Proposing a novel comprehensive evaluation model for the coal burst liability in underground coal mines considering uncertainty factors

Jin Zhou,Cho Chen,Mingzheng Wng,Mnoj Khndelwl

a School of Resources and Safety Engineering,Central South University,Changsha 410083,China

b Bharti School of Engineering,Laurentian University,Sudbury,Ontario,Canada

c School of Engineering,Information Technology and Physical Sciences,Federation University Australia,Ballarat,Australia

Keywords:Coal burst liability (CBL)Unascertained measurement (UM)Analysis hierarchy process Information entropy Synthetic weights Comprehensive evaluation

ABSTRACT Coal burst is a severe hazard that can result in fatalities and damage of facilities in underground coal mines.To address this issue,a robust unascertained combination model is proposed to study the coal burst hazard based on an updated database.Four assessment indexes are used in the model,which are the dynamic failure duration(DT),elastic energy index(WET),impact energy index(KE)and uniaxial compressive strength (RC).Four membership functions,including linear (L),parabolic (P), S and Weibull (W)functions,are proposed to measure the uncertainty level of individual index.The corresponding weights are determined through information entropy (EN),analysis hierarchy process (AHP) and synthetic weights (CW).Simultaneously,the classification criteria,including unascertained cluster (UC) and credible identification principle (CIP),are analyzed.The combination algorithm,consisting of P function,CW and CIP (P-CW-CIP),is selected as the optimal classification model in function of theory analysis and to train the samples.Ultimately,the established ensemble model is further validated through test samples with 100% accuracy.The results reveal that the hybrid model has a great potential in the coal burst hazard evaluation in underground coal mines.

1.Introduction

Coal resources,which are known as the food of industry,still play a major role in industry,such as electricity,building materials and chemical engineering.The valuable and non-renewable resources are being exhausted and depleted due to uncontrolled exploitation.And the tendency to extract solid mineral resources at greater depth is inevitable [1].However,the geological conditions and mechanical properties of coal mass are complex at greater depth[2],which means that the coal burst control has been a challenging mission [3].

Coal burst is defined as the violent ejection of coal/rock from the work face with a sudden release of accumulated energy [4].In most cases,the coal burst is associated with the mining disturbance,which can cause catastrophic damage to personnel and equipment[5],as shown in Fig.1.Thus,many scholars[6–15]carried out studies on the issues,including on-site monitoring techniques [16] and assessment methods.For example,some scholars employed mathematical analysis [17] and fuzzy comprehensive evaluation [18] to assess the coal burst liability (CBL)according to the spatial distribution characteristics ofAEevents.Various destress methodologies,such as destress blasting and water infusions,are used to mitigate the degree of coal burst.Yardimci and Karakus[19] assessed the effect of destress blasting according to the location and roof stability.Guo et al.[20] investigated the relation between the coal burst potential indexes (i.e.,RC,WET,KEandDT)and the saturation time of coal mass in order to explore the effect of water infusion on coal burst proneness.They found that the tendency of coal burst has a negative correlation with the saturation time.In recent years,many rock burst studies are carried out[21–29],which has been getting wider attention in the geosciences.The investigation of coal burst prevention would be able to provide valuable strategies for other rock mass engineering,given the burst control principle is similar for rock and coal masses[30].Thus,it is necessary to explore more efficient and effective methods for coal burst control.However,the disturbance of onsite tests may trigger coal burst hazards,which puts the operators into a dangerous environment.As for laboratory test,the test process is complicated and time-consuming [31].Furthermore,the properties of rock specimen and rock mass are largely different,which is unable to reflect the actual conditions absolutely through the indoor tests.Currently,the Chinese national standard(GB)[32],namely four parameters,(i.e.,RC,WET,KEandDT) is a commonly used method for identifying the coal burst propensity in China,but the criterion is not capable and applicable in some complex situations,where the indexes belong to different grades separately.In view of the aforementioned analysis,it seems that evaluation ofCBLwith reliable mathematical models is available with the development and application of artificial intelligence [33–36,101–103]in mining engineering,e.g.,principal component analysis (PCA)[37],but,the performance of these models need to be further validated through an inspired amount of data.The key objective of this research is to propose a new combination algorithm based on an unascertained measurement model,which has been accepted in various engineering fields for a highly-efficient and reliable method through the gathered database.The key contributions of this research are summarized as follows:this work incorporates an updated database including 121 coal burst case studies to assess and study this issue.The evaluation with non-linear membership functions are rarely considered in unascertained measurement theory in previous work.Two novel membership functions,i.e.,SandWfunctions,are added to support the non-linear evaluation.Meanwhile,the evaluation performance of multiple ensemble models consisting of different membership functions and weights are analyzed.Ultimately,the proposed uncertainty model is capable of making up for the deficiencies ofGBin terms of the evaluation accuracy.

