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1、英文原文 Application of Grey Relational Clustering and CGNN in Analyzing Stability Control of Surrounding Rocks in Deep Entry of Coal Mine Wanbin YANG 1, Zhiming QU2 （1.Beijing University of Science and Technology, Beijing, 100083； 2. Hebei University of Engineering, Handan, 056038） AbstractWith combina
2、tion of grey neural network （CGNN） and grey relational clustering, the models are constructed, which are used to solve the prediction and coMParison of surrounding rocks stability controlling parameters in deep entry of coal mine.The results show that grey relational clustering is an effective way a
3、nd CGNN has perfect ability to be studied in a short-term prediction. Combined grey neural network has the features of trend and fluctuation while combining with the time-dependent sequence prediction. It is concluded that great improvements coMPared with any methods of trend prediction and simple f
4、actor in combined grey neural network is stated and described in stably controlling the surrounding rocks in deep entry. I. INTRODUCTION GREY system technology states the uncertainty of small sample and poor information. With the development and generation of the unknown information, the real world
5、will be discovered and the system operation behavior will be mastered properly. Through original stability with the pre-processing, the grey system law will be described. Though the real world is expressed complicatedly and the satisfied irregularly, the integrated functions will be appeared as a ce
6、rtain inner regular pattern 1. The studying of grey system technology is based on the poor information which is generated by parts of the known information to extract valuable stability and to properly recognize and effectively control the system behavior. The neural network is dependent on its inne
7、r relations to model, which is well self-organized and self-adapted. The neural network can conquer the difficulties of traditionally quantitative prediction and avoid the disturbance of mans mind. The grey relational analysis is based on the similarity of geometric parameters curve to determine the
8、 relation degree.The closer the curve shape similarity is, the greater the corresponding sequence correlation is. The similarity is described with correlation coefficient and correlation degree which describes the effect on the results by various factors.The greater the correlation is, the greater t
9、he iMPact extent is.While analyzing a practical system, the data series with the behavioral characteristics are identified. Additionally, it is necessary to ascertain the effective factors influencing system behavior characteristics, namely, sub-factors 1, 2. Though the objective system are expresse
10、d complicatedly,the development and change are still of logic laws and the different functions are coordinated and unified. Therefore,how to find its inner developing regularities from the dispersed stability seems to be important. In the light of the description above, it can be found that the comb
11、ination among grey relational clustering will take great effect on stability control of surrounding rocks in deep entry in coal mine. The combined grey neural network model will be built in solving and analyzing this problem. II. GREY RELATIONAL CLUSTERING A. Grey Relational Clustering As the genera
12、l system of grey trend relation, D. J. CHEN, etal 3-6 has done a lot of work. In order to apply it into the practice, the basic idea about his study is introduced. The similarity and approximation in the dynamic system behavior can be expressed using grey trend relation （GTR） With the aid of GTR, th
13、e implicit system operation laws maybe stated aptly.Generally, the general system theory is applied in the general GTR system, and combining with GTR, the systemized models of GTR analysis will be deduced. It is assumed that U is the referred factor set and W the coMPared factor set, uy R is the set
14、 of GTR in （B, W） The matrix is called the GTR matrix for ， and , while the set （B, W） is finite. Where , the trend relation and ,the trend relation function. ., And Q is the general GTR system, . In order to illustrate and serve application in this paper,some definitions are introduced here. V is t
15、he evaluating space of system Q and H is the evaluating functions. Thus, the relation between Q and evaluating space are described as .Therefore, the general GTR system model is defined as ;.The general GTR system is generalized, which includes the problems using the GTR analysis. In order to solve
16、different problems, the GTR should be not alike in the light of B, W and H. On the basis of GTR matrix, the GTR clustering method is to assemble the observed index or objects into many definable classifications. The clustering can be seen as the observed object set of the same classification. Actual
