Research and Application of Rock Burst Hazard Assessment of the Working Face Based on the CF-TOPSIS Method

. Coal mining activities have intensifed


Introduction
Coal is a pivotal source of energy in China's energy portfolio [1]. However, with the gradual exhaustion of shallow coal seams, deep mining has become increasingly prevalent, leading to a higher probability of deep rock bursts [2,3]. Tus, to ensure the safety of coal mining operations, accurate and efective prediction of rock bursts in deep mining must be based on scientifc and rigorous principles [4].
Numerous scholars have conducted extensive research on predicting rock bursts [5]. Teir proposed measures can be categorized into mine-wide prediction (intelligent hazard-level judgement), regional prediction (utilizing three spatialtemporal monitoring methods), and local prediction (employing a multiparameter monitoring and early warning index system for rock bursts) [6][7][8][9][10]. Given the complexity of factors contributing to rock bursts, evaluating the level of rock bursts in mines can be challenging. Wu et al. [11] judged rock burst hazard levels by utilizing a rock comprehensive prediction model, which involved determining the hazard index of rock bursts. To predict the static properties of coal and rock mass, Jiang et al. [12] developed a possibility index diagnosis method that considers mining stress and the burst tendency of coal seams as primary indices. Zhu and Zhang [13] introduced the Lagrange function to optimize the decision model and address the issue of determining the weight of rock burst disaster system evaluation models. Han et al. [14] established the division method of geological dynamic zones, incorporating fault structure and coal rock characteristics to enable accurate coal mine prediction. Based on the cloud model and D-S theory, Chen [15] evaluated the hazard of rock burst, while Cai et al. [16] further developed the spatiotemporal forecasting method for rock bursts using multidimensional microseismic information. To address the challenge of predicting dynamic disasters caused by various factors and the heterogeneity of coal and rock in mining operations, Meng et al. [17] studied the general patterns and hazard control factors of rock bursts. Additionally, in regional prediction methods that involve "strong time and space" considerations, several techniques such as the generalized artifcial neural network [18], particle swarm optimization KNN, cloud model, and decision tree [19,20] have yielded promising results in rock burst prediction. However, each prediction method has its limitations. For instance, the convergence speed of intelligent algorithms like generalized neural networks may be slow. Decision tree algorithms can be prone to overftting and may overlook correlations, while the analytic hierarchy process may exhibit strong subjectivity. Similarly, the conventional objective weighting method may fail to account for interindicator correlations [21][22][23][24][25].
Given that rock bursts can be afected by numerous factors [26,27], this study optimizes the correlation and confict of CRITIC and constructs the CF comprehensive weight evaluation index through a combination of the FAHP's subjective weight approach [28]. Te improved TOPSIS rock burst closeness evaluation and prediction model yields more accurate and reasonable predictions of rock burst grade. Te accuracy of these predictions is verifed through a practical example, highlighting the efectiveness of the proposed approach.

Comprehensive Weighted Prediction Model
Rock bursts occur due to the infuence of multiple factors, and the rock burst of each factor on rock bursts can vary. As such, determining a reasonable comprehensive evaluation model for rock bursts and assessing the hazard level of the working face are of paramount importance.