Fig.1.Destruction caused by severe coal burst in underground coal mines [38,39].

2.Description of unascertained measurement theory

Unascertained information is seen as a weak uncertainty that can be interpreted via subjective probability or membership functions [40].For the object to be evaluated,nobjects constitute the sample set ψ={ψ1,ψ2,...,ψn}.For individual samples ψo=(1 ≤o≤n),the characteristics can be extracted by many quantitative and qualitative factors.Then,mcharacteristics are performed to describe the specimen attribute composed of an index set Φ={φ1,φ2,...,φm}(1 ≤p≤m).Qop(o=1,2,...,n;andp=1,2,...,m)is the quantified value ofpth index.There areGpossible evaluation classes for each object,and they are stored in evaluation space Λ={ξ1,ξ2,...,ξG}.The evaluation space Λ can be considered as an ordered partition,while the grade vector ξq(q=1,2,...,G)meets the condition ξ1>ξ2>...>ξGor ξ1<ξ2<...<ξG.

2.1.Quantifying the uncertainty correlation using membership functions

2.2.Objective weights calculation using entropy theory

The index weights in evaluation space are needed to distinguish as the multiple-index measurement matrices were constructed.The information entropy,as one of the objectivity weights,which is the term originating from thermodynamics,reflects the degree of information disorder.The weight distribution was calculated,shown in Eqs.(8) and (9).where ζp(p=1,2,...,m)is the entropy value,from which the objective weight vector (ϖ1obj)pcan be obtained.

2.3.Subjective weights calculation using the analysis hierarchy process(AHP)

AHPproposed by Saaty [43] divides the evaluation objects into goal hierarchy,criterion hierarchy and index hierarchy.In this work,the index weights are calculated based on the designer’s knowledge.The superiority of this method is that it can adjust the weight assignment through the pairwise comparison matrix compared to the objective weight.A situation where the calculated weights are far from the actual conditions can be largely avoided[44].

2.3.1.Establishment of pairwise comparison matrix

For index set Φ={φ1,φ2,...,φm},supposingcij(1 ≤i≤m;1 ≤j≤m) is the score of index φito φj,which is the significance level in designer’s expectation.On the contrary,cjiis the value of index φjto φi,andcijcji=1.Then,the pairwise comparison matrix is constructed as presented in Eq.(10).

2.3.2.Computation of weight vectors and consistency check

According to the pairwise comparison matrixCm×m,the maximum eigenvalue λmaxand related eigenvector can be achieved easily.Then,the consistency check is used to examine the feasibility of index weights that we assigned.The process of checking is shown in Eqs.(11) and (12).

The consistency index(CI)is calculated by Eq.(11)andmis the dimension of the comparison matrix.To check the criterion,consistency ratio (CR) is obtained viaCItoRI.The comparison matrix is reasonable and the corresponding eigenvectors can be regardedas the index weights(ϖ2sbj)pafter normalization asCR<0.1,otherwise,the comparison matrix needs to be reconsidered.The values ofRI[45] are shown in Table 1.

Table 1Basis to select the value of RI.

Table 2Coal burst database used for establishing comprehensive evaluation model.

Table 2 (continued)

Fig.4.Distribution of the mines corresponding to the sample set.

2.4.Synthetic weights

The synthetic weights ωpis proposed to combine the data characteristic and subjective judgment to increase the feasibility of weight assignment,which can incorporate the objectivity and rich experience simultaneously from the aforementioned weight methods (Eq.(13)).

2.5.Calculation of composite measurement vectors

Index measurement vectordetermines the level of index φpbelonging to grade ξq.Comprehensive evaluations are usually achieved based on the specimen,which means that the degree of sample ψobelonging to grade ξqneeds to be clear.Thus,composite measurement vectors δoqare calculated in function of the multiple index measurement matrix and related weights (Eq.(14)).

2.6.Principle and priority of credible identification

Given that the evaluation space Λ is the ordered partition,thus,credible recognition criterion λ is employed in this work,which has better performance than the conventional identification methodologies,such as maximum measurement principle.The grade Λq(1 ≤q≤G) is considered as the assessment result that satisfies Σξq≥λ (Eq.(15)).Generally,0.5 ≤λ ≤1 and it is common that λ=0.6–0.7 [46–49].