17、ly, any observed objects have many characteristic indexes which are not accurately classified. Through GTR clustering, the factors of the same classification are collected and the complicated system will be simplified 3-6.Z, the factor set of GTR system, has h factors. Each one represents a sequence
18、, .is the specific relational mapping, the trend relation of on the referred factor.;,; .Composed of Z and , the GTR system is called self-relational system of GTR. is GTR matrix, H the evaluation rule and V the evaluation space.As to, is the threshold of clustering analysis and the evaluation rule
19、is defined as . and are the similar terms of characteristics while ,. At the classification of threshold ,the system characteristic variable is the trend relational clustering. The system output is the clustering, which is expressed as.Where, is the set including a group of characteristic variables,
20、 the same as above and. kpqiuyRQ=)()()0(kbq),2,1(nk=),2,1(pq=)()0(kwi),2,1(hi=)(kqix)()()()0()0()0(kwkbkziqqi-=D),3,2(nk=1,0,bauyRWBQ),(=VWBH:uwRWBQ),(=VWBH:minkkzZi,2,1;,2,1),(=JijJjziz),(jiijzzJJ=Zzzji,Mji,mjmiij,2,1;,2,1=YJYY),(Y=ZQ1,0cgcJJjZiZjicJsaa,2,1,=W=VVaVsmsB. Grey Relational Clustering P
21、rediction Assuming that is the GTR time-dependent sequence and is the known model set. Each model set, in the light of GTR sequence, can be supported by a group of prediction data,. is the GTR ofand.The meaning of andis the same with that and.Z and F is the prediction set, where k =1,2,n,i =1,2,h, j
22、=1,2,m . Q = （Z,F）, ） is the GTR prediction system if H : is the prediction and evaluation rule of GTR and V is the evaluation space of system prediction effect. The system is mapped as . III. CGNN )()0(kZJmjfj,2,1=),2,1)(njkfj=jJQ)()0(kZJ)(kfj)()0(kZZi=)(kfFi=)()0(kZJ)(kfj),2,1(nj=sQoptVFZH:Using G
23、M （1, 1） to predict sequence is one of the most frequently applicable fields. Because the grey model is in the light of stability to acquire the regularities, some predictable errors maybe appeared and many differently independent models will be setup to many related sequences, which can not conside
24、r the relations among stability sequences sufficiently. Generally, the shortcoming can be made up through setting up the combining models such as A. Combined grey neural network （CGNN） prediction model. is the input sample, and y, the single output,the implicit node output,the weight connecting with
25、 implicit and output nodes.The connect weight value is 1 between input and implicit nodes because the signal is transmitted to the implicit layer by the input node. The output of NO. i implicit node is.Where i is the number of implicit nodes, .is the radial function which is expressed by Gaussian ke
26、rnel function. is the input sample. is the center of radial basis function of neuron. is the width parameter of radial basis function of neuron. is the Euclidean norm.The activation function of implicit node has different expressions. The Gaussian kernel function, ,is always used, and the output of
27、RBF neural network is. Two stages are included in RBF network. and of all implicit nodes are calculated by k-average clustering algorithm and all the input samples in the first stage. Then, according to training samples and least square method, is solved after the implicit layer parameters are calcu
28、lated. In the light of the reasonable input parameters and the prediction principles, the input and output stability based on radial basis function can be calculated, trained and predicted by the functions in MATLAB tool. Combining with neural network, the GM （1, 1） is used to setup the grey neural
29、network prediction model. A series of prediction values can be acquired to the raw series stability while GM （1, 1） is setup to many series. But a certain deviation still existed, which is related to the raw unintuitive series. Thus, the relationship between series and the deviation of prediction an
30、d original stability should be taken into account. The prediction value is considered as the input samples of neural network, and the original stability as the output sample. Using a certain stability structure, the TnxxxX),(:21TnuuuU),(21=TnwwwW),(21=iiiCXRus-=mi,2,1=RXiCthiisiCX-25.0exp)(xxR-=iCis
31、iwnetwork will be trained and series of well-trained weight and threshold values can be acquired. The prediction in one or more different time of different GM （1, 1） is as the well-trained input of network from which the final prediction in the next time or next different time will be carried out. A
32、s to the algorithm, the CGNN prediction is introduced in detail in reference 1, 7. In stability control of surrounding rocks in deep entry in coal mine, it is very complicated that the variables inside the stability system are produced at the beginning of the model setup. The variables explained in