Improved Objective Weighting
Method. Te entropy weight method (EWM) is an important means of reducing subjective factors in the evaluation process. However, EWM has limitations in refecting the interrelationship between criteria, which may afect the accuracy of the evaluation results. To address this issue, a new approach called criteria importance through intercriteria correlation (CRITIC) was proposed by Diakoulaki in 1995. CRITIC serves to optimize the weighting procedure and improve the objectivity of the evaluation process by taking into account the interrelationship between criteria [29,30]: (1) Te index data matrix X � (x ij ) m×n is established, and indicator types are unifed.
x ij � x ij (1) , where x ij is the original data of the infuencing factors of rock burst and x (1) ij is the positive value of the index.
(2) Standardized processing of forwarded matrices is (3) Te correlation coefcient between the infuencing factors is obtained by the processed matrix.
Tere is a connection between the infuencing factors, and the deviation product can well measure the degree of correlation between the two variables: (3) ξ ij indicates that (i � 1, 2, 3 · · · n; j � 1, 2, 3 · · · n) is the correlation coefcient between the ith indicator and the jth indicator, and the value of ξ ij is between (0, 1). Te greater the value of ξ ij , the greater the correlation between the two factors. (4) Te information amount of the comprehensive measurement index is as follows: Information measure C j is defned based on contrast strength and confict concepts: where C j represents the defnition of information measure, σ j represents variance, and ξ ij represents the correlation coefcient. In the present study, an optimized criteria importance through intercriteria correlation (CRITIC) approach is proposed to enhance the objectivity of weight determination. While Zhang and Xiao [31] proposed the use of CRITIC, this method has not been applied in the feld of rock burst hazard assessment. Te signifcant diferences in infuencing factors of rock burst pressure are addressed by optimizing the CRITIC approach in order to account for these diferences. Due to the large variations in rock burst pressure infuencing factors, the value of the consistency coefcient (C j ) may become too large, leading to errors in the determination of weight factors. Te coefcient of the variation method is utilized to enhance the CRITIC approach and address errors stemming from excessively large C j values. Furthermore, the method is optimized to accommodate situations where notable variations in indicator values pose challenges in implementing the coefcient of the variation approach: where j is the number of index values and σ j is the variance. In Zhao et al. [32] evaluation of power quality classifcation, the 1 − ξ ij value refects the confict between diferent evaluation indicators. However, when the relationship between indicators is negative, weighting may become disproportionately large. To address this issue and account for the conficts among coefcient values, a positive confict transformation method is introduced to optimize the weight determination process. By applying this approach, the issue of disproportionately large weights resulting from negative correlations between indicators is efectively mitigated: where v i is the introduced coefcient of variation and ξ ij is the correlation coefcient. (5) Calculation of the index weight of the information measure index is where w Aj represents the weight value of the index j.

Determining Subjective Weight by FAHP.
Te traditional AHP method fails to maintain consistency in thinking when facing multiple evaluation indicators. It is difcult to test the consistency of the judgment matrix, which fails to provide a strong scientifc basis. In order to further optimize the reliability of the subjective weight, the author uses the fuzzy analytical hierarchy process (FAHP) to establish a multiobjective, multilevel structure of the subjective weight of the rock burst subjective decision model [33]. A number of experts with rich work experience compare and judge the two factors of rock burst, construct the judgment matrix J � (a ij ) n×n , and calculate the average value of each a ij obtained by many experts to obtain A � (a ij ) n×n . Te subjective weight w Bj is obtained by summing the fuzzy judgment matrix A by rows and exchanging them mathematically: Te subjective factor weight calculation equation is as follows:

CF-TOPSIS Regional Static Prediction before Mining.
Te technique for order preference by similarity to ideal solution (TOPSIS) can better describe the strength of multifactor comprehensive infuence of rock burst without the objective function and test [34]. TOPSIS avoids errors caused by subjective factors in data and is often used for multiple indicators and evaluation units [35]. In this paper, through the optimized CF combination weight, according to the distance between the positive and negative ideal solutions, the rock burst pressure level and the working face to be measured are sorted to realize the prediction of the rock burst hazard level of the working face before rock burst pressure mining. Te optimized objective weight and the subjective weight are combined to obtain the CF comprehensive weight: where W AB is the comprehensive index weight coefcient and w Aj and w Bj represent the values of the objective weight and subjective weight after optimization, respectively.

Original Judgment Matrix.
Te rock burst level scheme set is set as G � G 1 , G 2 , · · · , G m , and the index set to be evaluated is e � e 1 , e 2 , · · · , e m . Te binary comparison decision matrix, as presented in equation (10), serves as a means of identifying the internal correlated signifcance of factors [36]. Te evaluation index e ij represents the jth evaluation index of the ith scheme. Te initial evaluation matrix is as follows:

Standardized Decision Matrix.
Te evaluation index can be divided into the consumption index and proftability index. For the consumption index, the smaller the value, the better. For the proftability index, the larger the value, the better. Because each evaluation index has diferent dimensions and units, it has no comparability, so e ij is standardized to get the decision matrix B � (b ij ) m×n : Shock and Vibration where b * ij is the proftability index and b ij is the consumption index.