Assuming that the grade value ξqis θq,the sample scorecan be calculated by Eq.(16),from which the sample priority is observed.

where θqis determined by the sortation of vectors ξqand the expectation of designers.

3.CBL evaluation using unascertained measurement theory

The violence and suddenness of coal burst is a long-standing issue that needs to be solved in an effective and efficient manner.The mechanical response of coal mass is affected by many factors,e.g.,underground water and gas pressure,which are different from the factors of rock mass.GBwas considered as an efficient methodology to assess the coal burst proneness.However,it has a weak performance in some complex cases.Consequently,unascertained measurement theory is utilized combining with synthetic weight to classify the burst potential of sample databases.The technique routine is summarized in Fig.3.The samples are mainly derived from 12 provinces,China,e.g.,Heilongjiang province,Shandong province and Shanxi province(Fig.4),and the outliers are removed from the dataset (Table 2).It is clear that the training sample set constructed in this work is representative of the inspired amount.Four evaluation indexes (DT,WET,KEandRC) are investigated to realize theCBLclassification.The index correlation and classification basis [32] are presented in Fig.5 and Table 3.

3.1.Calculation of unascertained measurement value

In this study,another two membership functions (SandWfunctions) are added into the algorithm to extend the ability of uncertainty measure in addition to commonly-used linear and non-linear methodologies.Considering the complexity of underground engineering and the simplicity of linear function,the linear and non-linear evaluation regarding coal burst risks are carried out simultaneously based on the given functions to choose the hybrid model with optimal structure.The second sample is taken as an example.The single index measurement vectors (Fig.6) are calculated based on Eqs.(1)–(4),shown in Fig.7,which meets Eqs.(5)–(7) requirements.

3.2.Weight analysis and composite measurement

Weight calculation,which assigns more influence on the important factors,determines the accuracy of evaluation results.Subjective and objective weighting methods are performed simultaneously to promote the rationality of weight allocation.For the subjective weights,a pairwise comparison matrix is constructed by researchers based on the rich field experience.To remove the uncertainty for decision-makers during the index importance comparison as much as possible,the rating interval of 1–9 was replaced by 1–4.The eigenvectors corresponding to the maximum eigenvalue are the index weights after the consistency check is satisfied (Eqs.(11) and (12)).In this study,the subjective weighting ofDT,WET,KEandRCare specified as {0.4673,0.16,0.095,0.2772}.Besides,the commonly-used weights {0.3,0.2,0.2,0.3}[37]are also applied to validate the feasibility of indexweight determination.Then,the synthetic weights of individual samples can be achieved according to Eq.(13),as shown in Table 4.

Table 3Classification basis regarding the influential factors.

Table 4Weight distribution of CBL evaluation parameters.

Fig.5.Correlation matrix of CBL evaluation indexes.

Fig.6.Single index measurement vectors of sample (Pingdingshan sixth mine).

3.3.Composite measurement vectors and CBL classification

Sample/composite measurement is able to size the main characteristics of the object to be evaluated compared to the single index measurement.In this study,the comprehensive measurement vectors are calculated via multiple index measurement matrix and synthetic weights,see Eq.(14).

The attribute characteristic of samples can be observed clearly in the composite measurement vectors context.After that,a high-efficient attribute identification criterion is necessary,which has a capability of classifying theCBLreasonably.In the past,a lack of suitable division criterion leads to a low accuracy,which turns out to limit the combination model extension to other fields.Consequently,credible recognition principle is used to categorize theCBL,which outperforms the maximum measurement principle in ordered partition space Λ [48].The composite measurement vectors of the second sample are presented as {0.306,0.615,0.079}according to Eq.(15) (λ=0.6),then,0.306+0.615 >λ=0.6,that is,the grade of the second sample is ξ2,which corresponds to be weak inCBLclassification.The evaluation results for the rest of the samples under different membership functions are computed as sample 2.In Fig.8,the accuracy of different ensemble models are visualized,and the evaluation results with optimal structure are listed.The accuracy of all unascertained measurement-based ensemble models is more than 80%,which indirectly proves the reasonability of this model inCBLevaluation.Additionally,the evaluation performance of the optimal ensemble model is shown in Fig.9,using a confusion matrix.It is clear that the accuracy ofP-CW-CIPis 91%.

As noted in Fig.8,A*represent the index weight collected from the literature.

3.4.Priority sortation to coal burst database

Fig.7.Uncertainty measurement of different functions.