33、the model should be selected correctly, which, on one hand, relies on the further study and cognition by the model builder to the system and on the other hand, on the quantitative analysis. To solve this problem, the grey relational principle will bring active action on it. Let y be the system varia
34、ble, are the positive or negative correlated factorsis the relation on the basis of to y. Given the lower threshold value, ,can be deleted while,in which parts of explaining variables relating to the weak relation can be deleted in the stability system. To the network and using the method above, the
35、 input variables of network are selected, which can simplify the input samples greatly. Letbe grey prediction value, the prediction value by neural network, prediction value by optimal combined model. The prediction errors areand respectively.The corresponding weighted coefficients areand ,and ,.Thu
36、s, the errors and variations are as. . As to, in order to determine the functional minimum value, let nzzz,21ieiz0eiz0eei1l2lcl21,hhch21,wwcw121=+ww2211aaawwc+=2211hhhwwc+=),(2)()()()(21212221212211hhhhhhhCovwwVarwVarwwwVarVarc+=+=1w),()1(2)()1()()(2111221121hhhhhCovwwVarwVarwVarc-+-+=and. 0)(1=wVar
37、chObviously, ,then and . Because ,let, then the weighted coefficients of combined prediction are 0)()(212wVarch121ww-=0),(21=hhCov111)(gh=Var222)(gh=Var,. IV. CASE STUDY In the process of low stability control of surrounding rocks in deep entry in coal mine, the stability control parameters of surro
38、unding rocks will cause serious accidents in coal mine production safety. How to forecast the stability control of surrounding rocks and control the ultra-limit of stability of surrounding rocks has been the focus of disasters and difficulties. In the recovery process, stability control of surroundi
39、ng rocks is influenced by many factors and constraints such as Tensile strength, Elastic modulus, Possion ratio, Appearance density, Inner friction angle, Cohesion, Residual inner friction angle, Residual cohesion, Tensile strength and so on. Therefore, the stability control system of surrounding ro
40、cks is a multi-variable system whose characteristic equation is of generally high-order, which is difficult to use the same analytical style to quantitatively describe of the stability control changes of surrounding rocks and the complex function relations among the factors. No matter what means are
41、 often unable to obtain all the information. All decisions are made between some pieces of known information and partial unknown information. Therefore, the stability control system of surrounding rocks is grey. Through the study, it is found that, using the grey control system theory, the modeling
42、and forecasting techniques are applied to analyze the stability control changes of surrounding rocks. Based on grey relation clustering models, the dynamic models are created to solve the practical problems in order to avoid the difficulties is solving high-order differential equations. At the same
43、time, the application of the dynamic prediction model can better predict the stability control changes of surrounding rocks so as to forecast and control the stability control changes of surrounding rocks to prevent accidents. A. Prediction of stability control of surrounding rocks at upper corner o
44、f working face In a coal mine, the working face is at the level of -736 meters underground. Using the grey relational analysis, some main variables influencing the stability control of surrounding rocks are selected 2 and the measured data is shown in TABLE I. In TABLE I, data group 1-7 are used to
45、establish GM （1, 3） prediction model to forecast the stability control of surrounding rocks of upper corner at the level of -736m of A1 working face, which is coMPared and analyzed with the 8th measured data. Then, the prediction model is analyzed by the grey errors and accuracy. According to the pr
46、ediction model, the original sequence is coMPared with the measured values shown in TABLE II. From the results, it can be seen that the prediction model residuals and relative errors meet accuracy requirements. TABLE I MEASURED DATA 21 July 26 July 31 July 5 Aug 10 Aug 15 Aug 20 Aug 25 Aug Group 1 G
47、roup 2 待添加的隐藏文字内容1Group 3 Group 4 Group 5 Group 6 Group 7 Group 8 Stress of surrounding rock 0.55 0.54 0.61 0.62 0.67 0.66 0.69 0.67 Pressure of surrounding rock 633 589 583 603 645 684 721 722 Strength 0.93 0.95 0.94 1.01 1.11 1.20 1.22 1.20 TABLE II ORIGINAL DATA RESIDUAL CHECKING Date k )(01kx )(
48、01kx )(01ke %/e20 July 1 0.55 0.5503 0.0003 0.055 25 July 2 0.56 0.5503 -0.0097 -1.73 30 July 3 0.62 0.6175 -0.0025 -0.40 5 Aug 4 0.61 0.5908 -0.0192 -3.15 10 Aug 5 0.67 0.7012 0.0312 4.66 15 Aug 6 0.68 0.6988 0.0188 2.76 20 Aug 7 0.72 0.7214 0.0014 0.19 With the elapsed time and the increasing information, a group of forecasting models can be created. Only 4 forecasting models are simulated so the models are changed with time. The models above are checked over the gre
