As one of the five major coal mine disasters, the water inrush disaster poses a serious threat to the safety of the country and people, so the prevention work for that becomes very important. However, there is no perfect assessment system that can better solve the complex dependence relationships among disaster-causing factors of water inrush disasters. This study applied the knowledge of Complex Networks to research water inrush disaster, and based on that, the early warning evaluation system that combined ANP and Cloud model was established in order to solve the complex dependence problem and prevent the occurrence of water inrush. Moreover, this evaluation model was applied to the example Y coal mine to verify its superiority and feasibility. The results showed that the main cloud of goal was located at the yellow-strong warning level, and the first-level indicators were, respectively, at that the yellow-strong level of mining conditions, the yellow-strong warning level of hydrological factors, between the yellow-strong warning level and purple-general level of the geological structure, and among the blue-slightly weak warning level, purple-general level, and yellow-strong level of the human factor. The prediction results were consistent with the actual situation of the coal water inrush disaster in Y mine, which further proved that this early warning evaluation model is reliable. In response to the forecast results, the authors put forward relative improvements necessary to strengthen the prevention ability to disaster-causing factors among hydrological factors, mining conditions, and geological structure, which should comprehensively increase knowledge, technology, and management of workers to avoid leaving out disaster-causing factors. Meanwhile, the warning evaluation model also provides the relevant experience basis for other types of early warning assessment networks.
With the rapid development of the Chinese market economy, the utilization rate of primary energy has generally increased. For example, the reserves of coal are about 90% [
Therefore, the early warning work of coal mine water inrush is very important. Since the early 20th century, scholars at home and abroad have already started exploring and researching this area. With the rapid development of computer technology, the different scientific systems have been merged to form many prediction methods for water inrush disasters. Yang et al. established the risk assessment model of floor water inrush through the GA-BP network model [
Water inrush disaster is a complex nonlinear problem [
The Complex Network model is composed of nodes and connected edges [
The connected edges include a single route and multiple route [
The Complex Network model is defined in the form of graph theory [
The method of recording a Complex Network is by constructing an adjacent matrix. If a connected edge between any two nodes exists, it will be recorded as 1 in an adjacent matrix; otherwise, it will be recorded as 0. The adjacent list is one of the most common ways to store the content of a Complex Network. It is consists of many sets of numbers. There are two numbers in each row in the adjacent list, which represent two different numbered nodes. Moreover, the space between two numbers indicates that a connected relationship exists. Therefore, the adjacent matrix and adjacent list are interdependent, as shown in Figure
The nodes relationship of Complex Network for (a) adjacent matrix; (b) connected relationship; (c) adjacent list.
Analytic Network Hierarchy Process (ANP) is a comprehensive and multiple objective decision-making method based on AHP, proposed by T. L. Saaty in 1996 [
Water inrush disaster is a Complex Network problem. There are many interdependent and feedback decision elements. Therefore, using ANP to calculate the weights of all elements in a water inrush disaster network can better solve the actual prevention problems.
In 1995, academician D. Y. Li proposed the Cloud model concept based on the limitations of probability theory and fuzzy mathematics on the analysis of uncertainty problems [
The three characteristic numbers of the Cloud model are Ex (Expected Value), En (Entropy), and He (Hyperentropy), which are expressed as C (Ex, En, He). Ex is the expectation of cloud drop
The Cloud Generator is an algorithm to realize the mutual conversion between qualitative and quantitative in Cloud model [
Cloud model generator. (a) Forward Cloud Generator and (b) Backward Cloud Generator.
Through collecting a large amount of data of water inrush disaster from related papers and websites, we drew the network relationship of water inrush disaster, as shown in Figure
Complex Network model diagram of the coal mine water inrush disaster.
The nodes with fewer connection relationships to other nodes in Figure
Topological characteristics are unique attributes of the Complex Network model [
Degree centrality is a measured method to the importance of nodes, which includes in-degree and out-degree. Out-degree is from a certain node pointing to other nodes. The nodes with larger out-degree values are the main factors leading to water inrush disasters. For example, the out-degree value of dynamic water pressure is 9, which indicates the dynamic water pressure can cause 9 nodes to be catastrophic. In-degree is directed by other nodes to a certain node. The factors with a larger in-degree value are the root cause of water inrush disaster.
However, there is not exiting any relationship between out-degree and in-degree. A node with a larger out-degree value may not necessarily have a larger in-degree value. Therefore, when considering the degree centrality of the node, the out-degree and in-degree should be comprehensively analyzed.