The values of three grades are presented as {60,80,100},according to Eq.(16).Then,the scores of individual specimen are obtained with different combination methodologies.The entire scores of samples are presented below based onP-CW-CIPcombination model(Fig.10).The sample score andCBLare positively correlated,and the red and green lines shown in Fig.10 are assumed as the boundary to classify theCBL.From Fig.10,it can be said that the majority of samples (over 90%) may suffer from a different levels of coal burst hazard,from which the efficient hazard control techniques can be employed to remove this negative impact effectively.

3.5.Engineering validation with unascertained model

TheGBplays a major role in identifying the coal burst risk for a long time,the GB principle is to judge the burst intensity comprehensively according to the evaluation of four correlative parameters.However,the results implemented by empirical criterion are ambiguous in the situation,where these indexes belong to different grades respectively.Generally,in this case other assessment outcomes which are similar to this condition are employed as a reference.In this work,11 new coal burst samples are used to validate the reliability of the hybrid model,which is selected in section 3.3.Table 5 illustrates the coal burst parameters and its evaluation results judged with distance discriminant analysis (DDA) as well asGB.TheCBLof all engineering cases cannot be judged byGBabsolutely as shown in Fig.11.Wang et al.[95] investigated the similar conditions to distinguish the intensity and to validate performance of the proposedDDAmodel.In some cases,the aforementioned comparison technique is able to improve the credibility of estimation.But the comparison sample is hard to gather,of which the attribute label is clear.The optimal combination of unascertained models is performed to classify theCBL.On the one hand,it is able to examine the applicability of this hybrid algorithm.On the other hand,this algorithm can also classify the species,which is hard to distinguish withGB,via the parameters and the corresponding division criterion.In Fig.12,theCBLcan be classified through the accumulative comprehensive measurement vectors andCIP.The evaluation results are shown in Table 5,which are perfectly consistent with the actual situation or other evaluation methods.

Fig.8.Evaluation performance of different hybrid models.

Fig.9.Confusion matrix of the P-CW-CIP model.

3.6.Comparison and discussion

In previous studies,few ones focused on the process that selects an optimal model,the existing hybrid models are usually designed for possessing specific cases.In this study,a process to establish an optimal hybrid algorithm is introduced through a theoretical analysis and calculation.Entropy-based method (EN) can prevent the subjective disturbance of the designers,while it may result in the severely deviating weights from the actual situation.ForAHP,the weights assignment is feasible in most of the cases,which can make full use of the rich engineering experience of designers and planners.However,the sensitivity of the index importance is different,which can generate the uncertainty factors to evaluate the results.Last but not the least,choosing a reasonable classification tool to judge theCBLaccurately is very crucial.Usually,maximum measurement principle is not accepted in this case,andUCandCIPare considered as the common classification criteria.However,the application scope of the former is not clear and it sometimes gets unacceptable classification results.Therefore,there are 24 possible combination styles including L-EN-UC,L-EN-CIP,L-AHP-UC,LAHP-CIP,L-CW-UC,L-CW-CIP,P-EN-UC,P-EN-CIP,P-AHP-UC,PAHP-CIP,P-CW-UC,P-CW-CIP,S-EN-UC,S-EN-CIP,S-AHP-UC,SAHP-CIP,S-CW-UC,S-CW-CIP,W-EN-UC,W-EN-CIP,W-AHP-UC,W-AHP-CIP,W-CW-UC and W-CW-CIP to describe theCBL.According to the evaluation results,it can be seen that the accuracy of all uncertainty-based hybrid models exceeds 80%.The models P-CWCIP and P-AHP-CIP achieve the best performance (Fig.8) with 91%and 89% accuracy,which proves that the subjective weights used in this work are reliable.Considering the ability of synthetic weights to reduce the subjective disturbance on weights assignment,this studyP-CW-CIPhybrid model is selected as the best one to estimate theCBL.

For the samples,GBis hard to categorize,and empirical comparison seems to be an inspired way to get rid of the dilemma but it is impractical and time-consuming to search suitable case history.Thus,eleven new coal burst samples with complete intensity labels,some of which cannot be classified byGB,are gathered to test the performance of combination algorithm P-CW-CIP(λ=0.6).As shown in Table 5,the evaluation results are in accordance with the field description orGB,through which the performance of this robust combination is validated.It means that the evaluation results obtained by unascertained measurement theory are reliable.

Table 5Coal burst parameters adopted for model tesing.

The unascertained measurement model considering the index importance with synthetic weight is able to evaluate theCBLreasonably,and the advantages of this model in comparison with other researches are summary below:

Fig.10.CBL sortation via the specimen scores.

Fig.11.Discriminant results of individual index using GB.

