on safety risks through evaluation theories, Pi et al.9 established a comprehensive evaluation model for explosion risks of coal mine gas by applying prospect theory and interval numbers. Knowing the underground hazards, Su10 combined the risk matrix method and the LEC (likelihood, exposure, exposure) method to scientifically identify the risk factors in confined space in coal mines. Huang et al.11 built a coal mine risk identification and evaluation model based on IAHP-SPA(improved analytic hierarchy process - set pair analysis) by constructing a risk identification index system for underground coal mines, thereby achieving hierarchical management and control of underground coal mines.

In recent years, an increasing number of studies have used Bayesian networks (BN) and fault tree analysis (FTA) to construct accident analysis models12–14. Among them, BN is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). In the context of CSR management, BN can be used to model the complex interactions between various risk factors, hazards, and potential accidents. In these models, hidden dangers are considered as the main risk factors and are comprehensively analyzed through causal networks15,16. Current research on industrial safety risks predominantly concentrates on risk identification and risk control, which are generally executed sequentially rather than simultaneously investigating safety risks from both perspectives. Furthermore, elements expressed as hidden dangers are not only critical in the context of CSR but can also be considered as main risk factors in accident analyses constructed with causal networks, such as BN and FTA17. This dual perspective allows for a more comprehensive understanding of risk propagation and control. Unlike traditional accident analysis methods that often consider risks in isolation, our approach integrates the complex interactions of multiple risk factors using network theory, providing a more holistic view of risk propagation and control18. Moreover, as a result of insufficient in-depth exploration of key risks and hazards in the process of risk evolution, targeted and reasonable measures for risk control are scarcely proposed. Furthermore, the complex network theory has been widely adopted to investigate risk factors19–22, yet its application in the field of CSR analysis is still in a blank currently.

In view of the above facts, risk causes of mine accidents were explored in this study, and complex network theory was introduced to construct a CSR evolution model based on the risk-hazard-accident logic. This approach underscores the interconnectedness of hidden danger and their potential to escalate into major accidents if not properly managed. The importance of network parameters, such as node centrality and network density, is emphasized as they provide insights into the critical points of intervention for preventing accident escalation. The advantage of using network parameters, such as node centrality and network density, lies in their ability to reveal critical intervention points that are not easily identified through traditional analysis methods. Besides, the characteristic indicators of the established complex network were investigated, and the key nodes that affect potential hazards were analyzed. Moreover, the main factors affecting CSR were discovered. This study aims to provide a new clue for research on the identification and control of CSR and leverages BN to enhance the understanding of CSR by integrating the probabilistic modeling capabilities of BN with the structural insights provided by complex network theory. This combined approach allows for a more comprehensive analysis of coal mine safety risks, addressing both identification and control in a unified framework.

Complex network theory

The complex network theory, which is proposed based on the graph theory, enables models that involve complex relationships in social and engineering problems to be constructed systematically. Taking full advantage of the complex network theory can facilitate the solution of prominent problems of complex and interrelated structural networks23. In this theory, individuals are denoted by nodes; relationships between individuals are represented by edges; and topological structures of complex networks are constructed by abstracting and peeling off real-world relationships. In addition, the network density, characteristic path length, degree centralization, network diameter, clustering coefficient, and global efficiency are commonly used for quantitative analysis on complex networks24,25. The analysis process of complex network theory can be explained as follows. Firstly, the important nodes and interrelationships of the problem are peeled off, and the actual problem is modeled abstractly. Next, the essence of the established model is revealed, and the evolution characteristics of the system are analyzed from the perspectives of systematic structural characteristics and life cycle evolution. Finally, the key nodes in the system are discovered, and a deeper understanding of the complex system can be acquired.

Construction of complex network of CSR evolution

Analysis on CSR factors

Mine accidents are normally induced by the joint effect of multiple factors, including human factors, equipment factors, environmental factors, inherent factors, management factors, other hidden dangers in production etc. A mine accident often undergoes a series of evolution and propagation before it breaks out. It starts with the inherent risk factors in mining activities; as coal production progresses, the control measures for inherent risks gradually fail and evolve into potential hazards; after the rectification of safety hazards fails, they eventually lead to mine accidents.

Based on the above analysis, risk causes from 63 mine disaster reports published by the National Coal Mine Safety Supervision Bureau were extracted. After that, the hidden hazard factors in the reports were reanalyzed, and then the evolution logic of the mine disasters was established to be “risk factors-safety hazards-mine disasters” (RF-SH-MD). For simplicity, the 24 risk factors, 13 safety hazards, and 7 types of mine disasters are signified by RF 01–24, SH 01–13, and MD 01–07, respectively, as listed in Tables 1, 2 and 3.

Table 1 Numbers of coal mine safety risk factors.