Weighted Standardized Decision Matrix.
Te weighted standardized decision matrix E is obtained by multiplying the column vector of matrix B with the total ranking weight W n of the determined comprehensive weight index layer: 2.3.4. Close Degree Analysis. Te positive ideal solution of the proftability index set l 1 is the maximum value of the row vector, the negative ideal solution is the minimum value of the row vector, and the value of the consumption index set l 2 is the opposite: where E + and E − are the positive ideal solution and the negative ideal solution, respectively. In order to better optimize the distance between the evaluation object and the ideal solution, the infuence of each infuencing factor on the rock burst of low pressure is diferent. Te greater the weight, the greater the possibility of rock burst. Zhu and Zhang [13] incorporated the weighting coefcients w AB into the positive and negative ideal solutions to develop the CF-TOPSIS model. Trough this approach, they were able to optimize the rock burst of the weight coefcients on the evaluation of the rock burst of ground pressure while also conducting proximity analysis. Te deviation equation resulting from the weighting coefcients and the Euclidean distance of the ideal solutions were also examined: where e + i and e − i are the element corresponding to the positive and negative ideal solutions and F + i and F − i represent the distance between the positive and negative ideal solutions.
Te calculation equation of closeness analysis is as follows: where H + i is the value of the closeness degree of the evaluation object, and the range is (0, 1), which refects the degree of closeness of the evaluation object to the positive ideal solution.
Te evaluation matrix is constructed by the close degree analysis of the TOPSIS method. Te comprehensive evaluation result vector Q of the CF-TOPSIS model is calculated as follows: where Q is the comprehensive evaluation result vector, H is the evaluation matrix formed by the closeness degree between each evaluation object and the positive ideal solution, and W is the criterion layer weight calculated by the comprehensive weight method. Te CF-TOPSIS comprehensive evaluation model is shown in Figure 1.  Table 1, the FAHP criteria layer can be divided into the following levels First, the stability level of the goaf support layer, which includes indicators such as the distance between the hard and thick rock layers and the coal seam inside the overlying fracture zone, mining depth, and thickness of the remaining coal seam, is used to evaluate the stability of the goaf support layer. Second, the stability level of the working face, which includes indicators such as the historical number of occurrences of the same level of coal seam rock bursts, the ratio between the stress increment of the structure and the normal stress %, the uniaxial compressive strength/MPa, and the elasticity index are used to evaluate the stability of the working face. Tird, the level of mining technology, which includes indicators such as the working face length, the width of the segment coal pillar, and the relationship between the working face and the adjacent goaf, is used to evaluate the rationality, efciency, and safety of mining technology. Terefore, the basic parameters of the 8003 working face are entered in Table 1, and the CF-TOPSIS evaluation model is employed to predict its rock burst hazard.

