Research on the Human–Machine System Efficiency in Deep Mining Under the Coupling Effect of Multiple Factors

Abstract

Currently, deep mining has become the development trend of underground mines, and the harsh working environment underground seriously affects the efficiency of personnel and equipment operations. The operational efficiency of the human–machine system composed of personnel and equipment is not only affected by the status of personnel and equipment, but also closely related to the interaction between human–machine–environment. How to ensure the efficient operation of human–machine systems has become the key to improving the quality and efficiency of mines. Therefore, in order to analyze the interaction relationship between human–machine–environment in the process of human–machine system operation and explore the variation law of human–machine system efficiency. This paper constructs a deep mining human–machine system efficiency system dynamics model under the multi-factor coupling effect of deep well mining, guided by system dynamics theory, and obtains the variation laws of system efficiency under single-factor changes and multi-factor coupling effects. The research results solve the problem of difficulty in quantitatively describing the logical and quantitative relationships between various elements in the study of human–machine system efficiency, providing new ideas for the study of underground work efficiency. Through mathematical modeling, the temperature threshold for the efficient operation of the human–machine system is determined, and the quantitative relationships among temperature, humidity, and wind speed are elaborated, providing a reference for ensuring the efficient operation of the human–machine system in deep mining.

1. Introduction

With the consumption of shallow resources, deep mining has become the future trend of mining development. The “three highs” environment during deep mining has become an important factor affecting underground safety and efficient production. How to ensure that the human–machine system [1] composed of personnel and equipment maintains high operational efficiency in harsh environments has become the key to improving the quality and efficiency of mining enterprises. In order to analyze the human–machine system efficiency during underground operations, that is, the overall operational efficiency of personnel and equipment during the production process, and clarify the impact and changing patterns of human–machine system efficiency, relevant experts and scholars have conducted extensive research from the three aspects of human–machine–environment and achieved significant results.

The underground environment has a significant impact on work efficiency, mainly due to external conditions such as temperature, humidity, and wind speed. Niemela et al. [2] pointed out that when the ambient temperature exceeds 25 °C, the efficiency of personnel operations will gradually decrease as the temperature rises. Sugiuchi et al. [3] studied the relationship between employee work efficiency and environmental conditions such as temperature, humidity, and carbon dioxide concentration. It has been proven that environmental temperature has the greatest impact on work efficiency. Arata et al. [4] analyzed the relationship between office environment, work efficiency, and employee health by investigating the impact of various environmental factors on work efficiency and personnel health. Zhao et al. [5] conducted experimental research on the impact of different thermal and humid environments in metal mines on the work efficiency of underground workers, providing a basis for improving work efficiency in deep mining enterprises. Alipio [6] proposed that the factors affecting homework efficiency mainly include environmental parameters such as temperature, lighting, and wind speed, and established a correlation between work efficiency and environmental parameters through machine learning, completing the prediction of work efficiency. Fátima et al. [7] found that adjusting the ambient temperature in the office can improve employee satisfaction and work efficiency. Cui [8] studied the effects of different combinations of environmental temperature and wind speed on human comfort and work efficiency. This provides a reference for improving the work environment and enhancing work efficiency. Wen [9] obtained the optimal working mode and sleep schedule for construction workers under high temperature through simulation, providing theoretical guidance for ensuring workers’ safe operation. Tsutsumi et al. [10] proposed that in low-humidity environments, there is little difference in subjective thermal sensation among personnel, and the work efficiency of personnel is basically the same under different humidity conditions. After the humidity exceeds 70%, personnel are prone to feeling tired. Dong et al. [11] found that the comfort and work efficiency of personnel are influenced by various environmental factors such as thermal environment, acoustic environment, and lighting environment. Ismaila [12] proposed that environmental temperature is the main factor affecting work efficiency, while humidity and light have a relatively small impact on efficiency. Onder et al. [13] proposed that hot and humid mine environments can create pressure on the human body, and the humidity conditions of mine air have a significant impact on the health, safety, and productivity of employees. Lan Li [14] analyzed the impact of different environmental factors on work efficiency and established an evaluation method for work efficiency, obtaining a mechanism model for personnel work efficiency under multiple influencing factors. Li Wei [15] found through experiments that in high-temperature and high-humidity environments, there is a negative correlation between personnel work efficiency and environmental temperature, and when the temperature is high, work efficiency is significantly affected by the type of noise. Zhang Jinggang et al. [16] conducted a study on the work efficiency of underground personnel and found that high-temperature and high-humidity environments increase personnel fatigue, thereby increasing the probability of errors during operations.