The closeness centrality of a node represents the distance to other nodes. The greater the closeness centrality of a node, the closer the distance to other nodes. For example, in shipping logistics network, if you need to select a transit center that is closer to all logistics points, you should select the node with the greatest closeness centrality [
In the network of water inrush disaster, there are 102 nodes with closeness centrality not less than 1. It shows that the distances between nodes in the entire network are relatively closer. Moreover, it is more convenient for each node to influence others. In the network, the closeness centrality of coal body cementation degree is the largest, which is 2.125. It indicates that the coal body cementation degree is closest to other nodes in the entire network and it is easiest to activate other disaster-causing nodes.
The greater the intermediary centrality of a node, the larger the possibility of being a transit center. If this transit node suddenly disappears, it will have a certain impact on the connected relationship between other nodes, making it difficult to spread the information between nodes and even paralyzing the entire network. In the network, the intermediary centrality of dynamic water pressure is the largest, with a value of 9. It shows that dynamic water pressure is the most important “transit center” in the entire network.
Eigenvector centrality is an extended feature of degree centrality. Its main idea is that the importance of a node depends not only on the degree value but also on the characteristics of neighboring nodes. In the network, apart from the eigenvector centrality of the water inrush volume that is 1, others are less than 1. Therefore, the nodes adjacent to the water inrush volume are the most important in the entire network. In addition, the degree value of coal seam thickness is the largest, being 14, but its eigenvector centrality is not the largest.
By analyzing the topological characteristics, understanding of the nature and overall structure of network has deepened. According to the requirements of different topological characteristics, the most important nodes are selected, as shown in Table
The most important multiple nodes.
Nodes | Degree centrality | Closeness centrality | Intermediary centrality | Eigenvector centrality |
---|---|---|---|---|
Coal seam thickness | 14 | 1 | 1 | 0.333150175 |
Depth of mining floor failure | 12 | 0 | 3 | 0.285557293 |
Coal seam burial depth | 9 | 1 | 2 | 0.21416797 |
Working surface length | 6 | 1 | 0 | 0.630880426 |
Key position of the water barrier | 8 | 0 | 1 | 0.190371529 |
Karst collapse column | 5 | 0 | 6 | 0.320266341 |
Water inrush volume | 1 | 0 | 1 | 1 |
Fault | 5 | 0 | 3 | 0.231522494 |
Aquifer | 3 | 0 | 2 | 0.559491103 |
Mining depth | 3 | 1.333 | 0 | 0.183929612 |
Water barrier thickness | 4 | 1 | 0 | 0.095185764 |
Karst fissure development degree | 1 | 1.9 | 1 | 0.511898221 |
Dynamic water pressure | 10 | 1 | 9 | 0.023796441 |
Collapse column | 3 | 1 | 6 | 0.071389323 |
Ordovician water channel | 2 | 0 | 1 | 0.160133171 |
Mining methods and processes | 3 | 1.2 | 0 | 0.071389323 |
Reduce the strength of fractured rock mass | 1 | 0 | 2 | 0.13633673 |
Complex geological conditions | 2 | 1 | 1 | 0.047592882 |
Folds | 3 | 1.6 | 5 | 0.023796441 |
Hidden troubles are not in place | 1 | 1 | 0 | 0 |
Illegal production | 1 | 1 | 1 | 0 |
Production organization management chaos | 1 | 1 | 0 | 0 |
Production technology management chaos | 1 | 1 | 2 | 0 |
Based on the Complex Network model of coal mine water inrush disasters, the “ANP-Cloud” early warning evaluation system was established in this article. The implementation steps are described in detail as follows.
The constructed index system should meet comprehensiveness and scientificity. It takes the “coal mine water inrush disaster decision system” as the overall goal. Moreover, it divides 161 nodes obtained from the Complex Network model into four first-level indicators: geological structure, hydrological factors, mining conditions, and human factors. Then, the first-level indicators are correspondingly divided into the second-level indicators. According to the research requirements, the top 23 important second-level indicators are selected, as shown in Figure
Network index system of the coal mine water inrush disaster.
The ANP model is consists of a control layer and a network layer [
Factors of network layer contain the second-level indicators from Complex Network. The relationships of mutual feedback and dependence between the second-level indicators form a network system, as in Figure
The network relationship diagram in ANP model.
The weights calculated process in ANP are extremely complicated. Thus, it is based on Super Decisions (SD) software for scientific weights calculation in this article [
First of all, we need to build a network relationship model. It is very important to clarify the dependence and feedback relationship between indicators in the ANP model, which has a certain influence on the correctness of the decision. The connected relationship of all elements is entered, consulting related literature to the SD.
Secondly, it is necessary to collect expert evaluation data. There are connected relationships between elements in the same and different dimensions. The important influence degree of other elements that have a connection relationship with the certain element is judged. Ten experts in the relevant field were consulted by 1 ∼ 9 scale scoring method [
1∼9 scale scoring method.