Comprehensive Weighting Prediction and Rock Burst
Hazard Assessment. Table 1 is imported into the improved CRITIC objective weighting model and then substituted into equation (7) together with the subjective weight obtained by FAHP, which yields the ideal evaluation index for rock burst factor assessment, as presented in Table 2.
Comparison of the weights in Table 1 reveals diferences in the degree of infuence of diferent rock burst criteria on rock burst events. Specifcally, the relationship between the primary and secondary factors afecting rock burst is A3 > A2 > A4 > A1. Tis analysis is of signifcant value in guiding the optimal selection of rock burst criteria.
Equations (1)-(4) are utilized for the creation of a line chart showcasing index weights for the unoptimized CRITIC model. In order to optimize said model, the integration of equations (5) and (8) is carried out to obtain the optimal CRITIC objective weight. Once the optimized objective weight and the FAHP subjective weight w Bj are substituted into equation (12), the weight curve is derived and compared with real-life conditions. Figure 2 is obtained by comparing the outcomes of the unoptimized and optimized CRITIC models with the optimized CRITIC + FAHP model. Trough comparison of weight values before and after optimization, as illustrated in Figure 2, slight increases in the weight values of indicators A2, A4, and A5 are observed after FAHP optimization, while the weight of indicator A3 decreases slightly. Te CF weight evaluation model enables a more reasonable weight index to be applied that aligns with actual site conditions, surmounting limitations encountered by conventional models that exhibit signifcant diferences. Verifcation of the optimized results through feld analysis confrms their alignment with staf subjective evaluations.
In the comprehensive index method, rock burst events are categorized into four grades: no, weak, medium, and strong. Weak, medium, and strong critical values of rock burst correspond to S1, S2, and S3, respectively, with the value of S representing the working surface value to be measured. When S < S1, there is no rock burst hazard, and  Te CRITIC method is conducted without the inclusion of the coefcient of the variation method and the confict forward optimization method. Furthermore, the total ranking of the TOPSIS hierarchy is not considered, and weight and equation (17) with w AB are not added. Te obtained TOPSIS model is unoptimized, as illustrated in Figure 3(a). Subsequently, a comprehensive evaluation model is established by combining FAHP with the unoptimized TOPSIS model, as depicted in Figure 3(b). Ultimately, the comprehensive evaluation results for the CF-TOPSIS model are presented in Figure 3(c). Figure 3(a) shows that the comprehensive evaluation index of traditional CRITIC and traditional TOPSIS methods for rock burst is w � (0, 0.3933, 1, and 0.5807) and that the evaluation grade of the rock burst index is medium. In contrast, Figure 3(b) shows that, with the combination of FAHP and unoptimized TOPSIS, the evaluation index of rock burst is weak and w � (0, 0.4594, 1, and 0.2056). Both models exist, and when S < S1, it is difcult to accurately predict the hazard of rock burst in the working face to be measured, since the index cannot be negative. Moreover, only when S � 1, a strong level of rock burst can be determined. Terefore, the critical value interval of traditional models has certain limitations.
Te CF-TOPSIS evaluation model produces an evaluation index of w � (0.0569, 0.3638, 0.8360, and 0.5352), which is medium in 8003 coal mine conditions. When no rock burst danger exists, the result of the working face prediction indicates no rock burst hazards when w < 0.0569. Conversely, when w ≥ 0.8360, a strong rock burst hazard is predicted, as shown in Figure 3(c). Tis method is only suitable for research at coal mine experimental sites, and there may be some special conditions or factors at other sites that may not be applicable to other sites. Terefore, this method cannot simply be applied to other sites and needs to be adapted and improved according to the specifc situation.

Prediction of Rock Burst under Microseismic Monitoring
Technology. Te process of microseismic event evolution, from a dispersed pattern in space to self-organized concentration, is a distinct characteristic of rock burst precursors. Te energy level of a single event per day is classifed as moderate hazard, ranging between 10 4 -10 6 J, with the potential for a strong rock burst hazard exceeding 10 6 J.
Based on the microseismic monitoring data obtained from the 8003 working face, as illustrated in Figures 4 and 5, the majority of microseismic events recorded near the working face possessed an energy range of 10 4 -10 6 J, which accounted for 88% of the total events within the considered time period. Te weaker events with energy levels below 10 4 J comprised 11.75% of the total events observed. Tere was only one instance of a microseism event with an energy level exceeding 10 6 J, which occurred during directional blasting for decompression in the roadway at the site. Consequently, based on a comprehensive assessment, the rock burst hazard level for the 8003 working face can be classifed as medium.

