A NEURAL network model for real-time roofpressure prediction in coal mines

A Neural Network Model for Real-time Roof PressurePrediction in Coal MinesXiating Feng Yongtia Wang Jianguo Yao Department of Mining Engineering Department of Mining Engineering Center Coal Research Northeastern University Northeastern University InstituteShenyang P R China 110006 Shenyang P R China 110006 Beijing P R China 1000013 irm@ yjwang@1 1ntroductionThe fundamental research task of strata control at coal mining faces is to determine the physico-mechanical properties and structure of roof strata, as well as the extreme intensity of roof pressure exerted on the support and each step of its occurrence. The kernel of roof pressure research both in the theoretical and practical aspects, however, is the determination of roof pressure occurrence steps and their intensity.It is well known that practically the effective method of roof pressure measurement is to measure the resistance change of face supports or props. The roof pressure is then indirectly determined by the load measurement, taking the face supports. This is the common practice for in situ roof pressure measurement in China[1].For a particular complex mining face, three pressure time series can be obtained by measuring the working resistance of face supports, i.e. the initial resistance series P0, the maximum working resistance series P m, and the time weighted average resistance series P t.The initial resistance is the prop resistance developed by the hydraulic pump against the roof at the initial stage of installation and is an active force. The resistance increases due to the roof subsidence and is an active resistance. So, the initial resistance cannot represent the actual value of roof pressure. Although the maximum working resistance of props is different to the roof pressure caused by the prop moving, the time weighted average working resistance, though, can reflect the pressure on the props developed by the roof deformation to a certain degree. The measured load on the props at the underground mining fae includes not only the roof pressure, but also the influence of the prop loads at various stages. We choose the time weighted average working resistance of props at the roof pressure time series to determine the roof pressure. In other words, by using the three kinds of time series P t, P m and P0, one can identify the tendency and make predictions.Many authors have proposed various analytical methods concerning time series problems [2,3]. For example, there are ARMA(n,m). AR(n) and MA(m) models for stationary series. As for non-stationary series, the finite difference scheme is used to convert it to a corresponding stationary series. In addition, there are the auto-adapting model, threshold autoregressive model, mixed auto-regressive model, sparsecoefficient model, bi-linear and exponent auto-regressive models, etc. As a complex system, roof pressure is hardly subject to liner analytical method of time series. A new method of nonlinear series modeling for roof pressure based on neural network method is therefore proposed in this paper.The artificial neural network (ANN) is a new branch of intelligence science and has developed rapidly since the 1980s[4-6]. The ANN is an information processing system simulating the structure and functions of the human brain. It consists of numerous simple processing elements connected together according to certain rules and is able to respond dynamically to an outside stimulus and process information. Like the human brain, the structure and processing sequence of ANN are parallel. The ANN has a very strong learning ability and can adapt itself to the outside environment by learning. In an ANN, knowledge is not stored in specific memories, but distributed in the whole system. In order to store knowledge, there must be numerous connections. The ANN can learn from incomplete and inaccurate data with strong noise, and has a very strong ability of error-tolerance. The ANN, if properly trained, can give an approximately optimal solution from limited and distorted information. The ANN has many configurations and can provide the method to solve problems involving complex systems. The ability of ANN for coping with incomplete information further encourages us to explore the extrapolating ability of roof pressure prediction based on the time series of non-ideal roof pressure data.Figure 1. A multiplayer feedforward neural network for representing roof pressure series (p =1,2,…,N )2 Establishment of Nonlinear Dynamic Model for Roof Pressure SeriesSuppose a measured roof pressure series {}),...,,(21n t x x x x =. Modeling the roof pressure series is toestablish a relationship between the pressure p n x +and its previous series p p n p n x x x ,...,,21−+−+as(1)whers N is sample number.Let p n x + be represented by an output node and p p n p n x x x ,...,,21−+−+be represented by input nodes toconstruct a multiplayer feedforward neural network as shown in Fig1. There may be one or more hidden layer(s) between the input and output layer in order to represent a complex nonlinear mapping of roof pressure series. According to literature [7], the network may contain two hidden layers. The node threshold function is sigmoidal, as x e x f −+=1/1)(.Instead of using