Research on the in-situ stress inversion method of mine based on GA-BP algorithm

. In-situ stress is the basis for designing mine roadway supports. Firstly, based on the GA-BP algorithm, establish a numerical analysis model, apply orthogonal tests, to establish the relationships between in-situ stress and lateral pressure coefficient, different rock parameters. Then, the optimization model is built by setting the sum of squares difference between measured and calculated in-situ stresses as optimization targets. Finally, using the model to solve the in-situ stress. Results show that the relative error between GA-BP algorithm inversion results and measured values is 2.9% averagely, while the relative error between BP algorithm inversion results and measured values is 4.4% averagely. Inversion methods can provide reference for similar mine in-situ stress inversion.


Introduction
The in-situ stress acts on mine rock distortion and damage fundamentally [1], its magnitude and distribution have a great influence on mine exploit, channel design and support parameters [2][3][4].The borehole stress relief method could measure in-situ stress, but the actual results are inferior in terms of dispersion and reflecting local insitu stress only due to impacts of site, funding and testing techniques [5].
Scholars have done lots of research on nonlinear optimization algorithms for in-situ stress inversion.Yang [6] et al. obtained in-situ stress field in complex geological bodies using numerical analysis and genetic programming algorithm.Meng Wei [7] et al. took geothermal temperature into account in tress inversion, obtained in-situ stress of the geological body.Zhao Chen [8] et al. improved lateral pressure coefficient method by considering factors like strata stripping, rock mechanical character, and faults.
Analysis shows that, the in-situ stress inversion has strong dependence on the accuracy of measurement points.In this paper, Genetic Algorithm (GA) and BP neural network are used to invert the in-situ stress in coal mine.

Study of in-situ stress inversion method 2.1 Measured in-situ stress acquisition
During in-situ stress measurement, points should lay out in stable rock layers of appropriate thickness, avoid interfering with tunnel construction or other production processes.
Actual measurements of in-situ stress get three main stress magnitudes, azimuth and dip angles.The data with higher dispersion and errors will be cut out to prepare for inversion.

Creation of in-situ stress influence function
In-situ stress consists of self-gravity and geological movement of the rock mass.The tectonic stress is related to rock properties and geological tectonic.This paper mainly consider the self-weight stress and structural stress.
For lithology, the elastic modulus E and Poisson's ratio μ are regarded as inversion objectives, and rock masses divided into n zones to discuss separately.
In a block dominated by a self-weight stress field, the vertical stress at any depth H below the surface is equal to the gravity of the overlying rock per unit area [9].
Where, σ z vertical stress, MPa; γ i the weight of the i th layer of rock, kNꞏm -3 ; H i the thickness of the i th layer of rock, m.
Therefore, the rock weight γ is chosen as one of the insitu stress inversion factors.
Tectonic stress field is controlled by horizontal tectonic motion.In-situ stress field changed by considering ground uplifting by tectonic movement and denudation.Thus, the lateral pressure coefficient is set as the inverse factor.
Establish in-situ stress inversion objective function as： Where, σ k the k th principal stress, the k th principal stress function.Analysis shows that basic ideas of in-situ stress inversion are concluded as follows: based on easy-to-get k ꞏ f()

GA-BP algorithm inversion analysis
BP neural networks were proposed by Rumelhart, which training multilayer feedforward networks by error back propagation [10], has merits of high nonlinearity, robustness and parallel processing capability.
Based on the literature [11], the output equation of each node of the hidden layer is calculated: Calculate the formula for each node of the output layer: According to the study, the excitation function is determined Sigmoid function.
Output layer node weight adjustment formula: Put the learning rate of stochastic gradient descent as η(0.1~0.
Make the implied layer signal error .
Genetic algorithms (GA) achieve self-adaptive search for optimal solutions by simulating selection, crossover, and mutation actions in biological genetic and evolutionary [12].The basic components of a genetic algorithm can be defined as: Where C individual coding method, E individual fitness evaluation function, P 0 initial population size, M population size,  selection operator,  crossover operator,  variation operator, S genetic algorithm termination condition.
GA algorithm operates on the threshold, weights of BP neural network layers to obtain the optimal solution and then use it as the new weight threshold of BP neural network to complete optimization.The GA-BP neural network model flow chart is as follows.

Instance Analysis
In order to obtain the coincidence of inversion of in-situ stress using GA-BP algorithm, this paper takes the threemining area of a mine as an example for analysis.
The average thickness of loose layer in the three mining area is 224m, the average thickness of bedrock is 60.3m, and the maximum mining depth has reached 800m; the dip angle of coal seam is 8°~18°, the average dip angle is 13°; the coal thickness is 3.7~5.1m,the average coal thickness is 4.4m; to the north is the trackway of the three-mining area and the working face to be mined, to the south is the fault YF16 and 3303 working face mining void area, to the west is the 4# magmatic rock engulfment area, and to the east is the three-mining area tape downhill.The roadway deformation is serious during 3301 working face chute boring, the coal and rock is identified to have medium impact tendency, the threat of impact power disaster is high.