Characteristic Analysis of Large Energy Signals.
Te coal mine in Shanxi, China, has a mining depth ranging from +925 to +945 meters. As multistage large-scale mining methods are employed and mining depth deepens, safety hazards such as rock burst become increasingly prominent. To ensure mine safety, an independently developed microseismic monitoring system with a sensor sampling frequency of 2000 Hz is installed in the mine. During the safety monitoring process, signifcant energy microseismic events are detected. Trough eliminating irrelevant interference signals, the collected on-site microseismic signals, coupled with large energy vibration signals, are analyzed as depicted in Figures 6 and 7.
It is evident from the decomposition results presented in Figure 8 that the frequency of the microseismic signal persists in the time domain. Additionally, the timefrequency diagram illustrated in Figure 9 reveals that the   Shock and Vibration 7 large energy signal displays traits such as short time duration, discontinuity, and high frequency. Tese attributes are indicative of a typical blasting signal. It is noteworthy to remark that the fndings presented in this study provide valuable insights into the characteristics of microseismic signals, which can be leveraged for optimizing blasting processes and enhancing safety measures in mining operations. From the perspective of a trigger mechanism, microseismic events are the release of rock accumulated energy, and the process is relatively slow, mostly in the form of shear failure [37][38][39]. Te blasting signal mainly produces longitudinal waves, with strong energy and fast attenuation, which is a typical rock burst response [40][41][42][43]. Terefore, it is preliminarily judged that the large energy signal is a blasting signal. Trough subsequent feld verifcation, it is further confrmed that the large energy signal is a blasting signal [44].

Drill
Cutting Method. Te current study focuses on the solid coal side of the 8003 working face and aims to determine and analyze the size of stress and the degree of rock burst danger. To achieve this, the pressure relief blasting method was utilized to measure the amount of pulverized coal (in kilograms) in the borehole. Additionally, the amount of drill cutting was measured at intervals of one meter, and the drill cutting absorption index was measured at intervals of two meters. If the measured amount of pulverized coal at the test site exceeds the critical value or the pressure of ∆h 2 (drill cutting absorption index) exceeds 200 Pa, it indicates an increased hazard of rock burst occurrence. Te actual and critical values of the cuttings absorption index are depicted in Figure 10.
Te ∆h 2 value serves as a comprehensive indicator of the coal damage degree. To obtain this value, it is necessary to extract drill cuttings at predetermined locations and subsequently sieve them with apertures of 1 mm and 3 mm before transferring the resultant particles to the coal sample bottle. After waiting for 3 minutes from the time of particle generation to sampling, the coal sample bottle is started. Te absorption reading, recorded 2 minutes thereafter, equates to the ∆h 2 value. Te 8003 working face is subjected to measurement of an average of once every three days. Based on the August data analysis, 84% of the drill cuttings' absorption index was lower than the critical value of 200 MPa,    while 16% of the drill cutting absorption index (200 MPa on August 9th and 220 MPa on August 22nd) reached the critical absorption index value, necessitating further attention and assessment. Subsequent testing revealed that the actual drill cuttings did not achieve peak values on August 9th and August 22nd. As such, it was concluded that there was no imminent hazard of strong rock bursts. Overall, the 8003 working face poses a rock burst hazard.

Conclusion
(1) Te present study proposes the CF-TOPSIS model for predicting rock burst hazard. To avoid any bias resulting from a single model, FAHP and CRITIC weight models are employed to determine the weight of rock burst factors. By incorporating the TOPSIS prediction model, the CF-TOPSIS prediction model for rock burst is obtained. (2) Te optimization of the traditional model is required to address its inadequacy in assessing the nonrock burst hazard phenomenon under rock burst conditions. Additionally, there is a need for enhanced accuracy in predicting the rock burst hazard associated with the working face being measured. Furthermore, it is important to compare the moderate rock burst hazard with the traditional model. (3) Te combination weighting method was utilized to obtain the total ranking of the CF evaluation index, revealing that distinct rock burst criteria exert varying degrees of infuence on rock burst. Te primary and secondary factors infuencing the rock burst of the 8003 working face were determined as follows: the distance between the hard and thick strata in the overlying fractured zone and the coal seam (A3) possesses the greatest impact, followed by mining depth (A2), the ratio of stress increment to normal stress in the mining area (A4), and the number of rock bursts in the same horizontal coal seam (A1). (4) Tis study examines the factors infuencing rock burst from multiple perspectives, optimizes the traditional critical value interval, and proposes an efective prediction method for rock burst. Field practice is used to verify the feasibility and accuracy of this method, ofering a novel approach to rock burst prediction.

Data Availability
All data generated or analyzed during this study are included within this article.

Disclosure
Feng Zhu and Haowei Song are the co-frst authors. Shock and Vibration 9