Number	Risk factor	Number	Risk factor	
RF01	Insufficient safety supervision	RF13	Gas concentration	
RF02	Unimplemented corporate principal responsibility	RF14	Rock burst tendency	
RF03	Illegal production	RF15	Goaf water	
RF04	Security management confusion	RF16	Coal dust explosion tendency	
RF05	Inadequate technical management	RF17	Geological structural complexity	
RF06	Inadequate safety training	RF18	Unexecuted technical measures	
RF07	Unreasonable labor organization	RF19	Unexecuted outburst prevention measures	
RF08	Technical management defect	RF20	Inadequate system implementation	
RF09	Inadequate risk identification	RF21	Poor safety awareness	
RF10	Inadequate hazard screening	RF22	Illegal operation	
RF11	Imperfect system	RF23	Imperfect information system	
RF12	Insufficient security investment	RF24	Defective system equipment	

Table 2 Numbers of coal mine safety hidden dangers.

Number	Safety hazard	Number	Safety hazard	
SH01	Inadequate supervision	SH08	Monitoring system failure	
SH02	Illegal production	SH09	Gas overrun	
SH03	Illegal operation	SH10	Electrical equipment hazard	
SH04	Insufficient safety management	SH11	Support hazard	
SH05	Insufficient safety awareness	SH12	High coal dust concentration	
SH06	Insufficient personal training	SH13	Exploring potential water hazard	
SH07	Insufficient technical measures			

Table 3 Numbers of coal mine accident types.

Number	Types of coal mine accidents	Number	Types of coal mine accidents	
MD01	Fire accident	MD05	Rock burst accident	
MD02	Coal dust explosion accident	MD06	Roof accident	
MD03	Gas explosion accident	MD07	Flood accident	
MD04	Coal and gas outburst accident			

Construction of network model of mine accidents

The accident chains of the reported mine disasters can be constructed according to RF, SH and MD in Tables 1, 2 and 3. Specifically, RF, SH and MD were taken as nodes; the correlations among them as sides; and the evolution paths as causal relationships. In this way, a CSR evolution model based on the complex network theory was established. Subsequently, visualized analysis on the constructed model was conducted with the aid of Pajek software, as displayed in Fig. 1.

Fig. 1 Complex network construction of coal mine safety risk evolution.

Feature analysis on CSR network

For the purpose of further exploring the correlations among RF, SH and MD, the network in the constructed CSR evolution model was divided into 7 accident subnets, namely coal mine fire accidents, coal dust explosion accidents, gas explosions, coal and gas outburst accidents, rock burst accidents, roof accidents, and water accidents. Subsequently, key parameters were obtained through continuous experimentation and analysis of proven literature references. Feature analysis was conducted on the 8 networks using Pajek software to obtain the values of characteristic parameters for both the complex network of CSR evolution (referred to as the CSR network) and its 7 accident subnets (Table 4).

Size and density of the network

The network size refers to the numbers of nodes and edges in a complex network26. Based on experiments and literature27–29, the constructed CSR network model contains 44 nodes and 184 edges, and the theoretical maximum number of all connected edges in the network is 1,840, which means that the density of this complex network is 0.10. Given that the density of a random network with the same network structure is about 0.34, it can be concluded that the CSR network is a sparse one. The CSR network is characterized by a relatively dispersed structure, uncomplicated evolution paths among RF, SH and MD, and influencing factors that slightly interact with each other.

On the other hand, the number of edges in the 7 accident subnets is larger than that in the CSR network, demonstrating that the CSR network is not formed by simple combination of the subnets. Failure in controlling one inherent risk can easily lead to complex changes in the overall network, thus developing into causes of multiple types of accidents. In addition, among the 7 subnets, those corresponding to gas explosion accidents and coal and gas outburst accidents occupy the highest density, 26%, while that of water accidents has the lowest density, 18%. This indicates that in the accident subnets, the correlation between risk factors and potential hazards is relatively closer and the interaction between risk factors is more significant, i.e., the evolution process is more complex.

Table 4 Characteristic value of coal mine safety risk evolution complex network of and accident subnet.

Parameter	Global network	Fire subnet	Coal dust subnet	Gas subnet	Outburst subnet	Burst subnet	Roof subnet	Flood subnet	
Number of nodes	44	12	14	13	14	11	11	10	
Number of edges	184	29	42	40	47	25	25	16	
Density of the network	0.10	0.22	0.23	0.26	0.26	0.23	0.23	0.18	
Average node degree	8.36	4.83	6	6.15	6.71	4.55	4.55	3.2	
Centralization—in-degree	0.21	0.85	0.75	0.72	0.63	0.85	0.85	0.91	
Centralization—out-degree	0.19	0.16	0.25	0.17	0.22	0.19	0.19	0.17	
Characteristic path length	1.73	1.63	1.57	1.51	1.48	1.49	1.49	1.65	
Network diameter	5	5	5	5	5	4	4	4	
Global efficiency	0.10	0.13	0.15	0.15	0.13	0.13	0.13	0.10	
Clustering coefficient	0.11	0.16	0.18	0.21	0.22	0.17	0.17	0.11	