Scale | Meaning |
---|---|
1 | The two elements are of the same importance. |
3 | The former is slightly more important than the latter. |
5 | The former is significantly more important than the latter. |
7 | The former is more important than the latter. |
9 | The former is the most important than the latter. |
2,4,6,8 | The intermediate value of each scale. |
Reciprocal (1,1/3, ..., 1/9) | The latter is more important than the former, with the same degree of importance as defined in 1∼9. |
Then, unweighted matrix and weighted matrix of elements are obtained by inputting all scored data from 10 experts into SD. If the values of the unweighted matrix and weighted matrix are 0, then there is no dependent and feedback relationship between the two elements.
Finally, the comprehensive weights are calculated. We can obtain the normalized matrix from the unweighted matrix and weighted matrix in SD. Moreover, according to the academical abilities and experiences of 10 experts, we set weighted coefficients as shown in Table
Expert rating weighted coefficients.
Experts | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 | S10 |
---|---|---|---|---|---|---|---|---|---|---|
Weighted coefficients | 0.09 | 0.07 | 0.14 | 0.09 | 0.011 | 0.09 | 0.14 | 0.09 | 0.11 | 0.07 |
Before constructing a risk early warning assessment model of water inrush disaster, the corresponding comment sets should be established. Moreover, the comment sets classified of early warning model should be based on the past examples of many coal mines water inrush disasters.
In this article, the influence degrees of disaster-causing factors in water inrush disaster are divided into five comment sets:s weak, slightly weak, general, strong, and stronger. It is expressed as
The golden section method is used to generate a corresponding closed comment set as (
In Equation (
In this article, the central cloud feature numbers are set Ex3 = 0.5 and He3 = 0.005. The calculation formulas (
All closed intervals (
Five standard comment sets.
Language value | Weak | Slightly weak | General | Strong | Stronger |
---|---|---|---|---|---|
Cloud model | (0, 0.103, 0.013) | (0.309, 0.064, 0.008) | (0.50, 0.031, 0.005) | (0.069, 0.064, 0.008) | (1, 0.103, 0.013) |
[0, 0.309] | [0.117, 0.501] | [0.407, 0.593] | [0.499, 0.883] | [0.691, 1] | |
Warning level color | Green | Blue | Purple | Yellow | Red |
Standard evaluation cloud model.
Ten experts in a related field were invited to conduct a questionnaire survey, which includes 2 second-level professors, 4 associate professors, 2 senior engineers, and 2 doctors. Moreover, the 23 important second-level indicators were scored reasonably, ranging from 0 to 100. The experts should give the highest and the lowest scores of indicators, respectively. Finally, the results to the domain [0, 1] are normalized.
The corresponding maximum and minimum cloud feature numbers C (Ex, En, He) of indicators are obtained by a Backward Cloud Generator. According to the calculated formulas (
Through formulas (
The comprehensive cloud feature number of goal is a summary for the evaluation model and its comprehensive degree is strongest because the correlations between the first-level indicators are much greater than those between the second-level indicators. We can use the integrated cloud algorithm to obtain the cloud feature number of goals, as in formula (
In Equations (
This article takes Y coal mine as an example to verify the feasibility of the early warning assessment model; the mine position is shown in Figure
The mine position of test Y coal mine.
The inclination angle of the coal seam is 10∼20°. The lithology of the floor is mainly medium and fine sandstone, with an average thickness of 19.80 m. There are some local vertical cracks and the sandstone fissure aquifer in the roof and floor of Y coal mine is a direct roadway water-filling source. The water-repellent layer is composed of sandy or calcareous clay with a thickness of 10–158 m, of which water blocking property is good. When encountering structures or karst collapse columns, Ordovician water directly filled roadway, which causes great harm to production.
Based on the disaster-causing factors of water inrush in coal mine Y, the evaluation system was established. It includes 4 types of the first-level indicators: mining conditions, hydrological factors, geological structure, and human factors expressed as
The index weights represent the contribution degree of each indicator to the entire evaluation system. Ten experts related to Y coal mine are invited to score indicators two by two according to the importance degree. The indicator’s comprehensive weights are output, conforming Inconsistency <0.1,″ as shown in Figure
Index comprehensive weights chart.
Ten experts related to coal mine Y are invited to score 23 major second-level indicators; the rules are shown in Table
Scoring criteria for water inrush disaster indicators in Y coal mine.
Disaster level | Degree of disaster | Rating ranges |
---|---|---|
1 | Weak | [0, 12.5] |
2 | Slightly weak | (12.5, 37.5] |
3 | General | (37.5, 62.5] |
4 | Strong | (62.5, 87.5] |
5 | Stronger | (87.5, 100] |
Combining the cloud feature numbers and weights of second-level indicators can obtain comprehensive cloud feature numbers of first-level indicators, as shown in Table
Comprehensive characteristic parameters and weights of each index cloud model.
