
Research Article


Fuzzy Bayesian Network Model for Roof Fall Risk Analysis in Underground Coal Mines 

Mohammad Javadi,
Gholamreza Saeedi
and
Kourosh Shahriar



ABSTRACT

Background and Objective: Roof fall is one of the greatest single hazards faced by underground coal miners. This accident may have detrimental effects on studyers in the form of fatal and nonfatal injuries as well as downtimes, equipment breakdowns, etc. Due to different impacts of contributing parameters on roof fall and illdefined or even immeasurable nature of such factors, this problem is an uncertain and complex issue. As a result, development of a methodology for roof fall risk evaluation under uncertainty condition has a remarkable role on safety of underground coal miners. Methodology: This study proposes a new quantitative assessment framework, integrating the inference process of Bayesian networks and fuzzy set theory with the traditional probabilistic risk analysis. The constructed Fuzzy Bayesian Network (FBN) based model has 12 root nodes contributing to the failure of the leaf node. The geology maps and data related to mining equipment at Tabas Coal Mine (TCM) are used to determine the prior probability of FBN root nodes. In addition, weighted sum algorithm is used to populate the conditional probability table of intermediate and leaf nodes. Results: The new model quantifies uncertainty in roof fall and also provides an appropriate method for modeling complex relationships in underground mining. Conclusion: Finally, the proposed approach is illustrated with an application for the TCM and found to be a powerful technique for coping with uncertainties and predicting roof fall risk.





Received: September 03, 2016;
Accepted: November 08, 2016;
Published: February 15, 2017
Copyright: © 2017. This is an open access article distributed under the terms of the creative commons attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.


INTRODUCTION
Roof falls continue to be one of the greatest single hazards faced by underground coal miners. The complexity of geological deposit and variability of mining parameters lead to the occurrences of roof falls^{1}. These accidents may have detrimental effects on studies in the form of injury, disability or fatality as well as mining company due to down times, interruptions in the mining operations, equipment breakdowns, etc^{2}. The hazardous nature of roof falls in underground coal mine operations can be illustrated from the statistics of mine accidents. It accounted for 18.18% of all fatal accidents in coal mines, contributing about 35.29% of all fatal accidents in belowground operations^{3} in 2005.
Several factors such as geological and stress conditions, mine layout and environment contribute to occurrences of roof falls in underground coal mines^{4}. Analyzing the roof fall risk during underground mining could increase the ability of mine designer and studies to reduce the detrimental effects of this hazard. Therefore, extensive research has been conducted to control and assess roof fall in coal mines. In these studies, it has been tried to find the relationship between the roof fall and contributing parameters. Kidybinski^{5} classified roofs of mines in the United State for the selection of suitable mechanized support for longwalls. Unrug and Szwilski^{6} proposed the roof quality index for determining the influence of strata control parameters on longwall mining design. Coal Mine Roof Rating (CMRR) has been introduced by Molinda and Mark^{7} and similar to Bieniawski’s RMR has a single rating between 0 and 100. When the CMRR value is close to 0, the roof is weaker while the value getting close to 100 shows that the roof is stronger. Mark^{8} evaluated the stability of extended cut by using some contributing parameters like entry with, cut depth, CMRR and depth of cover. Using statistical analysis of roof fall database from 37 coal mines, Molinda et al.^{1} found the relationships between the roof fall rate and CMRR, primary roof support, intersection span and depth of cover. Deb^{9} analyzed the coal mine roof fall rate. In this study, the relationships between CMRR, primary roof support and intersection diagonal span with roof fall rate were determined by using fuzzy reasoning techniques. Duzgun and Einstein^{2} proposed a risk and decision analysis methodology for assessment and management of risk associated with mine roof falls in underground coal mines. Duzgun^{4} introduced a risk assessment and management methodology for roof fall risk in underground mines. The data was collected from Zonguldak coal region, in Turkey; then the probability of roof fall was computed by fitting a distribution function to the annual roof fall, while the consequence was quantified based on a cost model. Palei and Das^{3} predicted the effects of contributing parameters such as number of bolts per row, anchorage strength of bolt, spacing between bolts, width of gallery, mean rock density and RMR on roof falls in underground coal mines. Palei and Das^{10} proposed a model to predict the severities of roof fall accidents based on some major contributing parameters in bord and pillar underground coal minig by using logistic regression model. Ghasemi and Ataei^{11} developed a fuzzy based model for predicting roof fall rate in coal mines based on Mamdani algorithm. Ghasemi et al.^{12} developed a practical methodology for assessment and control of the roof fall risk during retreat mining in room and pillar coal mines. Razani et al.^{13} applied a Fuzzy Inference System (FIS) to predict roof fall rate for controlling, mitigating and/or even eliminating the risk of roof fall. Gao et al.^{14} presented a numerical approach to simulate shear failure of a coal mine roadway roof. The distinct element code, UDEC, incorporating a proposed Trigon logic was employed in this study. Oraee et al.^{15} evaluated the effect of discontinuities characteristics on coal mine stability. For this aim, a practical rulebased approach was proposed to assess the risk of a roof fall.
The literature review shows that the behavior of the roof at longwall face has been given little attention. One of the major problems in predicting the roof fall risk at mine faces arises from the adherent complexity and uncertainty of contributing parameters related to the roof fall. Therefore, applying a proper technique that can simultaneously take into account both the complexity and inherent uncertainty connected with the roof fall problem helps designers to analyze the problem more accurately and precisely. In order to control the uncertainty of parameters affecting the roof fall at longwall faces, Bayesian Networks (BNs) which are based on probability theory can be utilized. Also, in order to increase the accuracy of BN results, the fuzzy logic can be applied. The main aim of this study is to develop a Fuzzy Bayesian Network (FBN) model to evaluate the probability of roof fall in order to obtain a more accurate, precise and robust model. The new approach explicitly quantifies uncertainty in roof fall analysis and also provides an appropriate method for modeling complex relationships and factors in underground coal mining, such as causal relation between variables, common causal factors, formal use of experts’ judgments and learning from data to update previous beliefs and probabilities. To show the capability and effectiveness of the constructed model, the data from Tabas Coal Mine (TCM) has been used as a case study.
Tabas Coal Mine (TCM) is the biggest and only fully mechanized coal mine in Iran which is located approximately 75 km South of the city of Tabas (Fig. 1).
 Fig. 1:  Location map showing Tabas coal mine 