Average node degree and centralization

The node degree is a major evaluation indicator for the influence of nodes in complex networks, while the average node degree of a network reflects the average influence of the nodes in this network[30]. According to Table 4, the average node degree of the CSR network is 8.36, which means that each hazard in the network is correlated with other 8.36 hazards on average, that is, a change in one hazard in the network may lead to changes of the other 8.36 hazards. Among the 7 accident subnets, the highest average node degree is 6.71 corresponding to coal and gas outburst accidents, and the lowest is 3.2 to water accidents. Therefore, particular attention should be paid to potential hazards of coal and gas outburst accidents to avoid the failure of control measures.

The centralization reflects the aggregation of hazards in the network and subnets. It can be seen from Table 4 that the out-degree is lower than the in-degree for centralization of both the CSR network and the 7 subnets. This means that the evolution is more concentrated in the RF-SH path than in the SH-MD path, i.e., many factors can affect coal mine accidents, but few types of accidents may occur.

Characteristic path length and network diameter

The characteristic path length is the average distance between all node pairs in a complex network19. When the characteristic path is shorter, the risks and hazards need to go through fewer steps in a complex network, and thus the risks propagate faster in this network. The characteristic path length of the CSR model is 1.73, indicating that a risk or hazard can affect the other nodes correlated with it through an average of 1.73 edges. In other words, a change in a risk or hazard in the CSR network can trigger changes of its associated risks or hazards after an average of 1.73 steps. Among the 7 accident subnets, the largest characteristic path length is 1.63 corresponding to fire accidents, and the smallest is 1.49 to rock burst accidents and roof accidents. Both values are smaller than 1.73, suggesting that mine accidents are more susceptible to safety risks and potential hazards.

The network diameter refers to the maximum distance between two connected nodes in a complex network. The diameter of the CSR network is 5, which demonstrates that in the network model, it takes at most 5 steps for a risk or hazard to affect another one, namely, the incidence of risks and hazards can be determined to be within [0, 5]. Moreover, the diameters of the 7 subnets are all smaller than or equal to 5, suggesting that the triggering of mine accidents also requires at most 5 steps.

Global efficiency

The propagation rate of risks and hazards in the CSR network reflects its global efficiency19. In Table 4, the global efficiency of the CSR network is lower than or equal to that of the 7 subnets, indicating that the connectivity of the CSR network is lower than that of the subnets, that is, risks and hazards propagate more slowly in the CSR network. Particularly, the subnets of coal dust accidents and gas explosion accidents have the highest global efficiency among the 7 subnets, the lowest being the water accident subnet. Hence, vital risks and potential hazards related to coal dust accidents and gas explosion accidents should be especially concerned in prevention and control of coal mine disasters and accidents.

Clustering coefficient

The clustering coefficient manifests the importance of certain nodes in the CSR network, its value lying in the range of [0,1]21. According to Table 4, the clustering coefficient of the CSR network is 0.11, signifying that the correlation between nodes in the overall network is relatively uniformly distributed. Meanwhile, the clustering coefficients of the 7 subnets are all larger than or equal to that of the overall network. Among them, the highest clustering coefficient is 0.22 corresponding to rock burst accidents, and the lowest is 0.11 to water accidents. Changes in the risk and hazard nodes with higher clustering coefficients can easily lead to sudden changes in the nodes associated with them, even resulting in strong coupling and chain reactions within the network.

Small-world properties

The small-world properties of complex networks feature a short average path length (no longer than 10) and a high clustering coefficient (no lower than 0.1)21. The two values of the constructed CSR model are 4.8 and 0.11, respectively, both conforming to the small-world properties of complex networks. Therefore, the small-world properties of the CSR network can be determined.

The small-world properties of the CSR network suggest that most risks or hazards in the network are not necessarily directly correlated, yet they are accessible through short paths, indicating the propensity for rapid CSR evolution and sudden mine accidents. Moreover, the good connectivity between risk and hazard factors in the CSR network also increases the randomness of mine accidents, resulting in the broadscale propagation of safety risks and easy triggering of chain accidents. Following that, the controllability of safety risks is decreased, and safety production in coal mines is severely affected.

Scale-free properties

In a scale-free complex network, most nodes are only correlated with a few nodes, while some are correlated with numerous nodes. Therefore, BA scale-free networks are usually symbolized by high clustering coefficients of local nodes. Considering the small size of the CSR network, the cumulative degree distribution was taken as the indicator for identification of its scale-free properties.