First-level indicators | (Ex, En, He) | Second-level indicators | (Ex, En, He) | ||
---|---|---|---|---|---|
Mining conditions ( | (0.682,0.100,0.006) | 0.1707475 | Mining disturbance | (0.762,0.090,0.005) | 0.09025 |
Depth of mining floor failure | (0.758,0.064,0.003) | 0.17396 | |||
Coal seam burial depth | (0.730,0.044,0.003) | 0.02349 | |||
Working surface length | (0.738,0.047,0.003) | 0.28202 | |||
Mining depth | (0.655,0.084,0.005) | 0.09082 | |||
Reduce the strength of fractured rock mass | (0.578,0.149,0.008) | 0.33941 | |||
Hydrological factors ( | (0.701,0.082,0.004) | 0.610605 | Key position of the water barrier | (0.745,0.092,0.005) | 0.23291 |
Ordovician water | (0.719,0.080,0.004) | 0.47482 | |||
Aquifer | (0.654,0.075,0.004) | 0.07802 | |||
Water barrier thickness | (0.669,0.073,0.004) | 0.12155 | |||
Dynamic water pressure | (0.571,0.108,0.006) | 0.06889 | |||
Ordovician water channel | (0.585,0.086,0.004) | 0.02381 | |||
Geological structure ( | (0.656,0.087,0.004) | 0.1647225 | Karst collapse column | (0.746,0.077,0.004) | 0.04282 |
Fault | (0.720,0.081,0.004) | 0.44905 | |||
Karst fissure development degree | (0.601,0.076,0.004) | 0.21256 | |||
Collapse column | (0.603,0.120,0.006) | 0.00821 | |||
Complex geological conditions | (0.585,0.108,0.006) | 0.28406 | |||
Folds | (0.575,0.106,0.005) | 0.00331 | |||
Human factors ( | (0.501,0.083,0.005) | 0.05393 | Mining methods and processes | (0.641,0.076,0.004) | 0.32893 |
Incomplete investigation of hidden dangers | (0.449,0.105,0.006) | 0.25707 | |||
Illegal production | (0.423,0.071,0.004) | 0.23631 | |||
Production organization management chaos | (0.427,0.065,0.004) | 0.08967 | |||
Production technology management chaos | (0.417,0.089,0.005) | 0.08803 |
The cloud model evaluation results of first-level indicators. (a) Mining conditions evaluation cloud. (b) Hydrological factor evaluation cloud. (c) Geological structure evaluation cloud. (d) Human factors evaluation cloud.
It can be seen from Figure
Figure
The evaluation cloud of hydrological factors is shown in Figure
Figure
Figure
The cloud feature numbers of goal are the inductive summary for the entire cloud model. In the early warning evaluation system of Y coal mine water inrush disaster, the comprehensive cloud characteristic numbers of goal are C (0.679, 0.086, 0.004). The corresponding cloud image is shown in Figure
The cloud model evaluation results chart of goal.
It can be seen from Figure
The predicted results are compred with actual disaster data of Y coal mine, which are consistent. It further proves that this early warning evaluation model of “ANP-Cloud” model based on Complex Network is reliable.
It is necessary to strengthen the prevented degree to hydrological factors, mining conditions, and geological structure. Moreover, we should comprehensively cultivate workers’ knowledge and technical capabilities. Moreover, construction technology management should be strengthened to avoid leaving out disaster-causing factors and eliminate illegal production.
In this article, the early warning evaluation system of the “ANP-Cloud” model based on Complex Network in water inrush disaster was established to solve the problem of complex dependence relationship among disaster-causing factors and prevent water inrush disaster. Moreover, the usability and reliability of this warning evaluation model were verified in Y coal mine. The main conclusions are as follows: The knowledge of the Complex Networks is used to establish a water inrush disaster network with 161 nodes and 149 connected edges. Through analyzing topological characteristics of the water inrush disaster network, 23 multiple importance nodes were obtained. Based on the Complex Network model of water inrush disaster, the early warning evaluation system of the “ANP-Cloud” model was established. The main implementation steps include establishing index system, index weights based on ANP, building Cloud models of comment sets, and comprehensive early warning assessment. Combining with the example of Y coal mine, the reliability and applicability of the evaluation model were further verified. The results show that the goal of the early warning evaluation system is a strong early warning level. Mining conditions, hydrological factors, and geological structures all belong to strong early warning levels. Moreover, human factors will have a certain effect on the other three first-level indicators. The predicted results are consistent with the actual situation of Y mine coal water inrush and the early warning evaluation system provides a base of experience for other types of network assessments.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This research was supported by the National Natural Science Foundation of China (Nos. 52074239, 51927807, and 51509149).