Dynamic assessment and system dynamics simulation of safety risk in whole life cycle of coal mine

Based on the accident causation theory, the mechanism and inducement of construction safety risk in mining enterprises are clarified. The safety risk system of mining enterprises is divided into five subsystems: personnel, material equipment, technology, environment, and management by rough set theory. The comprehensive weight of each risk factor is calculated by network analytic hierarchy process and fuzzy comprehensive evaluation method. Taking a mine in Shanxi Province as the research object, the causal traceability diagram and stock flow diagram of the risk system of mining enterprises are constructed by means of system dynamics model. The influence of various risk factors of the mine on the overall safety risk management level of the enterprise is simulated, and the numerical value of key personnel influence factors is adjusted. The sensitivity changes of safety productivity and safety risk management level of mining enterprises in different situations are analyzed. The results show that: (1) the management and personnel subsystem has the greatest impact on the safety risk management of mining enterprises, followed by the technology, material equipment, and environment subsystem. (2) Increasing safety input can improve the safety level and reduce the expected safety value time, otherwise it will reduce the safety level and delay the expected safety value time. (3) Further simulation of the personnel subsystem, it is found that the factors affecting the safety level of mining enterprises contain six factors, namely, the technical level of construction personnel, the management level of manager, the conduct code of construction personnel, the safety consciousness of practitioners, the basic quality of construction personnel, and the physical and mental state of construction personnel. (4) The conversion rate of personnel safety input to manager’s management level and the safety consciousness of practitioners presents a steep decline—slow rise—gradually steady development trend, which mainly because the benefits of safety input have certain time delay and lag.