Fig.12.The accumulation of composite measurement vectors of 11 samples.

(1) Different from conventional mechanism research,P-CW-CIP is able to efficiently interpret valuable information,e.g.,CBL,through the on-site data,which is also the development tendency of the future.On the one hand,various coal burst proneness corresponds to the different levels of characteristic parameters;on the other hand,a large volume of monitoring techniques that are undisturbed to coal mass provide the possibility of constructing a data-based algorithm.Several uncertainty evaluation algorithms have been developed and improved by many scholars in recent years,e.g.,fuzzy evaluation is able to deal with fuzzy uncertainty information,which also suffers from the loss of valuable information.Compared to fuzzy evaluation,it seems that unascertained measurement theory gains more attention to deal with uncertainty information based on its principle(normalization,non-negativity and additivity).Therefore,the developed model is capable of assessing theCBLin a safe environment on the basis of the inspired coal burst dataset compared to on-site tests.More importantly,the structure of the proposed model is simple,which is beneficial to be accepted in engineering.

(2) The number of specimens is not the main limit of this algorithm compared to the statistics method,that is,the evaluation result is still reliable in the case of small samples.For the structure of the proposed model,employing multiple non-linear membership functions can remove the uncertainty information existing in the engineering problems as much as possible.As aforementioned,both subjective and objective weights have their limitations.Thus,the weighted mean method,which considers the proportion distribution of different weights at the same time,is utilized to measure the index importance comprehensively.Furthermore,the weight is calculated based on the multiple index matrix,that is,the sample difference is highlighted in this model (each sample ψicorresponds to a weight ωp).In this way,the determination of weight is more scientific,which can be validated through the evaluation accuracy shown in Fig.8.

In engineering projects,many uncertainty factors contribute to the coal burst hazard,yet the current comprehensive evaluation methods are far from the engineering requirements.The proposed model shows a great potential in this field,but,the index system used is based on the previous researches,which leads to other important influencing indicators,for example,geo-stress is not explored,and the index sensitivity is not taken into account.Besides,the method to determine the value ofCIPis from literature,as a result,the criterion selection may suffer from the artificial disturbance for special engineering cases.Therefore,other classic algorithms,e.g.,set pair analysis,will be incorporated in the next research through which the proposed model can be further optimized.

4.Conclusions

In this paper,121 groups coal burst data and 11 groups test samples are constructed to select the optimal combination model,and the performance of the established model is tested separately.The indexes (DT,WET,KEandRC) are determined as the input variables of the targeted models.Multiple-index measurement matrix and weights distributions are calculated based on the dataset,then credible identification principle (λ=0.6) is performed to classify theCBLexplicitly.The results show that the uncertainty-based model performs well inCBLanalysis,which means that it can be seen as a supplement of conventional disaster evaluation methods.

(1) Two new non-linear membership functions (SandW) are created to quantify the uncertainty as it belongs to different classes simultaneously in addition to conventional linear and non-linear assessment approaches.Then,synthetic weights are employed to investigate the weights of individual indexes,which is able to incorporate the advantages of information entropy andAHPmethod.

(2) The subjective weights of index system are presented as{0.467,0.16,0.095,0.277},then,the combination models L-EN-UC,L-EN-CIP,L-AHP-UC,L-AHP-CIP,L-CW-UC,L-CWCIP,P-EN-UC,P-EN-CIP,P-AHP-UC,P-AHP-CIP,P-CW-UC,PCW-CIP,S-EN-UC,S-EN-CIP,S-AHP-UC,S-AHP-CIP,S-CWUC,S-CW-CIP,W-EN-UC,W-EN-CIP,W-AHP-UC,W-AHPCIP,W-CW-UC and W-CW-CIP are established via analyzing correlative part of the targeted model.The evaluation results show that the accuracy of established models exceeds 80%,and the ensemble model P-CW-CIP (λ=0.6) shows the best performance with 91% accuracy.Additionally,more than 90% samples of training dataset are at the risk of coal burst according to the sample superiority sortation.As for the test sample,the P-CW-CIP model shows great potential in CBL classification with 100% accuracy.

(3) In this work,other important influencing factors,e.g.,geostress,is not explored for the CBL evaluation.Meanwhile,the method used for identifying the most essential factors in CBL evaluation is not explored.Thus,these limitations need to be overcome in the next research.

Acknowledgements

This research was funded by the National Science Foundation of China (Nos.72088101 and 41807259),the Innovation-Driven Project of Central South University(No.2020CX040)and the Shenghua Lieying Program of Central South University (Principle Investigator:Dr.Jian Zhou).