Through summarizing the literature, it was found that research on equipment operating efficiency involves more fields such as industry, power grids and healthcare, mainly focusing on equipment efficiency evaluation and equipment management. He [17] constructed a complete performance evaluation index system based on equipment dynamic characteristic analysis. Aiming at key issues such as vibration suppression, efficiency improvement, and energy consumption optimization, an intelligent control method based on fuzzy PID is proposed, which is of great significance for improving mining efficiency. Wang [18] studied the impact of equipment operating parameters on excavation efficiency using a multi-factor orthogonal experimental method for a mining tunneling machine. By establishing an improved BP neural network model and determining the optimal combination of key parameters, the operational efficiency of the equipment can be effectively improved. Zhang [19] analyzed the main factors affecting the efficiency of equipment operation in open-pit coal mines and corresponding response strategies from three production processes: blasting, mining, and transportation. Yao et al. [20] conducted a study on the efficiency of furniture edge banding equipment and proposed management measures to improve operational efficiency from aspects such as personnel management and equipment management. Jin Cong and Feng Jie [21] used Data Envelopment Analysis (DEA) to analyze the effect of different input–output indicators on the evaluation of medical equipment operation efficiency. The results showed that the DEA method can effectively analyze equipment operation efficiency and is suitable for equipment operation management. Wu et al. [22] analyzed the factors affecting the comprehensive efficiency of rail transit equipment from the perspectives of input resources and output capabilities and proposed a rail transit comprehensive efficiency evaluation method based on the super efficiency DEA Tobit model. Zhang Yajun et al. [23] conducted research on the operational efficiency of anchor rod drilling machines based on the actual conditions of underground fully mechanized mining faces, optimized equipment layout, and proposed strategies to improve drilling machine operational efficiency, providing reference for similar equipment configurations. Wu Yunchao and Lv Zhijia [24,25] elaborated on the main factors affecting the operational efficiency of electrical equipment and proposed methods to improve equipment efficiency and optimize equipment management. Xia Muhu [26] analyzed the factors that affect the operating efficiency of pumping equipment and proposed effective measures to improve equipment operating efficiency. Tian Yanchun [27] analyzed the characteristics of mineral processing in mines and the requirements for equipment based on the current production situation and proposed measures to improve the efficiency of mineral processing equipment on this basis. Liu Jinqiang et al. [28] analyzed the efficiency of the electric shovel in the furnace body based on the loading efficiency and shovel capacity ratio of open-pit mines under different operating conditions and provided guidance for the reasonable arrangement of shovel positions and shovel specifications.

In summary, existing research results generally study personnel and equipment separately and rarely analyze human–machine systems as a whole. However, during deep well mining, there is mutual influence and correlation among human–machine–environment, leading to complex and dynamic changes in the human–machine system efficiency. It is impossible to accurately analyze it solely from the perspective of personnel or equipment. Therefore, in order to dynamically, clearly and accurately describe the interrelationships between various influencing factors of the human–machine system and explore the changes in the human–machine system efficiency during deep mining, personnel, equipment, and environment are considered as a whole, and the human–machine system efficiency is analyzed from the perspective of system modeling. The research on personnel work efficiency focuses on analyzing the impact of single factors such as temperature, humidity, and wind speed on personnel physiology and work efficiency, ignoring the coupling effect of multiple factors on the human body. However, research on equipment efficiency is mostly focused on analyzing influencing factors and evaluating efficiency. Therefore, it is necessary to comprehensively consider the impact of the coupled effects of various environmental factors on personnel and equipment operation processes, analyze the changes in overall operational efficiency under this coupled effect, and provide a reference for enterprises to optimize underground labor organization and ensure efficient operations on the basis of safety.

