A comprehensive risk assessment method for hot work in underground mines based on G1-EWM and unascertained measure theory

A risk assessment method for hot work based on G1-EWM and unascertained measurement theory was proposed to prevent hot work accidents in underground mines. Firstly, based on the risk influencing factors and classification criteria for underground hot work operations in mines, a single indicator measurement matrix was constructed using unascertained measurement theory; Secondly, a risk assessment index system for mine underground hot work operations was established. The combination weight coefficient of each index was determined using the order relationship analysis method (G1) and entropy weight method (EWM) and coupled with the single index measurement evaluation vector to calculate the multi-index comprehensive evaluation vector of the evaluation object; Finally, the model was validated and examined using engineering examples, and the evaluation level was determined using confidence identification criteria. The results showed that the proposed method, when used to evaluate the risk of hot work operations in tunnels and vertical shafts in metal mines, produces risk levels that are in line with reality III (Moderate Risk) for the vertical shaft and IV (High Risk) for the tunnels. The evaluation model results are consistent with the risk evaluation results the whole process of on-site hot work, which verifies the model feasibility. A unique strategy and method for risk management in hot work operations in underground mines is provided by the combination of weighting and unascertained measure models, which has theoretical and practical value. Future research could focus on refineing this model by exploring the applicability in diverse mining environments and integrating advanced analytical techniques to enhance the predictive accuracy and operational efficiency.


The unascertained measure theory risk evaluation model
Assume that the hot work risk evaluation object X corresponds to n evaluation indices, expressed as X = {x 1 , x 2 , . . ., x n } .If x i i = 1, 2, . . ., n has m risk levels, represented by R k k = 1, 2, . . ., m , then it can form an m-dimensional evaluation vector X i = {x i1 , x i2 , . . ., x im } , where x ij denotes the jth risk level of evaluation indicator x i in the hot work operation process.
By dividing x ij into P risk levels, the evaluation space T = C 1 , C 2 , . . ., C p of x ij can be obtained.If the risk level of kth is higher than the (k + 1)th risk level, this is denoted as C k > C k+1 , moreover C 1 > C 2 > . . .> C p , and C 1 , C 2 , . . ., C p is denoted as an ordered partition class 25 .

Determination of the single-indicator unascertained measurement matrix
According to relevant information of the evaluation object and the definition of an unascertained measure used to establish the single-indicator measure distribution function for whole-process risk evaluation of hot work operations, the single-indicator measure matrix of the evaluation object can be expressed as Eq.(1) 26-29 : where µ ijk is the degree of indicator assignment x ij at the kth risk level C k .

Entropy weighting method for calculating objective weights (EWM)
The entropy weight method is based on the degree of variation in each evaluation index, and can be used to calculate the corresponding entropy weight, for obtaining the objective weight of each index [29][30][31][32][33] .In the whole hot work operation process, each evaluation index exhibits quantitative outline and quantitative value differences, and it is necessary to first standardize the data.The objective weight of each evaluation index can be calculated as follows: Normalization of the indicators.Standardize the single-index measurement matrix.Let R ij represent the nor- malized indicator value.Then, the following can be obtained: Calculation of the information entropy of the indicators.
In the above equation, a ij is the weight of the jth indicator under the ith evaluation criterion, so a ij can be expressed as: Determination of the objective weights for indicators.The weight of the jth indicator is:

Order relationship method for calculating subjective weights (G1)
The order relationship method (G1) is a subjective weighting method proposed by Guo Yajun et al. 34,35 .This method builts upon the analytic hierarchy process (AHP) and involves ranking evaluation indicators based on their importance.Subsequently, weight can be quantitatively calculated by comparing the relative importance of adjacent indicators [36][37][38][39] .The specific steps are as follows: Determination of the order relationship between the evaluation indicators.Among the risk assessment indicators {x 1 , x 2 , . . ., x n } at the same level, the most important indicator, denoted as x * 1 , is selected by the expert according to the hierarchical evaluation criterion.The second most important indicator, denoted as x * 2 , is selected among the remaining n−1 indicators, and the process is continued until the last indicator factor is selected after n−1 selections, denoted as x * n .Theorder of the available evaluation indicator is as follows: Calculation of the relative importance of the indicators.Referring to Table 1, which provides relative importance values for the risk assessment factors, the importance ratios r k between adjacent evaluation indicators x * k−1 and x * k are as follows: (1) where w k−1 and w k are the weighting coefficients of evaluation indicators x k−1 and x k , respectively.
Determination of the subjective weights of the indicators.Based on the relative importance of the indicators, the weight of the kth indicator can be calculate as follows: The weights of the other indicators at each level are:

Combination weights
According to the aforementioned methods, the evaluation process of the entropy weight method heavily relies on objective data from hot work sites, while the order relationship method more notably depends on the knowledge level and subjective experience of experts.To avoid subjectivity due to subjective weighting and considering the mathematical nature of objective weighting, the order relationship method and entropy weight method are combined in this paper to calculate weights [39][40][41] .The combination weight Z i for each evaluation indicator can be calculated as follows: where w i denotes the subjective weights; and v i denotes the objective weights.

Determination of the multiple-indicator unascertained measurement matrix
Based on Eq. ( 10), the weight of the risk evaluation index of the whole hot work operation process is Z i .If µ ik satisfies 0≤ µ ik ≤ 1 , µ ik can be expressed as follows: The the evaluation matrix (µ ik ) m×p for the whole hot work operation process with multiple indicators of unascertained measurement can be obtained as:

Identification of the confidence criterion
To comprehensively assess the risk evaluation level of hot work operations and ensure the accuracy of the assessment results, a confidence criterion is introduced.Let the confidence degree be noted as ≥ 0.5(usually 0.6 or 0.7).If the evaluation vector is an ordered partition class and C 1 > C 2 > . . .> C p , the following is satisfied: then the risk level of the evaluation object belongs to P 0 .

Selection of evaluation indicators
Although regulatory authorities have issued regulations to standardize hot work operations in underground mines, mining enterprises are still struggling to identify the risk factors involved in the entire hot work operation process s.Moreover, they face difficulties in defining safety measures and inspections before hot work operations and ensuring clear responsibility control throughout the hot work process.To address these issues, the factors that affect the safety of hot work operations are comprehensively analysed in this pape.The analysis considers recent hot work accidents, relevant laws, regulations, and the literature, and focuses on four key aspects: human, equipment, environment, and management factors.A total of 19 influencing factors are identified as evaluation indicators, and a risk indicator assessment system for hot work accidents is established.This system can help mining enterprises improve their safety measures and inspections and ensure the safety of hot work operations.

Criteria for grading and quantification of evaluation indicators
Based on the characteristics of hot work operations, the evaluation space T is divided into five levels {C 1 , C 2 , C 3 , C 4 , C 5 } , i.e., I, II, III, IV and V, representing an extremely low risk (I), low risk (II), moderate risk (III), high risk (IV), and extremely high risk (V), respectively.The specific grading criteria and assigned values forthe risk-influencing factors are provided in Table 2.

Implementation steps
Based on unascertained measure theory and G1-EWM method, a risk evaluation model for mine hot work operations is constructed.The specific steps are shown in Fig. 1.
Step 1 Construct a risk indicator system based on the hot work evaluation object and set the risk level for each index.
Step 2 Determine the subjective weights of each evaluation index using the order relationship method (G1).
Step 3 Determine the objective weights of each evaluation index using the entropy weight method (EWM).
Step 4 Calculate the combined weight of each evaluation index.
Step 5 Construct the single-index unascertained measurement function for the indicators according to the definition of unascertained measurement theory.
Step 6 Determine the multi-index unascertained measurement function for indicators.
Step 7 Determine the risk level of the evaluation object based on the confidence identification criteria.

Model application
Adopting a metal mine in Yantai, Shandong Province, as an example, the underground mining operation exhibits a production scale of 330,000 t/a.The mine has been excavated down to the mid-level of − 390 m, and the area from − 390 to − 630 m is part of a new system.The construction involves six major systems: underground drainage system, a ventilation system, a water supply and firefighting system, a lifting and transportation system, a power supply and distribution system, and safety precautions.The mine also manages the beneficiation plant and production mine jointly, involving a significant number of hot work projects such as pipeline welding and equipment maintenance.Currently, 80 personnel are qualified in terms of melting welding and thermal cutting operations.Through the analysis of various aspects, including the mine hot work operation management system, approval processes, safety training before hot work initiation, safety inspections, and personnel violations during hot work, a total of 19 risk factors related to the entire hot work operations process were selected for measurement and evaluation.Because of the uncertainty in the underground hot work operation locations, it is necessary to evaluate the risk factors for hot work operation at different locations in the underground minesto determine the corresponding level of safety protection according to the evaluation results and ensure the safety of the hot work operation process.In this paper, we evaluate the risk consideringtwo typical hot work operation scenarios: mine shafts and tunnels.