In-situ stress measurement
In order to optimize the design of underground roadway support and scientific prevention of rock burst, the research group carried out in-situ stress measurement.
K1 locates in the upper track lane of -534 three-mining area, with less lane lay-out at same level.k2 locates in -740 three-mining area lower track road, belongs to deep roadway, which is affected little by mining.K3 locates in -602 five-mining area track downhill refuge, without mining influence.The relevant parameters of the boreholes are shown in Tab.1, the stress relief curves and cores are shown in Fig. 2, the measured results are shown in Tab.2.

Establishment of mining area influence function
To obtain training and test samples, numerical analysis models were established and in-situ stress inversion analysis was carried out based on actual measurement data, shown in Figure 3. .Clarify the value of the lateral pressure coefficient in this mining area is 0.6~2.3.To get training samples, every set of parameters in Tab. 4 was brought into model and FLAC applied for calculation to get 36 sets of principal stresses for 3 measurement points.Taking parameters as input and corresponds to the principal stresses as output, some training samples corresponding to the orthogonal analysis calculation scheme are shown in Tab. 5.

Network learning training.
In this paper, a two-layer BP neural network model is used, with 10 neurons in the input layer, 9 neurons in the output layer, 1 implicit layer, 21 nodes in the implicit layer selected by experience and trial-and-error method, and 429 thresholds for the network connection weights.a flexible BP algorithm is chosen, and the maximum number of network iterations is set to 1000 and the target fit difference is 0.001.
Genetic algorithm optimization weight threshold parameters are set as follows: population size 50, selection operator 0.08, crossover probability 0.4, variation probability 0.1, and maximum genetic generation 100 generations.The neural network is floating-point encoded with different inter-layer connection weights and implied layer thresholds.Random traversal sampling is used for the choice operator and advanced recombination operator is used for the crossover operator.
The BP and GA-BP algorithms were trained for 36 sets of samples respectively, to make the results representative, divided into training set (30 sets) and test set (6 sets), each set performed 20 times of network training, and the results were taken for comparison with in-situ stress actual data.
Comparing R 2 for 20 training sessions of GA-BP and BP, the R 2 of GA-BP model is 0.9778 and BP model is 0.8668.It can be seen that GA optimizes BP's initial weights and thresholds, which improves the network convergence success rate and certain extent.So the GA-BP model is significantly better than the BP model.

Error analysis and algorithm comparison of inversion results.
To verify the reliable of results, Tab.6 shows error analysis of measured in-situ stresses with GA-BP, BP algorithm inversion values.Fig. 4 shows comparison of relative errors between GA-BP and BP.Evidently, relative errors between three principal stresses obtained by inversion using GA-BP and measured principal stresses ranged from 0.1%~6.3%, the relative errors of BP ranged from 3.4%~9.7%.The mean relative error of BP algorithm is 0.044 and the MSE is 0.720, while the mean relative error of the GA-BP algorithm is 0.029 and the MSE is 0.431.The mean squared error of the GA-BP algorithm is smaller than BP algorithm, which show that the GA-BP neural network is better than the BP.The inversion results of GA-BP algorithm are close to measured values, which has a better agreement.

Conclusion
The inversion parameters selected based on the actual works , with reasonable classification of rock, considering mixed parameters of lateral pressure coefficient, capacity, elastic modulus and Poisson's ratio, to get more approximate inversion results.
The three-dimensional fast Lagrangian method is used to calculate the sample structure of the algorithm, and the orthogonal test design scheme is used to simulate the engineering practice more reasonably and reduce the numerical simulation conditions.
The GA-BP algorithm is used to invert the in-situ stress of the mine.Combining the self-learning and adaptive characteristics of the neural network with the global parallel search method of the genetic algorithm, the distribution characteristics of the underground stress field can be simulated efficiently and truly, which plays an important role in the design and construction of coal mine engineering and disaster prevention.

Figure 3 .
Figure 3. Numerical analysis model.Considering that there are obvious differences in mechanical properties of each layer, the volumetric weight, elastic modulus and Poisson's ratio of the overlying loose layer, bedrock layer and coal seam are indicated by ; ;.Clarify the value of the lateral pressure coefficient in this mining area is 0.6~2.3.

Figure 4 .
Figure 4. Comparison of relative error between GA-BP, BP algorithm and actual measured values.

Table 2 .
Measurement results of in-situ stress.

Table 3 .
Values of rock mechanics parameters in each partition.

Table 4 .
Partial orthogonal analysis calculation scheme of in-situ stress inversion(Input samples).

Table 6 .
Comparison between GA-BP and BP algorithm inversion values and measured values