2. Applicability Analysis of System Dynamics

The factors affecting the human–machine system efficiency in deep mining include personnel physiology, equipment operation, environmental changes, and other factors. The mutual influence of various factors is not a simple linear mathematical model, which requires the use of computer data fitting to obtain. In addition, the indicators used to characterize homework efficiency or efficiency-influencing factors are not constant, and many indicators change over time. Therefore, the human–machine system efficiency also shows dynamic changes with increasing working time. Overall, the human–machine system for deep mining has characteristics such as dynamism, nonlinearity, and feedback. Common regression analysis and optimization methods cannot effectively address dynamic feedback issues. Machine learning can solve this problem, but it requires extensive training and carries the risk of overfitting, making it unsuitable for the research presented in this research. However, system dynamics [29] models the information feedback problem of complex systems through computer simulation and analyzes the behavior patterns at different stages. This method simplifies the system into several subsystems, enabling the system to consider causal relationships in a dynamic and multidimensional manner [30]. By applying this method from a global perspective, it is possible to better analyze the complex relationships and dynamic feedback processes among various influencing factors within the human–machine system in complex environments. Therefore, introducing the theory of system dynamics into the study and analyzing the variation in system efficiency with operation time can better solve the nonlinear and dynamic feedback problems in research. The specific analysis steps are shown in Figure 1.

3. Construction of System Dynamics Model

3.1. Analysis and Selection of Influencing Factors

The human–machine system, as a whole, engages in production operations, and the efficiency of system operations is inextricably linked to the status of personnel and equipment. In addition, the underground environment has a certain impact on personnel’s physiology and psychology, thereby affecting the human–machine system efficiency. Therefore, it is determined that the reasons affecting the human–machine system efficiency are mainly reflected in three aspects: personnel, equipment, and environment.

Personnel play a dominant role in the production process and are the main body of production. Even highly mechanized equipment cannot completely replace humans in completing production tasks alone. Due to the subjective initiative of human beings, their behavior and physiological reactions, such as work attitude and fatigue level, etc., can have an impact on the effectiveness of manipulating equipment. The factors that affect the human–machine system efficiency during personnel operations are reflected in multiple aspects, which can be summarized into two aspects: personnel operation factors and personnel physical condition factors.

Equipment, as an essential production tool in mines, not only reduces the labor intensity of personnel, but also greatly improves operational efficiency. However, the underground environment where the equipment is located is relatively harsh. The high-temperature and high-humidity conditions have a certain adverse effect on the equipment, thereby affecting its operational efficiency. It mainly includes two aspects: equipment operation factors and equipment failure factors.

During the underground mining, both personnel and equipment are constantly in the deep well environment, forming an interactive whole with the surrounding environment. As key indicators of the environment, changes in temperature and humidity have a significant impact on personnel physiology and psychology. At the same time, ventilation, as the main means of improving the underground environment, plays an important role in reducing environmental temperature and discharging polluted air. Therefore, the environmental impact factors are identified as three indicators: temperature, humidity, and wind speed.

3.2. Model Assumptions

Assumption of system boundary: In the process of studying the human–machine system efficiency, it is assumed that the physical health of personnel and the efficiency of operations are only affected by the equipment and environment during the operation process and are not affected by factors outside the system.

Assumption of work impact: The impact of the environment on the system is mainly determined by the selected environmental factors, not considering the impact of environmental factors outside the system, such as dust.

Assumption of work efficiency: At the beginning of the work, the efficiency of the system is relatively low, but not zero. Therefore, the system’s efficiency is assumed to be 60% at the beginning of the assignment.

3.3. Analysis of System Causal Relationships

Causal analysis is the key to constructing a causal circuit diagram, determining the feedback relationships between elements based on their causal chains and loop properties. Firstly, the system boundary is determined, and then the impact of changes in the three factors of human–machine–environment on the human–machine system efficiency is taken as the research mainline. Key indicators in the deep well thermal hazards evaluation index system are considered [31]. The main factors that affect and characterize the operational human–machine system efficiency are sorted out. Finally, the system is divided into personnel subsystem and equipment subsystem, as shown in Figure 2 and Figure 3. Then, the impact of temperature, humidity, and wind speed on the human–machine system is considered, and a causal relationship diagram is constructed that includes human, machine, and environment, as shown in Figure 4.