Introduction
Coal has long occupied a large proportion in China's energy consumption structure, and will continue to be an important energy source to support China's economic development for a long time to come. In 2020, China officially proposed the goals of "carbon peak" by 2030 and "carbon neutralization" by 2060, putting forward higher requirements for lowcarbon production and clean utilization of coal. The "14th Five-Year" Plan also calls for reducing energy consumption and carbon dioxide emissions per unit of GDP by 13.5% and 18% respectively by 2035. This means that the development direction of coal resource in time adjustment will become the first content of the future low carbon development strategy of our country. Therefore, mining enterprises must quickly identify the various risk factors that affect the Responsible Editor: Shimin Liu economic benefits and safety level of enterprises, and find the production and operation management mode suitable for the development of mining enterprises themselves, so as to improve the overall economic benefits of mining enterprises. Accordingly, from the perspective of safety input in the whole life cycle of the mine, this paper explores the impact path and internal mechanism of different driving factors on the safety level of mining enterprises, in order to reduce the risk rate of coal mine accidents from a multi-dimensional perspective, reduce casualties and economic losses, and scientifically and reasonably help achieve the "double carbon" goal on schedule.
Mishra redefined the risk assessment process as four sections, namely, hazard identification tool, risk assessment approaches, risk assessment parameters, and risk representation tool. In addition, a numerical ranking system was formulated for underground mines to choose among the probabilistic, possibilistic, and deterministic approaches (Mishra and Rinne 2014). Cui presented a cloud model and hybrid semi-quantitative decision method, this risk management methodology could help budget planning for risk treatment and provided an instructional framework to effectively reduce the negative effects of closed mines (Cui et al. 2020). Iphar introduced a fuzzy logic-based safety evaluation method to enhance the risk assessment process. In this way, risky situations and operations in mechanized underground coal mines have been determined by expert knowledge and engineering judgment in linguistic forms (Iphar and Cukurluoz 2020). Gul proposed a theoretical contribution by suggesting a Pythagorean fuzzy numbersbased VlseKriterijumska Optimizacija I Kompromisno Resenje (PFVIKOR) approach. Hazards could be categorized into different risk levels via compromised solutions of the fuzzy approach (Gul et al. 2019). Based on a novel procedure and presentation of preventive and preparative measures, safety risk of Iran's underground coal mines' incidents was assessed and classified by taking advantage of Iran's mining experts' opinions (Bagherpour et al. 2015). Niu, based on the theory of disaster causation and the whole life cycle theory, deconstructed the coal mine safety risk management into three standard links. What is more, the risk management model of coal mine safety, which was integrated with "data perception-data analysis-data service," was built by focusing on coal mine risk factors and combining with big data technology (Niu and Zhao 2022). By analyzing the advantages and disadvantages of hazard and operability analysis (HAZOP) and layers of protection analysis (LOPA), Zhang constructed the Bayesian model to complete the analysis and calculation of the BN model. This method was applied to coal mine gas explosion accidents (Zhang et al. 2022a, b).
In view of the problems of the whole life cycle safety risk, relevant scholars have carried out some studies. Ren applied blockchain technology to the management of the whole life cycle data of nuclear power plants, in order to realize the real traceability of the whole life cycle data of nuclear power plants (Ren and Yang 2022). Jiao, based on Bayesian network, deep neural network algorithm, and internet of things technology, proposed the whole life cycle management mode of existing buildings, explored the key technologies of automated health monitoring platform based on internet of things, and helped the construction of smart towns (Jiao and Lai 2021). Yu used internet plus technology to combine two-dimensional code technology with hazardous chemical inventory management on the basis of reagent management platform, thus achieving standardized, refined and the whole life cycle safety management of hazardous chemicals (Yu and Wang 2021). Shang formed a systematic theoretical method for the whole life cycle of planning, design, construction, handover and operation and maintenance in the research on safety assessment technology of comprehensive pipe corridor, and constructed the safety assessment model of the whole life cycle of comprehensive pipe corridor by combining analytic hierarchy process and fuzzy comprehensive evaluation method ). Fang combined patent index method and S-curve mathematical model method to analyze the status and development trend of access control system security technology in different development stages, such as embryonic stage, technology introduction stage, growth stage, mature stage, and recession stage (Fang et al. 2019). Xu built a system platform around the whole life cycle monitoring and diagnosis of power equipment, performance optimization, and maintenance spare parts service, and studied the key technologies in the system, such as information collection and management, dynamic adaptive monitoring, health state prediction and evaluation, fault early warning and rapid intelligent diagnosis, remote and on-site rapid dynamic balance maintenance of rotor, and intelligent maintenance decisionmaking (Xu et al. 2013).
Zhao, based on in-depth analysis of the whole life cycle characteristics of health risks in mercury-contaminated plots, constructed the whole life cycle classification and control technology system for risks in mercury-contaminated plots based on three core risk factors: risk source, exposure route, and environmental receptor ). Qiang divided the phased results of pipe corridor construction into four risk identification units based on the whole life cycle theory. Then Delphi method and analytic hierarchy process were used to establish the risk matrix and calculate the weight to complete the risk screening and quantification (Qiang et al. 2019). An divided the whole life cycle of coal into five stages: coal mining, coal processing, coal transportation, coal utilization, and waste treatment, and focused on analyzing the impact of four heavy metals in the coal utilization stage on coal environmental behavior in Xuzhou region (An et al. 2016). Tong carried out unit decomposition of the coal mine life cycle, and built an evaluation model between dust and quantitative indicators by collecting dust inventory data at each stage for monetization analysis (Tong and Zhai 2013). Chen, based on the whole life cycle theory, started from the perspective of construction investment and management, adopted the project economic benefit evaluation method to analyze the economic benefits of the mine technical renovation and expansion project, and made a quantitative analysis of the project's break-even and sensitive factors .
From the perspective of research content, scholars mainly used the whole life cycle theory to divide research units, and then selected one or two mathematical models to quantitatively analyze the weight values of different life cycle stages. In addition, the existing risk assessment models tend to view the problem subjectively and statically, and there are few studies on identifying multidimensional risk factors according to different stages of the whole life cycle and conducting simulation prediction analysis on them, which leads to insufficient dynamics of risk assessment. In view of the existing research, there are few literatures on the economic risk and simulation caused by personnel safety in the whole life cycle of mining enterprises, which is still in the exploratory analysis stage. On the basis of existing research and from the perspective of multidisciplinary theory, this paper analyzes the internal and external risk drivers in the whole life cycle of mining enterprises, and draws the causality tracing diagram and stock flow diagram of the risk system of mining enterprises by using the system, dynamic, and nonlinear characteristics of the system dynamics model. To simulate the impact of each risk factor in the case mine on the overall safety risk management level of the enterprise, and adjust the value of key personnel impact factors, analyze the sensitivity changes of safety productivity and safety risk management level of mining enterprises under different circumstances, and clarify the risk-driving mechanism of the enterprise, in order to provide a more accurate risk assessment basis for the case mining enterprises and similar high-risk enterprises.