Fig. 2(ab): 
(a) Location of panels in minefield No. 1 and (b) Generalized stratigraphic column at TCM 
It has three minable seams (C_{1}, B_{1} and B_{2}). The C_{1} seam located in the Tabas coal minefield No. 1 is mined by longwall method. The thickness and dip of the C_{1} seam mostly vary from 1.82 m and from 1126 degrees, respectively. Lowstrength sandstone and siltstone layers have been formed in the hanging wall of the coal seam. The mine foot wall consists of siltstone and mudstone seams. The location of panels in the minefield and generalized stratigraphic column at mine^{16} is shown in Fig. 2.
In this study, data collected from East 2 panel has been used. Panel width and length are 217 and 900 m, respectively. From October, 2010 to July, 2013, this panel was extracted (approximately 33 months).
MATERIALS AND METHODS
Fuzzy set theory: Fuzzy Set Theory (FST) was first introduced by Zadeh^{17}. The FST provides a basis to generate powerful, widespread problemsolving techniques, especially in the field of decision making^{18}. The FST has been employed in various studies such as multi criteria analysis system^{19}, wave parameters prediction^{20}, coronary heart disease risk assessment^{21}, rock brittleness prediction^{22}, building damage risk assessment on mining terrains^{23}, the fuzzy Risk Analysis and Management for Critical Asset Protection (RAMCAP) introduction in order to extend RAMCAP^{24}, risk evaluation of tunneling projects^{25}, risk assessment of mining equipment failure^{26}, green supply chain practices evaluation in the mining industry^{27} and over break minimization in underground blasting operations^{28}.
A fuzzy subset A of U is defined by its membership function that can be any number between 0 and 1. Membership of 0 means that the value does not belong to set A, membership of 1 means that the value belongs to the set under consideration and membership anywhere between 0 and 1 determines the degree of membership. A membership function of fuzzy number Ã on R is described as μ_{Ã}(x): R→[0,1], which has the following characteristics^{29}:
• 
μ_{Ã}(x) is the piecewise continuous function 
• 
μ_{Ã}(x) is the convex fuzzy subset 
Fuzzy number: In general, the FST uses triangular, trapezoidal or Gaussian fuzzy numbers to convert the uncertain numbers into fuzzy numbers^{30}. Without loss of generality, Triangular Fuzzy Numbers (TFN) are often utilized to provide more precise descriptions and obtain more accurate results^{31}. Thus, in this study, TFNs are used for representing probabilities of nodes in the FBN model.
A fuzzy number Ã can be shown as: Ã = (a, b, c)
where, Ã is defined as a TFN and a, b and c are crisp numbers and a>b>c, so that a and c represent fuzzy probabilities between the lower and upper boundaries of evaluation information. A fuzzy number Ã = (a, b, c) is called a TFN if its membership function is given by Eq. 1: If assume two TFNs Ã_{1} = (a_{1}, b_{1}, c_{1}), Ã_{2} = (a_{2}, b_{2}, c_{2}) then mathematical operations are described as follows in Eq. 2:
Fuzzy linguistic variable: The fuzzy linguistic variable is a variable with values as words or sentences in a natural language. It helps experts to evaluate the importance of the child node on its parents’ with respect to other child nodes. In this study, a 5point scale has been used (Table 1). Figure 3 shows linguistic variables used for determining the importance weight of each node on its parents.
Fuzzy Bayesian Network (FBN): A BN, also called a causal network or Bayesian belief network is a powerful tool for knowledge representation and reasoning under conditions of uncertainty^{32}. This method is frequently applied in different aspects of science and engineering real world problems such as diagnosis, forecasting, automated vision, sensor fusion and manufacturing control^{33}. It has been extended to other applications including software risk management^{34}, transportation^{35}, project scheduling^{36}, ecosystem and environmental management^{37}, new product development project assessment^{38}, risk analysis during tunnel construction^{39}, fall risk assessment of cantilever bridge projects^{40}, safety risk analysis in construction projects^{41}, safety and risk analysis of managed pressure drilling operation^{42} and determination of safety integrity levels^{43}.
 Fig. 3:  Linguistic variables used in roof fall risk modelling 
Table 1:  Membership function of linguistic scale 

