Coal seam thickness prediction based on transition probability of structural elements

: Coal seam thickness prediction is crucial in coal mine design and coal mining. In order to 13 improve the prediction accuracy, an improved Kriging interpolation method on the basis of 14 efficient data and Radial Basis Function (RBF-Kriging) is firstly proposed to interpolate the cutting 15 data obtained in pre-mining, especially at the edge of the geological surface of coal seam by taking 16 into account the spatial structure and the efficient spatial range, ensuring the integrity of the edge 17 data during the movement of structural elements. Then, a structural element transition probability 18 based Gaussian process progression (STTP-GPR) method is proposed to predict the coal seam 19 thickness from the interpolated coal seam data. The experimental results demonstrated that the 20 proposed STTP-GPR method has superior performance in coal seam thickness prediction. The 21 average absolute error of thickness prediction for thin coal seams is 0.025 m which significantly 22 improves the prediction accuracy in comparison to

Among the large amount of interpolation methods, Kriging interpolation is widely used in the 45 field of coal mining. It takes the spatial correlation into account when dealing with data, achieving good performance in most cases [5].
In Kriging interpolation, the types of variation function model are finite, which make the 48 variation function very difficult to describe the spatial distribution characteristics of true data. In 49 order to overcome this shortage, an improved interpolation called Support Vector Machine-Kriging 50 interpolation (SVM-Kriging) was proposed in [6]. The SVM-Kriging uses Least Square Support Vector Machine (LS-SVM) to fit the variation function, and directly get the optimal variation 52 function for the real interpolated field by using SVM to fit the variation function curve 53 automatically. In [7], the Kriging interpolation method was used to study the coal quality 54 prediction model of cutting coal, and the parameters of optimal variation function model and 55 experimental variation function are determined based on data characteristics. Spatial distribution of 56 ash and heat is predicted by using the Kriging interpolation method. In [8] and [9], a method based 57 on dimensionless parameters and SVM was proposed for coal-rock interface identification.

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In the existing methods the spatial structure and spatial distribution in the region of the coal 59 seam geology transition, are seldom taken into account. Moreover, the coal seam thickness

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(STTP-GPR) method is proposed to predict the coal seam thickness from the interpolated data. Our 76 method can be used to generate the coal-rock interface and predict the coal seam thickness, where 77 those data will be used to guide the shearer drum to automatically adjust the coal cutting height in 78 automatically and intelligently coal mining.
where is the interpolation weiμht. Considering the unbiasedness condition yields:

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. (2) Since the weighting procedure depends on both the distance and statistical distribution of the 88 samples, the variation function is adopted to estimate the weight by fitting a spatial model to the

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Although the Kriging performs well in the coal seam thickness prediction, the variation function 100 model which is often chosen by experience may not express the cutting data accurately. In this 101 paper, the kriging method is improved by calculating the interpolation weight using efficient 102 samples and fitting the variation function through RBF.

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In order to ensure the nearest point has a greater influence on the interpolation point in the

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Kriging method, the variation function as shown in equation (3)

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Notice that utilization of the efficient samples not only improves the interpolation performance, but 122 also reduce the computational complexity.

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In the process of calculating the interpolation weights, the variation function often depends on exponential model, etc. it was shown in practical applications that the relative error is relatively 127 large, the spatial characteristics of the existing sampling points may not be well described by these 128 models, and the integrity of the direction and distance information in the data space cannot be

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Because of the relationship between the distance and the variation function, the variation 144 function must be greater or equal to 0. Using the RBF network to fit the variation function, the value 145 of variation may be less than 0, but the probability is almost 0 as the result of the efficient sample 146 chose at part 1.2. If the value of variation function fitted by RBF is less than 0, we will configure the 147 value is 0, because the distance of two points is too long and the effect of two points at the distance 148 is negligible.
Where and is plane coordinates of the location x  Step 2: Calculate the variation function values between point pairs as, , ( and one-to-one correspondence with distance, where, and 156 is the number of experimental variation function corresponding to the lag distance d,

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is the coal seam thickness at the point that its plane coordinates is ; 158  Step 3: Using RBF function to fit distance and variation function values and using the 159 following function where indicates the coal seam thickness at the interpolation point.
169 Figure 1 shows the flow chart of the proposed algorithm.
where m is the number of state,

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The flow chart of the proposed STTP-GPR algorithm is shown in Figure 7.
The simulated surface is shown in Figure 8. In this experiment, 30 sets of continuous data were 328 randomly generated from the simulated surface as a training set and a test set. The average mining From Figure 9, it can be seen that the trends of prediction data matches the real data very well.

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Overall, the maximum prediction error is less than 0.03m, and the average absolute error remains 345 around 0.02m. From Figure 8, it can be seen that the proposed STTP-GPR algorithm has a good 346 performance in dealing with the locality change problem, which verifies that the spatial distribution 347 of the coal seam near the prediction point plays an irreplaceable role in the prediction process.
Processing the structural distribution of coal seams correctly is the key to improving the prediction 349 accuracy of coal seams, and by expressing the structural distribution through transfer probabilities 350 in local regions. Figure 10 shows the 3D visualization of the real surface and prediction surface.

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The absolute average error in the test set remains around 0.025. The prediction error at the third 368 point and the last two points of the test set is relatively high due to that the coal seams are 369 mutational at these points. Analysis of the prediction error on all test sets shows that the overall 370 prediction error is less than 0.031. From Figure 12, it can be seen that the proposed STTP-GPR 371 algorithm has handled the coal seam mutation at second data and the last three data in test set that 372 their error is less than 0.03 very well by taking into account the spatial structure information and the 373 maximum error is less than the error predicted by GPR algorithm descripted in Section 4.3. From the 374 real coal seam data, it can be seen that the frequency of local fluctuations in the coal seam during its 375 evolution is relatively large, in the proposed STTP-GPR algorithm, the transition probability is 376 mainly divided by human experience in the calculation process, resulting in inaccurate division of 377 the interval or failure to describe the structure information. In the future, we will focus on the study of how to accurately express the local spatial structure information of the coal seam and the relationship between the local spatial structure information and the global spatial structure  The real surface and predicted surface are shown in Figure 13 in order to visually represent the 388 pros and cons of the prediction algorithm in the coal-rock interface identification process using the 389 real data. The predicted surface shown in Figure 13 is the upper surface of the coal seam is obtained 390 from the predicting and known data. The real surface is obtained from the known data in the test set.

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It can be seen that the predicted surface can accurately express coal seam movements and changes in 392 coal seam thickness, especially in local district.

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The average absolute error predicted by using the four prediction algorithms is shown in Table   404 1.From Table 1, it can be seen that the proposed STTP-GPR algorithm is superior to the other 405 algorithms. The prediction value of SVR algorithm changes with the change of kernel function, and 406 the kernel function usually depends on empirical selection. The neural network algorithm may over 407 fit in processing small sample data, and because of lacking of sample data, the prediction error is