Unit decomposition
The production and operation of mining enterprises is a complex, dynamic, and nonlinear opening process. Enterprise operation risk is driven by external risk factors such as policy and legal risk, environmental risk, and internal risk factors such as technological risk, economic risk, schedule risk, and management risk. In order to accurately control the safety input in the whole life cycle of mine, the whole cycle is divided into units. Combining with the actual mine operation situation in China, the whole life cycle of mine can be divided into the stage of exploration and construction, the stage of mine production, the stage of mine reconstruction and expansion, and the stage of scrap treatment (Kocsis 1961;Hitch et al. 2014), as shown in Fig. 1.

Risk assessment mechanism
System dynamics (SD) is a method for the systematic analysis of social and economic problems, which is first proposed  Fig. 1 The division of the whole life cycle of mine by Professor J.W. Forrester of Massachusetts Institute of Technology in USA. SD is a combination of qualitative and quantitative analysis method. It is a dynamic evaluation method based on complex feedback theory and computer simulation technology. It cannot only analyze the influence links of risks on projects and the internal influence relationship between risks in complex systems, but also analyze risks dynamically (Cooke. 2010). Using SD theory and method to construct the dynamic evaluation model of safety risk in mining enterprises can well realize the integrity which base on causal loop diagram and stock flow diagram, the continuity by means of simulation analysis, the intuitiveness by the final simulation comparison diagram.
In view of the complex and abstract nature of the safety production system of mining enterprises, directly fitting the collected key technical risk factors into the SD will make the risk system redundant, resulting in insufficient dynamics, and the number of key risk factors will directly affect the numerical relationship and the final results. On the basis of full investigation and literature research, the dynamic reduction algorithm of rough set theory (RS) is used to effectively simplify the key risk factors, and the whole life cycle safety risk system of mining enterprises is divided into five subsystems, namely, personnel, materials and equipment, technology, environment, and management subsystem (Yin et al. 2019). In terms of empowerment, subjective or objective empowerment methods were single used in the past, with a certain degree of one sidedness. According to the specific needs, this paper comprehensively uses the subjective and objective empowerment method to make the weight closer to the objective fact under the premise of conforming to the subjective will. In addition, since safety input is the sum of manpower, material resources, and financial resources in mine safety production, safety input also directly affects the safety level of the system. The dynamic evaluation process of safety risk of mining enterprises based on improved system dynamics in the whole life cycle is shown in Fig. 2.

Basic assumptions
Starting from the direction of safety production risk management in mining enterprises, this paper explores the impact of various subsystems and safety input on the safety risk management level of mining enterprises. According to the actual situation of the case mining enterprise, the following assumptions are made: (1) Taking human-machine-technology-environmentmanagement as the endogenous variable of the safety production system of mining enterprises, only the influence of the interaction of internal factors of the system is considered, and the other factors as exogenous variables are not considered.
(2) Safety input covers human, financial, material, and other inputs. Combined with the actual situation of the investigation, this paper only considers the safety capital investment, that is, the safety capital investment in the five subsystems of human-machine-technologyenvironment-management. (3) Security management has a certain control effect on the system, but it fails to completely eliminate the influence of other factors.

Causality diagram
With the increasingly perfect of data mining, data processing capacity, and computer simulation technology,

Fig. 2
The system dynamics evaluation process system dynamics has been widely used in regional development, risk assessment, ecological compensation, policy optimization, and other fields. Based on the theoretical model analysis framework (Yu et al. 2019), this paper clarifies the system boundaries, key variables, and safety production objectives, and clarifies the interaction relationship and action path of each subsystem (Zhang et al. 2022a, b).
With the help of the causality equation ( R j ), the system is divided into several subsystems ( P ). Its description relation can be expressed as: In formula (1), S is the total system, P is the subsystem, and R j is the relationship matrix used to describe the relationship between variables, which is generally an equation or a table function. In the SD model, the subsystem is composed of several flow level variables, velocity variables, time functions, and auxiliary variables. According to the characteristics of SD model, the following mathematical description is given: In formula (2), T is the transfer matrix, V is the relationship matrix, L, R, and A are the level variable, flow rate variable, and auxiliary variable, respectively, and their differential equations can be written as (LET is the level variable, RAT is the flow rate variable): Based on formula (1-3), Vensim PLE is used to construct the system dynamic causality diagram of the five subsystems of human-machine-technology-environmentmanagement of mining enterprises, as shown in Fig. 3.
According to Fig. 3, there are five positive feedback loops in the safety risk management level of mining enterprises.
(1) Safety input ↑ → Management safety input ↑ → Management safety level ↑ → Safety risk management level of mining enterprises ↑.
(2) Safety input ↑ → Environmental safety input ↑ → Environmental safety level ↑ → Safety risk management level of mining enterprises ↑.