According to the calculation results of the relevant parameters of the CSR network, its cumulative degree distribution follows the power-law distribution of function P(x)∼1.358×x-0.337(R2=0.961) (Fig. 2). Consequently, it is identified to be a scale-free network, suggesting that risk and hazard nodes in the CSR network are concentrated. Therefore, CSR can be controlled more effectively by targeting the key risk and hazard nodes with high clustering coefficients and centrality in the network. Such targeted control can cut off the risk propagation chain and prevent the spread of risks and hazards in the network, thus reducing the probability of accidents.

Fig. 2 Cumulative degree distribution of coal mine safety risk evolution complex network.

Analysis on key hazards

In view of the diversity of influencing factors of coal mine accidents, it is of great theoretical significance and scientific value to analyze the key nodes in the complex network for prevention and control of mine disasters. Based on the constructed CSR network and centrality algorithms in the complex network theory, the key hazards in the CSR network are investigated in this section regarding degree centrality (DC), betweenness centrality (BC), and closeness centrality (CC).

The correlation between nodes and node pairs in the network acts as the bridge or pathway for the evolution of CSR. Thus, the importance of a node can be identified by removing it and then determining the global efficiency of the remaining network. However, due to the large number of nodes in some complex networks, improper removal of nodes can result in heavy workload. Therefore, nodes with high DC, BC and CC in the network were selected for analysis, which is also described as network interference. On this basis, different interference strategies were adopted to investigate the decline in global efficiency, and the key nodes in the CSR network were identified, which contributes to management and control of key hazards in coal mines.

According to the calculation results by Pajek, all the risk and hazard nodes were arranged in descending order of DC, BC and CC. Then, DC interference, BC interference and CC interference were performed on the CSR network respectively to identify the importance of the risks and hazards, and the change trends of global efficiency under the three types of interference were obtained19 (Fig. 3).

It can be observed from Fig. 3 that the global efficiency of the CSR network presents a downward trend under the three interference strategies. When the global efficiency drops to 0, correlated nodes no longer exist in the evolution network, which means that the evolution trend of safety risks and potential hazards is contained. According to the change trends of global efficiency under the three strategies, global efficiency declines the fastest under BC interference and fewer nodes are removed by the same standards.

In summary, the key hazards in the CSR network are the ones with high BC. Combined with the BC rankings of the nodes in the constructed network, the top ten hazards can be concluded as: unreasonable labor organization, inadequate risk identification, inadequate safety training, defects in technical management, inadequate technical management, complex geological conditions, insufficient safety awareness, insufficient safety management, failure to implement emergency measures, and insufficient supervision. Strengthened management, prioritized investigation and scientific control should be executed on these factors.

Fig. 3 Trend of global network efficiency under different interference strategies.

Conclusions

Based on the complex network theory, a complex network model for CSR was constructed, and the evolution paths of safety risks were analyzed. Furthermore, the key potential hazards in the process of risk evolution were explored. This highlights the critical role of hidden dangers in both predictive and reactive safety management strategies. Explaining the relationship between CSR and BN provides a robust framework for analyzing and managing coal mine safety risks, which not only addresses the identification of risk factors but also offers insights into their evolution and control. The approach differs from traditional accident analysis methods by integrating the probabilistic modeling capabilities of Bayesian Networks (BN) with the structural insights provided by complex network theory, offers several advantages, including a more comprehensive analysis of the interdependencies among risk factors and the ability to identify critical nodes for targeted interventions. Understanding network parameters such as node centrality and network density is crucial, as they highlight the pivotal elements within the safety risk network. This understanding enables targeted interventions, which can significantly mitigate the spread of risks and enhance overall safety. Finally, the following beneficial conclusions were drawn.

On the basis of the complex network theory and related evolution models, CSR and potential hazards were extracted from mine accident reports as nodes, and the accident chains in the reports were taken as edges. In this way, a complex network model of coal mine safety risk evolution was constructed.

According to the analysis on the characteristic parameters of the constructed complex network model, the complex network conforms to small-world and scale-free properties. Risks and hazards in the network are concentrated, indicating that failure in controlling one certain safety risk or hazard can easily lead to coal mine accidents.

The trend changes of global efficiency under BC interference, CC interference and DC interference were investigated, and BC was determined as the optimal indicator for analysis on the key hazards. Accordingly, the key hazards in the complex network of coal mine safety risk evolution were identified, laying a theoretical foundation for prevention and control of CSR.

Acknowledgements

This work is financially supported by the National Natural Science Foundation of China (Grant No. 52274159, 52374165) and S&T Innovation and Development Project of Information Institution of Ministry of Emergency Management (Project No. 2024507).

Author contributions

Eryi Hu contributed to the idea of research. Guorui Su performed the data analysis and wrote the manuscript.

Data availability

All data generated or analysed during this study are included in this published article.

Competing interests

The authors declare no competing interests.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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