In Figure 2, Figure 3 and Figure 4, there are relationships of positive and negative correlation between indicators. Positive correlation is denoted by “+” and indicates that the dependent variable increases with the increase in the independent variable. Negative correlation is denoted by “-” and indicates that the dependent variable decreases with the increase in the independent variable. From Figure 2, Figure 3 and Figure 4, it can be observed that there is a positive correlation between personnel work efficiency and technical level, personnel comfort level, effective working hours, and work attitude. As these indicators increase positively, personnel operation efficiency also improves. Simultaneously, personnel work efficiency is negatively correlated with work intensity and fatigue level. As work intensity and fatigue level increase, they will inhibit personnel operation efficiency, leading to a gradual decrease in work efficiency. Equipment efficiency is positively correlated with operating status, operating time, and completed workload, and negatively correlated with equipment energy consumption. Equipment energy consumption during operation is constrained by operating status and equipment operating time. As the operating status deteriorates and the operating time increases, equipment energy consumption gradually increases. The workload and equipment repair jointly affect the operating status of the equipment. A decline in maintenance effectiveness directly reduces the normal operating status of the equipment. Simultaneously, an increase in workload causes the equipment to transition from a normal state to an abnormal state, thereby reducing work efficiency.

3.4. Construction of Stock Flow Diagram

Based on the causal circuit diagram, we constructed a stock flow diagram, then analyzed the internal information flow of the system, completed quantitative analysis, and explored the dynamic changes within the system. According to the different properties of elements, they are divided into rate variables, state variables, auxiliary variables, and constants. The relationship between different variables is shown in Figure 5.

Figure 5 shows a partial stock flow diagram of the personnel subsystem, where personnel work efficiency and human–machine system efficiency are state variables representing the accumulated amount during the change process. The change in personnel efficiency and the change in human–machine system efficiency represent the inflow and outflow of personnel work efficiency, respectively. They are rate variables that determine the state of horizontal variables and have directionality. Factors such as personnel comfort level, work intensity, and fatigue level are auxiliary variables. Personnel training is a constant, and information can be directly or indirectly transmitted to state variables or rate variables. Based on this, all indicators are divided into variables, as shown in Appendix A, and a stock flow diagram of human–machine system efficiency can be constructed, as shown in Figure 6.

3.5. System Dynamics Equation Setting

To further clarify the quantitative relationships between various indicators, it is necessary to determine the basic equations of the stock flow chart by combining special functions in system dynamics with the specific quantitative relationships between indicators. This will enable quantitative analysis of the internal feedback relationships and change law within the system and facilitate the construction of a system dynamics model for the human–machine system efficiency system. The specific equation settings are shown in Appendix B.

3.6. Model Checking

VENSIM system dynamics simulation software is used to construct the model of human–machine system efficiency and test the logical relationships of various variables in the system. After completing the inspection, the model is simulated and the results are analyzed. The simulation process takes the excavation operation of an underground mine in China as an example. The simulation time is 8, the time step is set to 0.25, and the time unit is hours. The model is run in VENSIM, and the simulation results are obtained under the conditions of ambient temperature of 28 °C, relative humidity of 90%, and wind speed of 1.5 m/s, as shown in Figure 7.

The simulated workload is compared with the actual workload of the mine, the error between the two is calculated, and the effectiveness of the model is verified. The error calculation formula is shown in Equation (1):

$$\delta ={\displaystyle \frac{{\widehat{x}}_i-x_i}{x_i}}$$

(1)

where δ is the error of the i-th variable; x_i is the true value of the i-th variable; and ${\widehat{x}}_i$ is the simulated value of the i-th variable.

When the absolute value of variable error is less than or equal to 5% (i.e., |δ| ≤ 5%), accounting for more than 70% of all tested variables, and the average absolute value of variable error is less than or equal to 10% (i.e., $\overline{\left|{\delta }_i\right|}\le 10\%$), the simulation results can be judged to be true and effective. The workload and fatigue level of different underground work locations are verified, and the verification results are shown in

Table 1. Verification of the simulation results of the system dynamics model.

No.	Stope	Level (m)	Workload (t)		Relative Error (%)
			Simulated Value	Actual Value
1	S10167	−435	103.8	110	−5.64
2	S13165	−570	98.7	95	3.89
3	S14155	−615	101.3	100	1.30
4	S14160	−615	103.1	100	3.10
5	S14186	−645	105.9	110	−3.73
6	S15160	−660	105.5	100	5.50
7	S15162	−675	102.3	100	2.30
No.	Stope	Level (m)	Fatigue level		Relative error (%)
			Simulated value	Actual value
8	S15162	−243	9.4	10	−6.00%
9	S15175	−330	13.6	14	−2.86%
10	S10172	−440	7.3	7	4.29%
11	S19148	−537	14.5	14	3.57%
12	S17162	−537	11.7	12	−2.50%
13	S18156	−550	18.1	17	6.47%
14	S16146	−555	13.6	13	4.62%
15	S19156	−750	17.6	17	3.53%

Data source: The data of workload is obtained from statistics collected from various underground mining sites; the data of fatigue level is determined through actual underground surveys.