traditional methods such as statistical regressive analysis, etc. the nonlinear roof pressure series represented by equation (1) can be determined by using machine learning performed on a neural network. A training sample data set shown in Table 1 is used to train the multiplayer feedforward neural network to obtain a nonlinear mapping F which approximates the actual G (Table 2). Thus,(2)where is the computed value of neural network.2.1 Learning algorithmUsing the network, F(‘)can be written by(3) whereir W is the connection weight between the i th node on the input layer x F and the r th node on the hiddenlayer g Frq W is the connection weight between the r th node on the hidden layer g F and the q th node on thehidden layer h F Table 1. A sampling data set from measured roof pressure serics for training the networkq W is the connection weight between the q th node in the input layer F h and the j th node on the output layer F y .j θis the threshold for the j th node on the output layer F y .q θ is the threshold for the q th node on the output layer F h .r θ is the threshold for the r th node on the output layer F g .The nonlinear model represented by equation (3) can be obtained from the network learning by using back-propagation algorithm [4] .Step 1. Obtain an initial representation of F (.) arbitrarily as follows(4)where are the initial weights; are the initial thresholdsStep 2. Compute error of the p th training sample and the system error as(5)Step 3. If end the representation of the F (.). Else goto Step 4. Step 4. Modify the connection weights and thresholds by using optimal gradient-descent algorithm.(6) where(7)where y is input to the output node of the network;(8)h q is input to the q th hidden node on the hidden layer F h(9)f t is input to the r th node on the hidden layer F g(10)t is iterations;ηis learning rate, )1,0(∈η;a is momentum item, )1,0(∈a .At the t+1th iteration, the node thresholds are modified by(11) whereStep 5. Goto Step 1 to modify the representation F(.).Table 2. Outputs of the network for recorded roof pressure seriesTable 3. Outputs of the trained network on the learning sample data setTable 4. Extrapolating prediction of the trained network for subsequent pressure series2.2 Extrapolation prediction of roof pressureThe function of F(.) determined after learning from case histories can be used to extrapolate pressure occurrence by giving predicted time and peak value of roof pressure. Multi-step extrapolating procedure is used for roof pressure prediction. Along with the latest measured roof pressure, the previous predicted values are also taken as the input data. In turn, subsequent prediction can be made iteratively.For the T th extrapolation prediction, the formula can be written by… … …(12)(13) where T —steps of extrapolating of roof pressure;—a set of the learned weights of the network;—a set of the learned thresholds of nodes.2.3 Establishment of nonlinear dynamic model for roof pressureFor the given model order n , i.e. number of input nodes of the network, an optimal nonlinear dynamic model for roof pressure can be obtained by using the above method. The optimal order n can be determined by using the minimum-error principle for the extrapolating prediction of the network. The algorithm can be written as follows:Step 1:For each n , n =1,2,…,a measured data set of roof pressure {}N p x x x x p p n p n p n ,...,2,1;,...,,,21=−+−++was used to construct the F (.) in the formula (3), respectively.Step 2: Use the learned weights and thresholds to compute the extrapolating prediction q N n x++ˆ(q =1,2,…,T ) of the model with each order n according to equation (12)or (13). Step 3: Compute system error of the extrapolating prediction of the model with each order n as:(14)Step 4: Findwhere M (m ) is the maximum order of the nonlinear dynamic model. According to experiment,Then the order n which indicates E min is the optimal unmber of the input nodes of the network. Correspondingly, the learned representation F (.) is thus an optimal dynamic modeling on the roof pressure. The model can be used for extrapolating prediction of the roof pressure of the mining face. 3 Case Studies3.1 Case 1The caving system is used for the ＃6310 coal mining face of Nantun Coal Mine. The mining face is2.8-m-high and is surrounded by excavated mining areas in the four directions with barrier coal pillars 70m in length. The ＃6310 face is thus like an isolated island. The panel length is 300m with inclined face length 120m. The coal seam belongs to the Permian formation and is abundant in joints. The thickness of the seam is 4.3～6.2m with an average value of 5.5m. The dip angle is 2～8°, average is 6°. The hardness coefficient of the seam is f =1～2. The industrial resources of the face are 682,000 tons. The upper roof consists of medium-grained hard grey sandstone. 11.03～27.8m thick. The mmediate roof consists of black grey fine-grained sandstone. 