Causality diagram of personnel subsystem
Safety accidents in mining enterprises are closely related to people. As the main body of safety management, human risk factors have a great impact on each cycle of safety production in mining enterprises. If people's consciousness of safety protection is weak, basic quality is low, technical level is insufficient, or overload work, it will pose a threat to the safety production of mining enterprises. The causal feedback loop of the personnel risk subsystem is shown in Fig. 4 is not only affected by its own system factors, but also by other subsystems such as management and technology. The uses tree shows that when personnel risks lead to accidents, compensation strategies should be adopted according to the results. For example, the spread of accidents can be controlled by strengthening safety education and training and adjusting construction schedule.

Stock flow diagram of mining enterprises
According to the causal feedback loop and research hypothesis, the stock flow diagram of the safety risk management system of mining enterprises is constructed (Fig. 6). Considering the principle of typicality, comprehensiveness, applicability, and operability of the evaluation index, the SD model selects a total of 5 level variables, 5 rate variables, 14 auxiliary variables, 14 table functions, 26 constants, and 24 main NYNAMO equations. Assuming that the construction period of a certain stage of production in a mining enterprise is 24 months, the model sets the starting and ending time in months. Each variable can truly and objectively reflect the actual safety status of the human-machine-technologyenvironment-management subsystem of the mining enterprise, and accurately characterize the logical relationship and dynamic correlation between the index variables.
In Fig. 6, < time > is a shadow variable. B 1 is the proportion of personnel input, B 2 is the proportion of material and equipment input, B 3 is the proportion of technology input, B 4 is the proportion of environment input, and B 5 is the proportion of management input. The relationship of some main variables is shown in Table 1.

Model sensitivity test
The sensitivity test mainly tests the sensitivity of the model, and compares the state variable data under different schemes with the actual data to judge whether the simulation results are in line with the actual situation (Yin and Wei 2021;Booth 1994). In this paper, the one-way sensitivity analysis is used to verify the rationality of the model. Control the initial safety level of the five subsystems, increase 0.5 one  Table 2. By using Vensim PLE software, simulate the parameters and influence factors of different schemes in Table 2, compare and observe the simulation results of safety productivity under the six schemes before and after the change of parameters, and its effect is optimized compared with the original model in amplitude. The overall model is still running smoothly, and the evolution trend before and after is similar (Fig. 7). Therefore, it can be seen that the safety risk management system of mining enterprises has passed the parameter sensitivity test. The model can reflect the actual situation of each subsystem of mining enterprises and can be used to simulate the development trend of safety risk management level of mining enterprises.

Simulation analysis of mine safety risk management level
In this paper, a mine in Shanxi is selected as the research object, and the corresponding parameters are brought into the system dynamics equation through data statistical analysis. Through simulation, the change trend of  In the daily mining process of the case mine, with the capital investment of risk management on the construction site, the safety risk management level of the mining enterprise continued to grow, and the growth in the first 6 months was relatively slow, which also shows that the economic or social benefits generated by safety input have a certain time delay and lag. There is a feedback relationship between safety risk management level and safety input, and safety investment is a long-term investment process. After that, the growth rate of safety risk management has accelerated, indicating that the system risk has reached the expected control limit.
According to Table 2, adjust and control the change value of the safety level of the five subsystems of human-machinetechnology-environment-management one by one, so that the initial value of each subsystem increases by 0.5. By observing the change trend in Figs. 8 and 9, it can be seen that the change trend of the safety risk management level of the management and personnel subsystems is relatively significant, the change of the technical safety level is in the middle, and the change of the material, equipment, and environment level is relatively slow.
Based on the simulation data, calculate the change rate of each subsystem, subtract the Current average value from the average value of each group, and then divide it by the average value of each group to obtain the corresponding change rate, that is, the change rate of the safety level of the five subsystems of human-machine-technology-environment-management are 43.10%, 35.13%, 27.02%, 16.57%, and 49.09%, respectively. Finally, the influence degree of the five subsystems on the safety risk management level of mining enterprises is obtained as follows: management,

