Risk identification of coal spontaneous combustion based on COWA modified G1 combination weighting cloud model

To realize the scientific judgment of spontaneous combustion risk in the coal mine, the spontaneous combustion influence factors were analyzed from the three aspects of coal spontaneous combustion tendency, air leakage, and oxygen supply, heat storage and heat dissipation. And the basis for the evaluation of t spontaneous combustion grade was constructed. Combination ordered weighted averaging (COWA) calculation was introduced to optimizes G1 subjective weighting, and a COWA modified G1 combined weighting cloud model was proposed to identify the spontaneous combustion risk in the coal mine. Finally, the rationality of the model was verified with actual cases. The research results show that the spontaneous combustion risk level in the Lingquan coal mine is relatively safe, which is consistent with the actual situation. And the spontaneous combustion tendency of coal is the leading factor affecting spontaneous combustion risk.

Heat storage and heat dissipation conditions. Surrounding rock temperature is an important influencing factor of heat storage in goaf. The higher the surrounding rock temperature is, the higher the risk of coal spontaneous combustion is 21 . When the depth of the coal seam is deep, the higher the initial temperature of coal is, the shorter the spontaneous combustion period of coal is 22 . The complex geological structure in coal seam affects the mining speed and prolongs the contact time between coal and air 23 . Therefore, the heat storage and dissipation conditions are determined by the surrounding rock temperature, coal seam depth, and coal seam geological structure.
Classification of spontaneous combustion hazard. Based on the classification basis of mine spontaneous combustion 24,25 , the risk level of spontaneous combustion and influencing factors are divided into four grades: I, II, III, IV, which represent low risk, general risk , greater risk ,significant risk respectively, as shown in Table 1.
COWA modified G1 comprehensive weighting method G1 subjective weight determination. The G1 method is a subjective weighting method that can reflect the importance of indicators 26 . The calculation steps are as follows: (1) Experts sorted the importance of evaluation indicators to determine the sequence relationship of indicators; (2) Determine the importance ratio of adjacent indicators X k-1 and X k ; where r k is the importance ratio of adjacent indicators, d k-1 is the importance of indicator X k-1 , and d k is the importance of indicator X k .
(3) Based on the importance ratio r k of adjacent indexes, the weight of indexes is calculated by G1 method; (1) www.nature.com/scientificreports/ where ω k ,ω k−1 are the subjective weights of the kth, k − 1th indicators determined by the G1 method, and n is the total number of indicators.
COWA operator. The COWA operator arranges the indicator data in descending order, and combines the position of the indicators for weighting, reducing the influence of subjective extreme values on indicator weights. It is an objective weighting method 27,28 . The calculation steps are as follows: (1) The index data is processed in descending order to obtain a reconstructed data set where ω i is the absolute weight of the index and b j is the jth data value.

(4) Calculation of relative weight values of indicators:
where ω i is the relative weight value of the index.
Combination weighting under COWA correction condition. To take into account the subjectivity of decision-makers and the objectivity of data, and reduce the impact of subjective weighting extremum on weight, a COWA modified G1 combination weighting method is proposed. Based on game theory, the optimal combination of subjective weighting and objective weighting is realized by establishing combination weights and minimizing the difference between weights 29 . The calculation steps are as follows: (1) Assuming that the number of index weighting methods is m, the number of weight combinations is: where u i is the linear combination coefficient and ω T i is the weight of each assignment method. (2) Combinatorial coefficients ui solving.
If the optimal point of the combinatorial assignment method is realized, the optimization model can be constructed as: Then the first-order derivative condition for its optimal condition is: (3) Combined coefficients ui normalization processing: (4) Based on the above analysis, the optimal combination weights are: (1) Cloud model definition and its numerical characteristics In mine endogenous fire evaluation, assuming that U is the theoretical domain corresponding to the values of endogenous fire indicators, C is the qualitative concept in endogenous fire evaluation indicators, x denotes cloud drops, and u(x) is the affiliation degree of any cloud drop x to C in the theoretical domain U, then The cloud model is represented by expectation (Ex), entropy (En), and superb entropy (He). Ex is the center of the cloud graph, En characterizes the reliability of Ex, and He characterizes the uncertainty of En. The distribution interval of cloud drops x is [Ex-3En, Ex + 3En].
(2) Cloud Generator The cloud generator is divided into forward and inverse cloud generators. The forwarding cloud generator mainly realizes the conversion from qualitative concept to quantitative, and the calculation steps are as follows: where F max is the upper limit of the index value, F min is the lower limit of the index value, and k is the degree of index fuzziness, which is taken as 0.05 here.
Then, based on the graded values of Table 1 indicators, the cloud numerical characteristics of the mine endogenous fire evaluation indicators are calculated by Eq. (14), and for variables with unilateral boundaries, their numerical characteristics are obtained in the form of boundary parameters 33,34 , as shown in Table 2.
Comprehensive discriminative model construction. Based on the cloud numerical characteristics of the evaluation indexes of mine internal fires, Matlab software is used to generate the cloud diagram of evaluation indexes, determine the determinacy of each index under different hazard levels, and then combine the G1 combination weights under COWA correction conditions to obtain the comprehensive rating of mine internal fires.
Ex = (F min + F max )/2 En = (F max −F min )/6 He = k www.nature.com/scientificreports/ where ψ x is the single indicator determinant and ω * is the optimal combination weight.