1.5～6.8m thick, with blocky structure andabundant in joints. The false roof consists of black grey mudstone, 0.05～0.2m thick, soft and broken.Roof pressure history can be interpreted on the basis of the measured face support resistance curve obtained by using hydraulic pressure cells installed at measuring station ＃40. Data for the initial resistance P0 and maximum resistance P m , as well as their time weighted average values for 114 cycles were recorded.In accordance with Qian and Liu [1], we chose the measured time weighted average working resistance P0 was the time series of roof pressure.The node number of the ANN determining the pressure series was taken to be 52 obtained by using the minimum-error principle of prediction. The network configuration was taken to be 52→52→6→1,i.e.52 nodes for the first hidden layer, six nodes for the second hidden layer and one input node. The sample pressure series was divided into two parts. The pressure data of the 53rd to the 106th cycles were used as a learning sample to train the network and establish the neural dynamic model of pressure series. The pressure data of the later 107th-114th cycles were used to verify the correctness of the model.During the network learning, η=0.05 and a=0.05. After 1403iterations, the outputs of the trained network were within error allowance. Table 3 shows the outputs of the trained network for learning sample data set. Table 4 shows the extrapolating prediction of the trained network on this roof pressure series. The measured and computed curve of the roof pressure series are computed in Fig2.From the above tables and figure, the relative errors of the learned dynamic modeling for the learning samples were less than 0.2%. The relation errors of the network extrapolating prediction were less than 6.6% on pressure peak and 0% on pressure occurrence step.Figure 2. Comparison of measured curve with computed curve of roof pressure series3.2 Case 2A complex mechanized mining system was used in ＃1 mining area of Xiaokang Coal Mine. The mining face had a strike length of 250m and dip length of 130m. The coal seam was highlyinterstratified with 20 slices and two groups of coal. The ＃29 measuring station was in the ＃7 seam with developed joints. The overburden consisted of mudstone, black grey sandstone and sandy calcrete. The immediate roof belonged to the 2nd type and the main roof was of II class. Both were stable.Roof pressure history can be interpreted on the basis of the measured face support resistance curve obtained by using hydraulic pressure cells installed at measuring station ＃29. Data of the initial resistance P0 and maximum resistance P m, as well as their time weighted average values for 106 cycles were recorded. By experience, we chose the measured time weighted average working resistance P t as the time series of roof pressure.Figure 3. Comparison of measured curve with computed curve of roof pressure seriesThe node number of the ANN determining the pressure series was taken to be 46 obtained by using the minimum-error principle of prediction. The network configuration was taken to be 46→46→6→1. The sample pressure series was also divided into two parts. The pressure data of the 47th to the 100th cycles were used as a learning sample to train the network and establish the neural dynamic model of pressure series. The pressure data of the later 101th–106th cycles were used to verify the correctness of the model.Let η=0.05 and a=0.05, and train the network to obtain optimal dynamic modeling on roof pressure of this mining face. After 11,479 iterations, the outputs of the trained network were within error allowance. The measured and computed curve of the roof pressure series were compared in Fig.3. It is shown from Fig.3 that the relative errors of the network extrapolating prediction were less than 5% on pressure park and 0% on pressure occurrence step.4 ConclusionsA knowledge of the evolution of roof pressure series is an important aspect of research. As a complex system, the roof pressure cannot be analyzed by using the linear time series method. A new method of nonlinear series modeling for roof pressure based on the ANN theory has been proposed in this paper. No prerequisite parameters and model types are required. The final model is constructed by the ANN itself from learning the history curve of roof pressure and expressed via the parallel distribution ofinformation in the ANN nodes. Thanks to the parallel structure of the ANN, data processing in the network is rapid enough for real-time prediction of roof pressure. In addition, the ANN is highly error tolerant and can provide correct answers even with individual distorted input data. It can be seen from the preliminary application of the two practical cases of roof pressure prediction, the ANN is able to provide real-time prediction of roof pressure characteristics (pressure intensity and occurrence step) with high accuracy and practibility.References[1] Qian M.G. and Liu T.C(1991). Mine pressure and Control. China Coal Industrial Press, Beijing.[2] Yang W.Q and Gu L(1998). Time series analysis and Dynamic Data Modeling. Beijing Science andTechnology University Press, Beijing.[3] Hannan E.J(1990). Multiple Time Series. John Wiley.[4] Rumelhart D.E. and McClelland J.L(1986). Parallel Distributed Processing (Edited by Rumelhart D.E. andMcClelland J.L.). MIT Press, Cambridge, MA.[5] Grossber S(1991). Nonlinear neural network: principles, mechanics and architecture. Neural Network1,17-61.[6] Hechit-Nielsen R(1990).Neuron Computing. Addison-Wesley, Reading, Massachusetts.[7] Hertz J., Krough A. and Palmer R.G(1990). Introduction to Theory of Neural Computation. Addison Wesley.。