Personnel subsystem simulation analysis
Coal mine environment is extremely complex, working conditions are very difficult, and employee behavior is affected by natural environment, social environment, technical equipment, group behavior, family and individual, and many other complex factors. The front-line employees of coal mine generally have low education, low quality, and relatively weak safety awareness. Most of the coal mines are young employees, most of them are not psychologically mature enough to pay enough attention to safety norms. In addition, most front-line employees are the main labor force of poor families and work under fatigue for a long time, so their safety behavior ability is very fragile. Especially in complex environments, it is difficult to judge and eliminate safety risks. In recent years, our government and coal mining enterprises always pay attention to safety training, but the actual effect is unsatisfactory. Especially in different environments, there are few skills training to solve practical safety problems on site, and employees' ability of safe behavior is still generally low, which leads to increased difficulty in behavioral safety management. Therefore, to improve the safety behavior ability of coal mine employees is not only to respect employees and reflect the "people-oriented," but also an effective way to fundamentally improve the level of coal mine safety risk management and curb accidents. In this paper, the personnel subsystem is extracted to

Causal tracing analysis
According to the causal tracing analysis results (Fig. 10a) of the safety level of the mine personnel subsystem, the increment of the personnel safety level has a great impact on the personnel safety level, and it is found that the increment of the personnel safety level has an overall upward trend. Then, Fig. 10b1-3 shows that the increment of personnel safety level is affected by six factors: management level of manager, technical level of construction personnel, basic quality of construction personnel, safety awareness of employees, code of conduct for constructors, and the change of management safety level on personnel. Among them, the change of management safety level on personnel is similar to the incremental change trend of personnel safety level, showing a marginal increasing trend. During the study period, the overall curve of the three variables, namely, the technical level of construction personnel, the basic quality of construction personnel, The management level of managers showed an inverted U-shape in the first 12 months and gradually leveled off in the second 12 months, which was quite different from the incremental fluctuation trend of personnel safety level. The changing trend of employees' safety awareness conforms to the S-shaped growth pattern of the system dynamics model. Further causal tracing is carried out for the management level of managers (Fig. 10c) and the safety awareness of employees (Fig. 10d). It is concluded that the management level of manager is mainly affected by the conversion of input to management level and personnel safety input, and the safety awareness of employees is mainly affected by the investment to safety awareness conversion rate and personnel safety input. It is found from Fig. 10c and d that the conversion rate of personnel safety input to manager's management level and the safety awareness of employees presents a steep decline-slow rise-gradually steady development trend. The main reason is that the benefits generated by the safety input have a certain time delay and lag, resulting in a reverse change relationship between the safety input and the conversion efficiency at the initial stage, but this relationship will not last for a long time.
In the later stage, with the increase of relevant intelligent technology maturity and the improvement of operation proficiency of construction personnel, the conversion rate of personnel input will gradually increase to a flat state.

Determination of parameter value and equation
According to the risk factor value of the personnel subsystem calculated in the previous, the key personnel factors are further adjusted and the changes of the safety level of the personnel subsystem are simulated (Tian et al 2019). The assignment is shown in Table 3.