Case analysis
Determination of index weights. The II 3 coal seam of Lingquan Coal Mine in Inner Mongolia is selected as an application example, the degree of charring and metamorphism of coal is 0.32, the coal seam buried depth 447 ~ 470 m; coal seam gas content 7.8m 3 /t; the geological structure is simple, the average thickness of coal remains 1.2 m, the average speed of advance 9 m/d, the average thickness 14.69 m, the lithology of the roof is medium sandstone, the measured water content 3.19%, ash content 12.14%, sulfur content 0.16%, the temperature of the surrounding rock is about 23 °C, and the natural firing period is 40d, which is easy to the spontaneous combustion coal seam. The values of qualitative and quantitative indicators were determined by expert experience, and based on the principle of weight determination by the G1 method, industry experts were hired to analyze the serial relationship and importance among the indicators, and calculate the subjective weights according to Eqs. (1)-(3), while determining the objective weights based on COWA operator according to Eqs. (4)-(6), and finally combining Eqs. (7)- (11) to determine the comprehensive weights of the indicators, as shown in Table 3.
Determination and analysis of risk grade. Based on the cloud numerical characteristics of mine endogenous fire indicators in Table 2, the risk level determinacy of each indicator was calculated by Eq. (13), and then combined with the comprehensive weights of each indicator of endogenous fire in Table 3, the comprehensive determinacy of the hazard evaluation model was calculated by Eq. (15) to determine the hazard level of endogenous fire in Lingquan coal mine. The determinacy of the risk level of endogenous fire in Lingquan coal mine was calculated as P(I) = 0.046, P(II) = 0.260, P(III) = 0.074, P(IV) = 0.095, respectively, and it is known that the risk boundary of endogenous fire in Lingquan coal mine is level II according to the principle of maximum determinacy, which is consistent with the actual situation of the mine. The calculation method and evaluation criterion of reference 3 were selected to analyze the risk level of endogenous fire in the Lingquan coal mine, and the result was a general risk level, and the results of the two methods were consistent, which showed the reasonableness of the COWA modified G1 combined assignment cloud model in the evaluation of endogenous fire in the mine. Meanwhile, the weights of each index in Table 3 were analyzed, and the weights were arranged in descending order, in which the secondary index sequence was spontaneous combustion propensity condition of coal > air leakage and oxygen supply condition > heat storage and heat dissipation condition, and the tertiary main index sequence was coal seam depth > surrounding rock temperature > water content > ash content > sulfur content, and the results were approximately the same as the findings of references 3 , which verified that the COWA modified G1 combined assignment weighting method was more effective in determining the endogenous fire risk. The scientific feasibility of the COWA modified G1 combination weighting method in determining the weights of fire indicators.

Conclusion
(1) Considering the three aspects of coal spontaneous combustion tendency condition, air leakage oxygen supply, and heat storage, the grade evaluation basis of fire risk index in mine is constructed. www.nature.com/scientificreports/ (2) The COWA modified G1 combination weighting cloud model is proposed to identify the fire risk in the mine, and the Lingquan coal mine is taken as the engineering background for verification. The risk level is relatively safe, which is consistent with the actual scene, and is consistent with the conclusion of the CW-TOPSIS method. (3) Based on the COWA modified G1 combination assignment method, the weights of each index are analyzed in descending order, among which, among the secondary indexes, the propensity of coal to spontaneous combustion has the greatest influence on mine internal fire, and among the tertiary indexes, the depth of coal seam, the temperature of surrounding rock, water content and ash content are the main factors affecting mine internal fire. Based on the COWA modified G1 combination assignment method, the weights of each index are analyzed in descending order, among which, among the secondary indexes, the propensity of coal to spontaneous combustion has the greatest influence on mine internal fire, and among the tertiary indexes, the depth of coal seam, the temperature of surrounding rock, water content and ash content are the main factors affecting mine spontaneous combustion.