A BN has many advantages such as suitability for small and incomplete data sets, structural learning possibility, combination of different sources of knowledge, explicit treatment of uncertainty and support for decision analysis and fast responses^{37}.
Numerous uncertainties about roof fall items such as geological condition, mining parameters and stress condition make the roof fall analysis a complex issue. Uncertainty generally occurs for reasons including uniqueness (no similar experience) and variability and ambiguity (lack of clarity, data, structure and bias in estimates)^{44}. One way to control the uncertainty of roof fall items is Bayesian belief networks. The BN is a combination of two different mathematical areas, namely graph theory and probability theory, which consists of a Directed Acyclic Graph (DAG) and an associated Joint Probability Distribution (JPD). A Bayesian belief network consists of qualitative and quantitative parts^{45}. The qualitative part of a BN, the socalled structural learning is the graphical representation of independence holding among variables and has the form of a DAG that is popular in the statistics, machine learning and artificial intelligence societies. The quantitative part of a BN, the socalled parameter learning, finds dependence relations as joint conditional probability distributions among variables using cause and consequence relationships from the qualitative part and data of variables. The network is commonly represented as a graph, which is a set of nodes and arrows. The nodes represent the probabilistic variables and the arrows represent the causal relationships between these variables. Nodes, which are the starting ones and do not have an inward arrow are called the parent nodes. Other nodes, which have inward arrows connected to them are the child nodes. In order to run the calculations, it is necessary to define the states and probabilities for each node.
In a BN, for example as shown in Fig. 4, nodes without arcs directing into them and with no parents are root nodes (Y1 and Y2) having marginal prior probabilities assigned to them while nodes with arcs directing into them are intermediate nodes (Y3, Y4, Y5 and Y6), possessing Conditional Probability Tables (CPTs). Nodes such as Y7 with no children are leaf nodes^{46}. Considering the DAG of Fig. 4, the JPD of the BN is the product of the conditional probability distributions of the variables Y1 = y1, Y2 = y2, … and Y7 = y7:
where, Ø(i) in Eq. 3 are the parents of the node i in the DAG and y1, y2, … , y7 are the states of variables Y1, Y2, … , Y7. Thus, Eq. 4 gives the joint probability distribution of the BN in Fig. 4: When constructing a BN model, researchers are faced with insufficient data relating to probabilities of root nodes. In the engineering practice, in the absence of sufficient data, it is necessary to study with rough estimates of probabilities^{47}. Under such uncertain circumstances, it is considered inappropriate to use conventional BN to estimate the system failure probability. The FST offers an analysis frame that can deal with imprecision in input failure probabilities for the estimate of probability of the leaf root and such analysis is termed Fuzzy Bayesian Network (FBN).
With regard to the FBN, it is essential to choose the proper fuzzy probability measure as to conduct the fuzzy Bayesian inference. The fuzzy marginalization rule and fuzzy Bayesian rule can be calculated by Eq. 5 and 6, respectively. Here, T stands for the leaf root and Xi stands for the root nodes. Combing with Eq. 2, the FBNbased inference techniques can then be fulfilled:
Proposed approach
Inputs: Various factors could affect the roof fall in underground mine projects. Table 2 shows the Common Cause (CC) items used in the last researches. One of the important matters in predicting the behavior of the rock mass is to choose parameters with the highest effect on designing.
 Fig. 5:  Major contributing parameters on roof fall during longwall mining 
Table 2:  Common cause items used in the last researches 

