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Water Inrush Source Identification of Mine Based on D-S Evidence Theory [Sensors & Transducers (Canada)]
[April 22, 2014]

Water Inrush Source Identification of Mine Based on D-S Evidence Theory [Sensors & Transducers (Canada)]


(Sensors & Transducers (Canada) Via Acquire Media NewsEdge) Abstract: Using the D-S evidence theory, according to the chemical analysis of the aquifer water in underground shafts, and selecting 6 kinds of ion concentration as the discriminate indexes for the identification of water inrush source, the model of water inrush source identification of mine was established. Firstly, according to 35 groups of sample data of the main aquifer in Jiaozuo mining area, China, the triangular fuzzy number described model of single element proposition was constructed by determination of the minimum, average and maximum values of sample data. And the generalized triangular fuzzy number described model of multi-element proposition was represented by the crossing area of the triangular fuzzy number described models of single element proposition. Then, the supporting degree of proposition was determined according to the generalized triangle membership function and the basic probability assignment of proposition can be obtained by the normalization of the supporting degree. Finally, the basic probability assignments were fused by the Dempster's combination rule. The experiment results show that the identification model based on D-S evidence theory has good classification performance, high prediction accuracy, and wide application prospect. Copyright © 2013 IFSA.



Keywords: Information fusion, Evidence theory, Basic probability assignment, Water inrush in mine, Water source identification.

(ProQuest: ... denotes formulae omitted.) 1. Introduction Water disaster as one of the main disasters in coal mine influences the safety production of coal mine severely. Water inrush accident has brought very serious personal injuries and economic losses to the coal mining enterprises. In serious accidents of coal mine in China, the water inrush accident in coal mine is the second only to gas accident in the occurrences and the number of deaths, which has been ranked on the first place for causing direct economic losses to the nation. Once the mine water inrush occurred, how to accurately determine the causes of water inrush, it is the key important to solve and further prevent water inrush disasters by searching for the water inrush resources. The hydro-geochemical method is an effective way to distinguish the resources of water inrush, this method is to establish the objective function by the analysis of the groundwater characteristics of the component content of different aquifer based on the collection of known aquifer water samples, and then use the objective function to identify the pending water resource, thus to judge the aquifer that the water inrush belongs to. Zhang et al. [1] have used the second theory of quantification of multivariate statistical analysis to build the linear model of water source identification. Yang et al. [2] have used the nonlinear methods of gray relational analysis and BP neural network to identify the water source. Yan et al. [3] have used SVM model to determine the water inrush source. Zhou et al. [4] have determined the water source through the establishment of the distance for the identification of mine water inrush.


As the prediction of mine water inrush is a matter of multi-source information fusion problem referring to hydrogeology, engineering geology, mining conditions, rock mechanics as well as many other factors. There are also the differences of impact of the sensitivity of the indexes of water inrush, and it is often not enough to reflect the essence of water inrush with only an index. Therefore it necessary to select multiple sensors or monitoring tools, and make reasonably comprehensive use of all kinds of sensors similar or heterogeneous information obtained from multi-sensors, use the information fusion technology to combine the redundant information that is complementary and in time and space according to some optimization criteria, so as to make the consistent and reliable estimation of the environment. As the D-S evidence theory is suitable for decisionmaking data processing of the multi-sensor data fiision, it satisfies the axiom system weaker than the probability, and it is able to handle the uncertainty, imprecise and incomplete information caused by unknown, which especially has advantages in terms of the uncertainty express, measurement and combination, and it has been widely used in the fields such as information fusion, decision analysis, pattem recognition, intrusion detection as well as trust management and so on. In this paper, we consider the high degree of complexity and uncertainty of mine water inrush, and put forward a model of identification of water inrush source based on D-S evidence theory. Firstly, there are brief introductions of D-S evidence theory and the method for the generation of the basic probability assignments (BPA) based on the triangular fuzzy number in Section 2. And then, we put forward the identification model of mine water inrush source based on the evidence theory in Section 3. The conclusions of this paper are in Section 4.

2. Brief Introductions of D-S Evidence Theory and the Construction of BPAs 2.1. D-S Evidence Theory Due to the space limitations, the brief introductions of evidence theory are in this section, and please refer to the reference part of this paper for more details [5, 6].