Constructing single-indicator measurement functions
According to Table 2, = the risk evaluation indexes of hot work operation include qualitative indexes and quantitative indexes, and some qualitative indexes must be combined with expert scores and the actual mine conditions to obtain more accurate evaluation results.The values assigned to the risk indicator factors involved in the hot work operations process in the shaft (= #1) and tunnel (#2) are listed in Table 3.In the case of analysing hot work operations in the shaft, according to the definition of the single-indicator measurement function and assignment results of the evaluation indicator factors in Table 3, the single-indicator unascertained measure function is used to construct the unknown measurement function of each indicator for evaluating the risk of hot work operation in underground mines, as shown in Fig. 2.Among them, Fig. 2a shows a linear graph of the single factor measurement function for 16 qualitative evaluation indicators.The 16 qualitative indicators are pre-job safety training (X 1 ), PPE usage (X 2 ), proper operation (X 3 ), licenced operation (X 4 ), cylinder stabilization (X 7 ), grounding of welding machine shell (X 8 ), flame-resistant cables (X 9 ), toxic and hazardous gas detection (X 10 ), worksite lighting (X 12 ), pumice on the work site slab (X 13 ), hot work operations classification and procedures (X 14 ), hot work permits (X 15 ), risk factor identification (X 16 ), specialized emergency protocols (X 17 ), fire extinguishers (X 18 ),  ).The single factor measurement functions for the 3 quantitative evaluation indicators are shown in Fig. 2b-d.

Determination of the subjective weights
The order relationships and relative importance of the risk factors at the various levels of hot work operations were determined by multiple experts and management personnel in the field of metal mining.The findings are provided in Table 4.

Determination of the objective weights
Based on the single-indicator measurement matrix and Eqs. ( 2)-( 5), the entropy value and objective weight of each indicator were calculated as listed in Table 6.

Determination of the combined weights
Asshown in Tables 4 and 5, there is a certain difference between the subjective and objective weights.Therefor it is necessary to calculate the combination of weights of the dynamic hot work operation process by Eq. ( 10), and the results are provided in Table 7.

Determination of the multi-indicator uncertainty matrix and risk level
The evaluation vector of the comprehensive evaluation objects can be obtained by matrixing the combined weight vector of the hot work operation risk evaluation indicators and the single-indicator measurement matrix provided in Table 6 through Eq. ( 11) µ ik1# = {0.3653,0.1059, 0.2582, 0.1338, 0.1369}.The confidence level is = 0.7 as calculated by the confidence identification criteria and Eq. ( 13), i.e., C1 + C2 + C3 = 0.7293 > 0.7.The safety risk level of tmine hot work operations was assessed as Class III, indicating a moderate risk level.Similarly, the calculated multi-index comprehensive measurement evaluation vector for hot work operations in tunnels is µ ik2# = {0.3654,0.1484, 0.1079, 0.1264, 0.2519}.According to the confidence identification criteria, C1 + C2 + C Table 4.The order relationship and relative importance of indicators at different levels.

Indicator level
Order of importance Order relationship Relative importance(r k ) Human factors