Simulation analysis of personnel subsystem
The safety level of the personnel subsystem is simulated by adjusting the key risk factors of the personnel subsystem. The other four subsystems remain unchanged, and the initial value of each risk factor of the personnel subsystem is increased by 35% successively. Current represents that the initial value of each factor of the personnel subsystem remains unchanged; Current6 indicates that the initial value of manager management level increases by 35%; Current7 indicates that the initial value of employee technical level increases by 35%; Current8 indicates that the initial value  of employee basic quality increases by 35%; Current9 indicates that the initial value of employee safety awareness increases by 35%; Current10 represents a 35% increase in the initial value of employee conduct code; Current11 indicates that the initial value of employee physical and mental state increases by 35%, and its personnel safety level change trend is shown in Fig. 11. By solving the change rate of each risk factor of the personnel subsystem, subtract the Current average from the average of each group, and then divide by the average of each group to obtain the corresponding change rate. The results show that the change rate of six risk factors of manager management level, employee technical level, employee basic quality, employee safety awareness, employee conduct code, and employee physical and mental state to the safety level of personnel subsystem is 14.65%, 19.93%, 5.54%, 29.10%, 23.78%, and 9.32%. According to the SD simulation results, the influence degree of internal factors of personnel subsystem is successively: employee safety awareness, employee conduct code, employee technical level, manager management level, employee physical and mental state, employee basic quality. The influence degree of the internal factors of the personnel subsystem is measured by the comprehensive weight. The ranking of the comprehensive weights of six internal variables in the personnel subsystem is consistent with the simulation results.

Conclusions
Formulate reasonable safety input distribution plan. The safety input of mining enterprises is mainly used in technology introduction, machinery and equipment, safety education and training, and other aspects. By establishing SD model, the safety risk management level of mining enterprises under different safety input distribution is simulated, and then the optimal safety input scheme is formulated according to the actual situation.
(1) It can be seen from the simulation results of system dynamics of the case mine that increasing safety input can improve the safety level and reduce the time required for the expected safety value, while on the contrary, it will reduce the safety level and delay and lag the time of the expected safety value. Therefore, when the funds are sufficient, we can consider proper increasing the safety input to improve the safety level of mining enterprises.
(2) The increase trend of safety level is the most obvious when safety funds are invested in the management and personnel subsystem. It can be seen from the stock flow diagram that the amount of capital investment directly affects the safety protection of construction personnel, technical level, safety education and training, safety supervision and hidden danger investigation, and other. Therefore, in the safety management of mining enterprises, it is necessary to ensure the safety input of people.
(3) In the process of the whole life cycle of mines, the safety of mining enterprises is affected by many internal and external factors. Among them, human behavior directly affects the construction plan. The level of mine mechanization can improve the construction efficiency and ensure the safety of machinery. Technology is the premise of mine enterprise construction, and advanced management technology can scientifically guide the construction process and accurately identify mine risks. Environment is an objective factor, which cannot be ignored, and the whole construction environment should be continuously monitored by intelligent technology. The so-called is "three points are technology and seven points are management." The management risk is the most sensitive to the mine safety risk, and effective measures should be taken to improve the mine safety management level.

Discussion
The main purpose of the safety risk management level simulation of mining enterprises is to study the fundamental causes of accidents. By using system dynamics, the internal action relationship of the system can be displayed with dynamic numerical values. The safety risk management system of mining enterprises is divided into five subsystems: human-machine-technology-environment-management. On the basis of risk factor identification, the system dynamics software Vensim PLE is used to define the relationship between the internal factors of the system, form the causality diagram and stock flow diagram of the safety risk of mining enterprises, carry out sensitivity testing, regulate the safety input level of the subsystems one by one, and compare and analyze the effect rate of each subsystem on the safety risk management system of mining enterprises. Then the causal traceability analysis of the personnel subsystem is carried out to intuitively display the causal feedback of the safety risk system of the mining enterprise, so as to provide reference for the managers to carry out dynamic risk management. The construction safety risk system of mining enterprises is affected by many internal and external risk factors (Koo et al 2019; Gul 2018). This paper only considers the key system variables involved in the construction process. The integrity and applicability of the system may be deficient, and the SD model constructed still has a certain gap with the actual mine. In the follow-up study, risk factors and relevant data should be further improved, and more variables should be added to the model. Besides considering safety input (Feng et al 2020), system objectives such as mine type and mining progress should be gradually included in the research scope.
Author contribution Lirong Li, Ke Yang, and Yanqun Yang are responsible for the topic selection and conception of the manuscript, while Yanna Zhu, Cheng Li, and Guisheng Zhang are responsible for the data processing and calculation and jointly complete the paper writing.
Funding This research is supported by Major special projects of science and technology in Shanxi Province (20191101016) and the Social Science Association research project of Anhui University of Science and Technology "Simulation and prediction of carbon peak carbon neutralization in coal life cycle from multi-scenario perspective" (SKL2021202209).
Data availability Data used in this manuscript is available from corresponding author.

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Competing interests
The authors declare no competing interests.