Clearly, no single parameter can represent the behavior of the rock mass. Different parameters have different effects on the rock and only when combined together, can represent the behavior of the rock satisfactorily^{48}. Regarding the fact that determining several parameters in the rock mass is difficult and partly impossible, methods or models need to be developed to simplify the real status of the environment^{49}.
In the present study, the most important factors affecting the roof fall at the longwall mine faces are divided into four groups (Fig. 5). Model framework: The model employs a FBN methodology to conduct a causal analysis on important variables influencing the roof fall risk and provides probabilistic results which can improve our decisions. The schematic framework of the proposed model is portrayed in Fig. 6.
For constructing the model, first, the mining engineers are interviewed to establish the structure of the FBN model for the Roof Fall Risk (RFR). Then the logic diagram is subsequently used to build up the failureconsequence scenario from the top to bottom nodes using a DAG.  Fig. 6:  A framework for using FBN roof fall risk analysis 
Table 3:  Descriptions of nodes in FBN model 

In accordance with what mentioned above, a FBN model is established (Fig. 7), where 12 root nodes contribute to the failure of the leaf node (roof fall risk). The descriptions and states of all nodes are illustrated in Table 3. RESULTS
In order to validate the FBN based model, several steps by using data collected from the E2 panel of TCM was carried out. The first step is determining the prior probabilities of root nodes.
 Fig. 7: 
Establish network model for RFR in longwall mining 
Table 4:  States of the root nodes in E2 panel zones 

To do this, the panel was divided into zones. Zoning was done based on the changes in one of the geological parameters like the immediate roof, the faulted zone condition and the like. Then, the geology maps and data related to mining equipment are used to determine the prior probability of root nodes (CC_{1}CC_{12}). The states of the root nodes in different zones are illustrated in Table 4. Determining the Conditional Probability Table (CPT) of intermediate and leaf nodes is the next step. In this research, weighted sum algorithm proposed by Das^{52} was used to populate the CPT. The input to the algorithm consists of a set of weights that quantifies the relative strengths of the influences of the parentnodes on the childnode and a set of probability distributions over the child node for compatible parental configurations. These are elicited from the domain expert. So, to populate the CPTs a questionnaire was distributed among experts. The questionnaire asked the experts to express the relative weight of parental nodes on the child nodes using the linguistic variables presented in Table 1. The experts’ opinions were integrated by using Eq. 3. Finally the integrated linguistic variables were defuzzified by using the best non fuzzy performance (BNP) method. The BNP value of the fuzzy number can be found using the Eq. 7:
Table 5:  Relative weight of parent’s nodes 