Result analysis
(1) As described in section "Determination of the multi-indicator uncertainty matrix and risk level", we can obtain a multi-indicator measurement matrix for the shaft and tunnel.According to the confidence identification criteria and Table 8, the risk level of hot work operation in the shaft is Level III, which belongs to the 'moderate risk' class, and the risk level of hot work operation in the tunnel of the mine is Level IIV, which belongs to 'high risk' class, which agree with the actual situation of the mine.The risk level of the 2 workplaces is 2# > 1#, i.e. the risk level of hot work operation is high in the tunnel than in the shaft, because the middle section of the mine extends from −390 to −630 m.This newly built system involves many pipeline welding, equipment maintenance and other projects, which increase the risk level based on the site conditions.(2) According to the results of the combination weights of the indicators in Table 7, combustible materials at the work site (X11) exhibit the highest weight (0.1690), indicating that the main cause of accidents due to fire operations is that combustible materials at the fire operation site are not removed, and high-temperature particles generated by impacting the surface of combustible materials trigger fire accidents.This is followed by the management of factors in the field of fire operations to identify the risk factors at the work site (X16), with a comprehensive weight of 0.0822.This value indicates that before fire operations, a detailed operation plan should be formulated for the operation site, and the risk and harmful factors at the site should be comprehensively recognized to ensure favourable safety preparation.Finally, the operation plan is an indicator of correct operations at the operation site in terms of personnel factors (X3), with a comprehensive weight of 0.0464, which indicates that compliant operation by personnel in the fire operation process exerts a greater impact on the whole fire operation project.(3) In terms of safety management, mines should develop a strict hot work operation approval system and operation site supervision system, from the intrinsic safety aspect to improve the hot work operation safety risk control, standardize the personnel operation behaviors, and realize effective control of whole stage hot work operation risk factor.

Conclusion
In this study, a novel risk evaluation method for underground mine hot work operations was proposed.This method incorporats both subjective and objective weightings approach into the evaluation process and was subsequently applied.The following conclusions can be obtained: (1) The unascertained measurement theory is applied in risk analysis of hot work operations in noncoal mines, leading to the development of an unascertained measurement model for assessing the risk throughout the entire process of hot work operations.The utilization of the confidence identification criteria effectively determines the final risk level of hot work operations.This approach successfully addresses the issues of multifaceted, fuzzy, and uncertain factors in the evaluation of risk levels in noncoal mine hot work operations.(2) A risk assessment index system for hot work operations in noncoal mines is established, considering human, equipment, environmental, and management factors.The combination of the combined weight method, the order relationship method, and the entropy weight is introduced to determine both the subjective and objective weights for each evaluation indicator.This integration enhances the rationality and accuracy of the evaluation results.(3) By applying the method proposed in this paper in risk assessment of hot work operations in vertical shafts and tunnels in a metal mine, we obtained risk level III (moderate Risk) for vertical shafts and risk level IV (high risk) for tunnels.Moreover, the risk assessment results for the two hot work operation areas showed a ranking of 1# > 2#.The evaluation process demonstrated high feasibility, and the results are consistent with the actual on-site conditions.These results provide valuable reference information for risk management and assessment of hot work operations in mining enterprises.(4) Considering the risk levels of various indicators calculated previously and the problems present in actual hot work operations.Hot work supervisors should pay close attention throughout the entire hot work process to the following aspects: Firstly, the approval process of the work permit before hot work operations, safety training, and on-site safety inspections, with a particular emphasis on the removal of combustibles on-site as a critical component; secondly, the monitoring of dangerous, toxic, and harmful gases during the hot The underground mine environment is complex.The limitation of this model is that the selected evaluation indicators cannot fully cover all potential risk factors, and indicators of human factors, such as the professional level, experience and behaviour.during hot work are difficult to quantify.And the model calculation process lacks a risk likelihood scale similar to that of literature [42][43][44][45] , which does not provide a specific and comprehensive risk measurement framework This model provides an important theoretical basis and assessment framework for risk management of underground mine hot work operations.Regarding other restricted space activities in mines only the evaluation indicators and indicator risk levels should be adjusted to obtain reasonable risk assessment results, which can provide a systematic reference for mining enterprises in safety management.

Figure 1 .
Figure 1.Specific steps of evaluation model for hot work operations.

Table 2 .
Risk indicator classification criteria for the hot work operation.

Table 3 .
Assignment of risk assessment indicators in mine shafts and tunnel.

Table 5 .
Subjective weight of evaluation indicators.

Table 6 .
Entropy and objective weight of evaluation indicators.

Table 7 .
Combination weight of hot work evaluation indicators.Weight 0.1690 0.0565 0.1006 0.0639 0.0605 0.0822 0.0657 0.0698 0.0476 -work process; and lastly, the extinguishing of fire sources after the completion of hot work operations.Hot work is one of the significant risks for mine fires and explosions.Effectively isolating combustibles and dangerous flammable and explosive gases at the hot work site can significantly reduce the incidence of fire accidents caused by hot work operations.