In D-S evidence theory, let's suppose 0 ={ 0X , 02 ,..., 0i,..., 0n } means all the possible answers that need judging all the recognizable problems. Any two objects in 0 are mutually exclusive, and we call the complete collection of discernment mutually exclusive events as the frame of discernment. 0. is a single element proposition of the frame of discernment 0 . In the information fusion system, such kind of proposition containing only a single element is the conclusion that the system needs to make decision or judgment.

The key issue of evidence theory is that it has to assign a basic probability assignment to each subset, which is defined as follows: Let's suppose 0 is the frame of discernment, and 2® is the power set of 0 , if the function: ... satisfies: VA g 2® } m(A)> 0 , and ..., then we call that m is the basic probability assignment function.

D-S evidence theory provides Dempster's combination rule by combining from multiple independent sources of information, its form is as following: ... (1) It can be seen from Eq. (1), if offered BPAs of all subsets, and they can be integrated by using Dempster's combination rule, so as to make the objective decision. However, due to the complexity and diversity of the background of evidence theory applied, how to determine BPA is still an open issue.

2.2. The Construction of BPAs Many scholars at home and abroad have done some researches on reasonable access to get basic probability assignment. Xu et al. [7] have proposed a BPA construction method based on confusion matrices. Pang et al. [8] have adopted minimum confirming principles to determine the BPA. Zhu et al. [9] have used fuzzy C-means clustering and adjacent information of space to obtain BPA automatically. Hu et al. [10] have created BPA based on neural network. Boudraa et al. [11] have constructed BPA based on fuzzy membership function in image processing. Guan et al. [12] have used the three methods of gray relational analysis, fuzzy sets and attribute measure separately to construct BPA. Jiang et al. [13] have put forward a new approach to construct BPA based on the distance measure between the sample data under test and the model of attribute of species. Deng et al. [14, 15] have put forward the method of BPA construction based on fuzzy similarity degree. But most of the existing methods are allocated only to BPA of single element proposition on the frame of discernment, then BPA becomes the probability of the probability theory, this will certainly greatly reduce the usefulness of these methods.

In this paper, we use the method for the generation of the basic probability assignments based on the triangular fuzzy number [16]. The richer the sample data, the more distinction the constructed generalized triangular fuzzy number will be, then generated BPA using the method to construct BPA is more reasonable, and it has provided a new way for the successful constructing BPA in the evidence theory. There are brief introductions of the method for the generation of the basic probability assignments based on the triangular fuzzy number. Please refer to the Ref. [16] for more details.

Suppose the frame of discernment 0 = {0X, 02,..., 0n}, for the measured value V of the index k, the measured values belong to the degree (point of the intersection of the vertical axis with the described model of triangular fuzzy number) of the described model of triangular fuzzy number of each proposition H, respectively pkH , pkH , f*H. of which, pkH >0, i =1,2,..., m ( m is the number of intersection point). The strategy based on the triangular fuzzy number described model has generalized BPAs as followings: 1) The supporting degree of the empty proposition is 0, namely Supka =0; 2) When m =1, the measured value V is only intersected with a triangular fuzzy number described model of single element proposition, then, the vertical axis °f the point of intersection is the supporting degree of the single element proposition; 3) When m >1, the measured value V is intersected with some triangular fuzzy number described models of proposition. For the intersected points of the triangular fuzzy number described models with all the single element propositions, take the maximum value of the vertical axis of the intersection as the supporting degree of the single element proposition; if other single element proposition Hi (except the single element proposition with the largest membership degree) has the membership degree pkH , there are at least the multi-elements proposition Hj including H. of membership degree pkHj, therefore, just abandon the supporting degree of the other single element proposition, and make the membership degrees of triangular fuzzy number of these multi-element propositions as the supporting degree of the multi-element propositions; 4) Use 1 minus the maximum membership degree as the supporting degree of the whole set 0 , and it is considered that the information of this part is completely unknown. Namely, Sup#= 1 - max {pku } (i =1,2,..., m); 5) Normalized the supporting degrees of the above obtained SupkHj , and then the BPA of each proposition can be received: ... (2) 3. Identification Model of Mine Water Inrush Source With the comprehensive consideration of the importance of ion and the validity of data, determine to use the Na++K+, Ca2+, Mg2+, Cl', S042' and HC03' as the indexes for identification of the water inrush source. We use 35 groups of sample data which are from four main aquifers of Jiaozuo mining area [1] to structure generalized triangular fuzzy number of each proposition. In the water category, I is the aquifer of second grey and Ordovician, II is eight gray aquifer, III is Roof Sandstone aquifer, and IV is the Quaternary aquifer (sand and gravel composition is mainly limestone). Therefore, the frame of discernment of the target identification system 0 = {I, II, III, IV}, the indexes of each category are Na++K+, Ca2+, Mg2+, Cl\ S042' and HCOf. The minimum, maximum and average values of the index can be determined according to the certain index for a class of samples, and a triangular fuzzy number can be established based on these three values. Herewith, we use the index of Mg2+ as an example to construct the triangular fuzzy numbers of Mg2+.