Table 6:  Fuzzy JPD of the leaf node (RFR) in FBN model under zone No. 5 condition 

The relative weight of the parent nodes are obtained and given in Table 5. Then the experts were asked to answer the following question using the linguestic variables from Table 1. Given the parental configuration what should be the probability distribution over the states of the child X?
In other words, we seek distributions of the type in Eq. 8:
where, X is the child node and has states (x^{0}, x^{1}, …, x^{n}) and Y_{i} are the parent’s nodes which have states.
Finally, Eq. 9 was used to complete the CPTs: where, W_{j} is the relative weight of the node j.
The final aim of this study is to calculate the probability distribution in risk event under the combination of or root nodes, i.e., CC_{1}, CC_{2},… and CC_{12}. In order to obtain this goal, in each zone the state of risk factors were treated as evidence input into a FBN model. As an example, the fuzzy JPD of the RFR node under the zone condition No. 5 is presented in Table 6. At the end, for different zones the CPT of leaf node (RFR) was calculated and defuzzfied using Eq. 7. The correlation between the RFR values and values of the extraction rate in E2 panel can prove the reliability of the FBN model. Higher extraction rate shows lower roof fall risks and better studying conditions.
 Fig. 8:  Relation between RFR in VH state and R, a linear regression analysis 
 Fig. 9: 
Compatibility rate of the RFR in VH state with the R parameter 
In this study, the parameter R is defined for determining the relation between the risk values and extraction rate. The extraction efficiency (R) is calculated from Eq. 10:
The relation between the RFR in VH state and extraction efficiency in the E2 panel is shown in Fig. 8. Also, the compatibility rate of the RFR values with the R is shown in Fig. 9. DISCUSSION
Development of a methodology for analyzing the roof fall risk has a remarkable role on mine safety. Factors like the geological and stress conditions, mine layout and configuration contribute to occurrences of roof falls^{4}. In the last studies, it has been tried to find the relationship between the roof fall and contributing parameters. Clearly, no single parameter can represent the behavior of the roof. In addition, only when different parameters combined together, can represent the behavior of the rock satisfactorily^{48}. Also, last studies show there are no doubt that the condition of a mine roof can be better expressed by using fuzzy set theory rather than traditional set theory^{9}. For this reason, some studies are done using fuzzy sets in the field of risk assessment in underground coal mining^{9,11,13,53,54}. Another major problem in risk evaluation arises from the complexity and uncertainty of contributing parameters. One of the ways to overcome the problems like this is using a Bayesian network based model. Bayesian belief networks was developed for knowledge representation and reasoning under conditions of uncertainty. This approach has the wide application in the any phases of the risk analysis^{34,3942}.
Considering the problems mentioned in the context of risk analysis, a new methodology was proposed, integrating the inference process of Bayesian networks and fuzzy set theory. The main advantage of this approach is considering all effective parameters on roof fall under uncertainty condition. Another advantage of FBN model is its possible utilization in new coal field where enough experience and data are not available. CONCLUSION
The complex nature of geological condition and variability of mining configuration lead to the occurrence of roof falls. The presented approach was a probabilistic methodology of risk analysis which developed based on fuzzy Bayesian network model. This methodology can simultaneously take into account both the complexity and inherent uncertainty associated with the roof fall problems. Application of the proposed methodin Tabas coal mine show that the FBN based model is a powerful technique for coping with uncertainties and evaluating the roof fall risk at longwall face. ACKNOWLEDGMENT
The authors are grateful to the Tabas coal mine management and engineers for their cooperation in conducting this study. The authors would also like to thank all the mining experts who took part in our research.

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