.

The test results show that the number of variables with an error of less than or equal to 5% is 11, which is greater than 70% of the validation data, and the absolute value of the average error is 3.95%. It can be seen that the model meets the authenticity test and has high credibility, which can be used for subsequent research on the changes in the human–machine system efficiency.

4. Analysis of Changes in the Human–Machine System Efficiency

In order to explore the impact of deep mining environment on the efficiency of human–machine system operation, simulations were conducted on temperature, humidity, and wind speed under single environmental element and multiple environmental element coupling conditions based on the system dynamics model. According to relevant research results, the human–machine system efficiency of ≥80% is defined as efficient operation.

4.1. The Impact of a Single Environmental Element on the Human–Machine System Efficiency

(1)

The impact of temperature changes on the human–machine system efficiency:

Keeping the humidity and wind speed constant, the working conditions of 26 °C, 28 °C, 30 °C, 32 °C, 34 °C, and 36 °C are simulated in sequence, and the variation curves of the human–machine system efficiency with time at different temperatures are obtained, as shown in Figure 8.

From Figure 8, it can be seen that temperature changes have a significant impact on the human–machine system efficiency, and the overall change pattern remains consistent at different temperatures. As the temperature increases, the efficiency of the human–machine system gradually decreases, and the higher the temperature, the lower the maximum efficiency of the system, but the time required to reach the highest value decreases. At 26 °C, the overall efficiency remained close to 0.8 until the end of the work, indicating that the work can be efficiently completed in this environment.

(2)

The impact of humidity changes on the human–machine system efficiency:

Keeping temperature and wind speed constant, the air humidity of 20%, 40%, 60%, 80%, and 100% is simulated in sequence, and the variation curves of the human–machine system efficiency over time under different humidities are obtained, as shown in Figure 9.

From Figure 9, it can be seen that the trend of changes in the human–machine system efficiency under different conditions is similar, with higher humidity resulting in lower system operating efficiency. When the humidity is between 20% and 80%, the higher the humidity, the greater the impact on work efficiency, that is, the change in unit humidity leads to a more significant decrease in work efficiency. When the humidity exceeds 80%, the impact on the human–machine system efficiency decreases. When the air humidity is 40%, the human–machine system still maintains high efficiency until the end of the operation.

(3)

The impact of wind speed changes on the human–machine system efficiency:

Keeping the temperature and humidity constant, the wind speeds of 0 m/s, 1 m/s, 2 m/s, 3 m/s, and 4 m/s in sequence are simulated, and the variation curves of the human–machine system efficiency over time under different wind speeds are obtained, as shown in Figure 10.

From Figure 10, it can be seen that when the wind speed increases from 1 m/s to 2 m/s, the system efficiency increases slightly. When the wind speed increases to 3 m/s, the system efficiency decreases, ranging between 1 m/s and 2 m/s. When it increases to 4 m/s, the human–machine system efficiency significantly decreases, approaching the operational efficiency in a windless state. This indicates that as the wind speed increases, the system efficiency shows a trend of first increasing and then decreasing, suggesting that higher wind speeds are not necessarily more conducive to improving the human–machine system efficiency operations. The impact of wind speed on work efficiency can be divided into two situations: ① no wind and excessive wind speed: poor personnel comfort, which is not conducive to efficient work; and ② moderate wind speed: the airflow has a good cooling effect, providing high comfort for personnel and improving operational efficiency.

4.2. The Impact of Multi-Factor Coupling on the Human–Machine System Efficiency

To fit the actual environmental conditions underground, the coupling effects of multiple environmental factors can be analyzed. They can be divided into four conditions: temperature–humidity coupling, temperature–wind speed coupling, humidity–wind speed coupling, and temperature–humidity–wind speed coupling.

(1)

The impact of temperature and humidity coupling on the human–machine system efficiency:

According to the different temperature and humidity, they can be divided into four working conditions: high temperature and high humidity, high temperature and low humidity, low temperature and high humidity, and low temperature and low humidity. Simulations were carried out for the above four environments, and the variation curves of the human–machine system efficiency with time under different conditions were obtained, as shown in Figure 11.