According to the triangular fuzzy number described method of proposition in Ref. [16] and Section 2.2, we obtain the minimum, average and maximum values of the Mg2+ content of aquifer I respectively 15.56, 19.59 and 24.81 based on the measurement data [1]. Then the triangular fuzzy number of the Mg2+ content of aquifer I is (15.56, 19.59, 24.81; 1). Fig. 1 is the described model of the triangular fuzzy number generated according to the index of Mg2+ content of aquifer I. Similarly, we can calculate the triangular fuzzy numbers of four aquifers for the Mg2+ content and them crossing areas of generalized triangular fuzzy number, as is shown in Table 1. Fig. 2 is the generalized triangular fuzzy number described models of Mg2+ content generated by 35 groups of training samples.

If we receive a test sample and its Mg2+ content is 19.59 mmol/L, and based on the generalized triangular fuzzy number, generated BPAs as follows: m ({I})=0.4654, m ({I,II})=0.1124, m ({I,IV})=0.1974, m ({II,IV})=0.1124, m ({I,II,rV})=0.1124, m ( 0 )=0.

For the complete 6 index values of this sample (23.76, 66.40, 19.59, 18.13, 57.26, 255.29) are used respectively to construct BPAs and get 6 evidence, as is shown in Table 2.

Using Eq. (1) to combine the 6 evidence in Table 2, the results is shown in Table 3. The conflict coefficient k in Table 3 is very small, which means that the method constructed BPAs can reduce the conflict between the evidence, and the constructed BPAs can be combined by Dempster's combination rule.

Finally, based on the maximum value principle of the basic probability assignments, we can judge the test sample belongs to aquifer I. Let's make the discrimination on the remaining three test samples according the same method, the discrimination results are shown in Table 4. Table 4 also lists the judged results by using the second theory of quantification (STQ) [1], supporting vector machines (SVM) [3] and the distance discriminate analysis (DDA) [4], From Table 4, it can be known that the discriminate results of our method are conforming to practical results. The discrimination results of water source category obtained by the proposed method of this paper are the same to the results of the other three methods, the error rate is 0. Therefore, the D-S evidence theory of discriminate model proposed by this paper can be applied to the identification of mine water inrush source, and the calculation of the identification process are linear calculation, which has smaller calculation amount compared with second theory of quantification, support vector machine and distance discriminate analysis, and it can meet the needs of real-time monitoring.

4. Conclusions In this paper, we put forward a method for identification of mine water inrush source based on the multi-source information fusion technology. The method firstly uses sample data of the mine water inrush to build the generalized triangular fuzzy number described models of single element proposition and multi-element proposition in the target recognition, and then to construct BPAs of proposition based on the membership degree of generalized triangular fuzzy number, and finally use the Dempster's combination rule to combine all the evidence. Through the analysis of the discriminatory of the four main aquifer of water inrush source of Jiaozuo mining area, China, the combination results by using Dempster's combination rule can effectively identify all kinds of water inrush source, which lays a theoretical and technical foundation for the identification of mine water inrush source based on D-S evidence theory.

Acknowledgements This research was supported by the National Natural Science Foundation of China (No. 61102117). The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

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Jianyu Xiao, Aili Yang School of Computer Science and Technology, Huaibei Normal University, Huaibei 235000, China Tel.:+86-561-3803659 E-mail: [email protected] Received: 23 August 2013 /Accepted: 25 October 2013 /Published: 30 November 2013 (c) 2013 International Frequency Sensor Association

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