From Figure 11, it can be seen that the optimal environmental conditions for work efficiency are low temperature and low humidity (temperature 28 °C, humidity 20%). Under this condition, the human–machine system can maintain efficient operation after 3 h. As the temperature remains constant and the humidity increases, the efficiency of the operation decreases. Compared with high-temperature conditions, the impact of humidity changes in low-temperature environments on the effectiveness of human–machine systems is more significant. This is because in high-temperature environments, an increase in humidity over a certain period of time can reduce the thermal sensation of personnel, and the airflow also has a certain cooling effect. But, as the human body accumulates heat, excessive air humidity will be detrimental to skin heat dissipation, leading to a rapid decline in the effectiveness of human–machine systems.

(2)

The impact of temperature and wind speed coupling on the human–machine system efficiency:

According to the different levels of two factors, they can be divided into four situations: high temperature and low wind speed, high temperature and high wind speed, low temperature and high wind speed, and low temperature and low wind speed. Simulations were carried out for the above four environments, and the variation curves of the human–machine system efficiency with time under different conditions were obtained, as shown in Figure 12.

From Figure 12, it can be seen that the optimal working environment is a low-temperature and low-wind speed environment. In these conditions, the system requires less time to achieve high efficiency and can be maintained for a long time. Under low-temperature conditions, as the wind speed increases, the system’s operational efficiency significantly decreases, while under high-temperature conditions, the impact of wind speed on operational efficiency is not significant, and operational efficiency is significantly lower than in low-temperature and low-wind speed environments. This is because compared to high-temperature conditions, an increase in wind speed in low-temperature conditions quickly takes away body heat, affecting the core body temperature and leading to a rapid decrease in human comfort, which is not conducive to efficient work and reduces work efficiency. Meanwhile, it can be seen that compared to wind speed, temperature has a more significant impact on work efficiency.

(3)

The impact of humidity and wind speed coupling on the human–machine system efficiency:

According to the difference in humidity and wind speed, they can be divided into high humidity and low wind speed, high humidity and high wind speed, low humidity and high wind speed, and low humidity and low wind speed. Simulations were carried out for the above four environments, and the variation curves of the human–machine system efficiency with time under different conditions were obtained, as shown in Figure 13.

From Figure 13, it can be seen that the most favorable condition for human–machine system operation is low humidity and low wind speed. Compared to humidity, wind speed has little effect on the human–machine system efficiency. The change in human–machine system efficiency caused by the change in unit wind speed under low-humidity conditions is greater than that under high-humidity conditions, indicating that the lower the humidity, the more significant the impact of wind speed on system efficiency. As humidity increases, the degree of impact of wind speed on system efficiency gradually decreases.

(4)

The impact of temperature humidity and wind speed coupling on the human–machine system efficiency:

Combining three factors can form eight different environments, as shown in

Table 2. Coupled environmental conditions of temperature, humidity, and wind speed.

No.	Temperature	Humidity	Wind Speed	Notes
1	1	1	1	Temperature	1 represents high temperature,
2	1	1	2		2 represents low temperature;
3	1	2	1
4	2	1	1	Humidity	1 represents high humidity,
5	1	2	2		2 represents low humidity;
6	2	1	2
7	2	2	1	Wind speed	1 represents high speed,
8	2	2	2		2 represents low speed;

. They were simulated separately and the variation curves of the human–machine system efficiency with time under different conditions were obtained, as shown in Figure 14.

According to the results, the eight types of work conditions can be classified into three categories. The first type of environment is condition 7 and condition 8, representing the optimal working environment, with a common characteristic of low temperature and low humidity. In this environment, the human–machine system can maintain efficient operation after 3 h. The second type of environment includes conditions 3, 4, and 6, where the system’s operational efficiency is lower than that of the first type. The third category includes conditions 1, 2, and 5, where the system has the lowest efficiency and is characterized by high temperatures. Therefore, it can be seen that temperature has the greatest impact on the human–machine system efficiency. In addition, changes in wind speed in the first type of environment result in significantly higher changes in system efficiency compared to the other two types of environments, indicating that the impact of wind speed on operational efficiency is more pronounced under low-temperature and low-humidity conditions, while high temperature or high humidity can weaken the effect of wind speed.

The ranking of the impact of three factors on the operational efficiency is as follows: temperature > humidity > wind speed.

5. Coupling Equation of Multiple Environmental Factors in Deep Well Working Face

To ensure efficient operation in deep mining, the environmental parameters of the deep well working face are determined based on the coupling effect of three environmental parameters. Then, the temperature thresholds under different conditions are obtained.

The humidity is set to 20% and the wind speeds are set to 1 m/s, 2 m/s, and 3 m/s, respectively, different temperature conditions are simulated, and the variation curve of the human–machine system efficiency with operation time is obtained, as shown in Figure 15. Based on the criterion of efficient operation in the study of the impact of a single environmental element on the human–machine system efficiency, the optimal temperature is selected based on the high efficiency of the system maintained at 0.8 or above during working hours.

From Figure 15, it can be seen that when the humidity is 20%, the wind speed is 1 m/s, and the temperature is 28 °C, the human–machine system efficiency remains at 0.8 until the end of the working time. Therefore, the maximum temperature required for efficient operation in this environment is 28 °C. Similarly, when the wind speed is 2 m/s, the max temperature is 29 °C; when the wind speed is 3 m/s, the max temperature is 30 °C. The method is repeated and the working conditions are simulated with humidity of 40%, 60%, 80%, and 100%, respectively. Finally, the highest temperature value that ensures efficient operation of the human–machine system under different humidity and wind speed conditions is obtained, as shown in

Table 3. Temperature thresholds under different environment conditions in underground working faces.

Humidity	Wind Speed	Temperature	Humidity	Wind Speed	Temperature
(%)	(m/s)	(°C)	(%)	(m/s)	(°C)
20	1	28	80	1	26
	2	29		2	26
	3	30		3	25
40	1	28	100	1	23
	2	28		2	24
	3	29		3	23
60	1	26
	2	27
	3	27

Note: The temperatures in the table are all dry bulb temperatures; when the humidity or wind speed is between the data in the table, the temperature threshold can be calculated using Equation (2).

.

By using the temperature values in Table 3 as the dependent variable and humidity and wind speed as independent variables for regression analysis, a temperature threshold model can be established to ensure efficient operation of the deep well human–machine system, as shown in Equation (2).

$$T=28.4-0.04·H+1.2·V-0.015·H·V (R^2=0.938),$$

(2)

where T—the max temperature for efficient operation of human–machine, °C; H—humidity, %; V—wind speed, m/s.

6. Discussion

To ensure the efficient operation of the human–machine system during deep mining, based on the theory of system dynamics and the factors affecting the human–machine system efficiency in deep mining are taken as key parameters. Modeling is conducted from the three aspects of human, machine, and environment. On this basis, the simulation of the human–machine system efficiency is completed, and the variation law of the work efficacy under the coupling effect of multiple environmental factors is obtained. This study is based on a large underground metal mine in China. The model is tested based on actual measured data, proving its effectiveness. Currently, the research results have been applied to this underground mine. By incorporating the underground environmental parameters into the coupling equation of multiple environmental factors, the environmental temperature that ensures efficient operation can be obtained, thereby guiding the ventilation and cooling work underground in the mine and providing favorable guidance for ensuring stable underground production efficiency.

However, in the process of constructing the model, the impact of equipment efficiency is mainly reflected in the impact of personnel on equipment efficiency, failing to reflect the impact of the environment on equipment. Moreover, the application scenario of the model is limited, and further optimization of the model is needed based on the characteristics of different underground mine environments to improve its applicability.

7. Conclusions

(1)

System dynamics can effectively express the dynamic and nonlinear feedback relationship between human–machine–environment. This method effectively addresses the problem of the difficult quantitative description of the logical and quantitative relationships between various elements in the study of human–machine system efficiency.

(2)

The human–machine system efficiency operation shows a trend of increasing and then decreasing with operation time. The order of the impact of environmental factors on the human–machine system efficiency is temperature > humidity > wind speed.

(3)

Based on the coupling effect of multiple factors, a coupling equation for multiple environmental factors was determined, describing the quantitative relationship between temperature, humidity, and wind speed. The temperature threshold for ensuring efficient operation of the human–machine system under different environments was obtained. These results provide a reference for efficient operation of the human–machine system in deep well mining.