Procedia Earth and Planetary Science 1 (2009) 536–543
Procedia Earth and Planetary Science www.elsevier.com/locate/procedia
The 6th International Conference on Mining Science & Technology
Application of fuzzy neural network in predicting the risk of rock burst Sun Jiana,b, Wang Lian-guoa,b,*, Zhang Hua-leia,b, Shen Yi-fengb a
State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221008, China b School of Sciences, China University of Mining & Technology, Xuzhou 221116, China
Abstract Rock burst is one of the coal and rock dynamical disasters that must be kept in mind in mining activities. With the increase of mining depth, the risk of rock burst becomes increasingly great. At present, the risk prediction for rock burst mostly is still in the stage of simple statistical study and single factor forecast, making the prediction precision be not a desired one. Using the knowledge of fuzzy mathematics and neural network, we propose a fuzzy neural network risk prediction model for rock burst trained with the improved BP algorithm based on the typical rock burst data. This method is an improvement of comprehensive index judgment and multi-index judgment with fuzzy mathematics. Practical engineering applications in Sanhejian Coal Mines indicate that this method is not only precise and simple, but also intelligent, with the predicted results well agreeing with the practical conditions. Therefore, this method can be applied to the relevant engineering projects with satisfactory results.
Keywords: rock burst; risk prediction; fuzzy mathematics; BP neural network
1. Introduction Rock burst is one of the coal and rock dynamical disasters, which is a serious threat to the safety production in coal mine due to its sudden, instantaneous vibratility, and tremendous destructivity [1-4]. At present, the mechanism of rock burst is still not very clear and precise forecasting rock burst is the precondition of prevention rock burst. The prediction methods of rock burst mainly include the method of experience analogy analysis, drilling bits, underground sound monitoring, micro-seismic monitoring, and water content rate determination and so on [2]. As these risk prediction methods of rock burst are still in the stage of simple statistical study and single factor forecast, we only consider the mining geology conditions and neglect the mining technical conditions, so the predicted results are not satisfactory in a desired precision. With the increase of mining depth, the risk of rock burst becomes increasingly great. How to precisely forecast and effectively prevent the rock burst is one of the important issues studied in the fields of mining and geosciences both at home and abroad [1-3].
* Corresponding author. Tel.: +86-516-83885205; fax: +86-516-83885205. E-mail address:
[email protected].
1878-5220 © 2009 Published by Elsevier B.V. Open access under CC BY-NC-ND license. doi:10.1016/j.proeps.2009.09.085
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In view of the complex nonlinear dynamics system of rock burst characterized by multi-input, multi-disturbance, single-output, the main factors affecting the rock burst risk, both the mining geological conditions and the mining technical conditions, are comprehensively considered. Using the knowledge of fuzzy mathematics and neural network, we propose a fuzzy neural network risk prediction model of rock burst trained with the improved BP algorithm based on the typical rock burst data. This method is an improvement of comprehensive index judgment and multi-index judgment with fuzzy mathematics. Practical engineering applications in Sanhejian Coal Mine indicate that this method is not only precise and simple, but also intelligent, with the predicted results well agreeing with the practical conditions. 2. Fuzzy neural network model 2.1. Effect factors and their fuzzification We selecte 10 factors including mining geological coditions and mining technical conditions as the major effect factors of rock burst after statistical analysis for many field data, i.e., mining depth (m), coal seam thickness (m) and its change, dip angle of coal seam (o), coal strength (MPa), roof strength (MPa), complex degree of geological structure, roof management situation, pressure relief situation, and coal noise (shooting). The subordination degree of the fuzzied 10 mainly effect factors with the fuzzy theory are presented as the input of neural network and the four risk grades of rock burst (without rock burst risk, weak rock burst risk, moderate rock burst risk, and strong rock burst risk) as the network output. Table 1 shows the corresponding relation between the effect factors of rock burst risk (10 input vectors) and the four risk grades of rock burst (four output vectors) [1-3]. However, the description of the four risk grades of rock burst given in Table 1 is a fuzzy concept without any strict determination limit [5]. Table 1. Corresponding relation between the effect factors of rock burst and their four risk grades The risk of rock burst Effect factors of rock burst
Without rock burst risk (A)
Weak rock burst risk (B)
Moderate rock burst risk (C)
Strong rock burst risk (D)
(1) Mining depth (m)
≤ 350
350 ~ 500
500 ~ 800
> 800
(2) Coal seam thickness (m)
≤ 0.7
0.7 ~ 1.5
1.5 ~ 2.2
> 2.2
(3) Coal strength (MPa)
≤ 12
12 ~ 16
16 ~ 20
> 20
(4) Roof strength (MPa)
≤ 20
20 ~ 40
40 ~ 60
> 60
(5) Thickness change of coal seam (m)
no
less
big
very big
(6) Dip angle of coal seam (o)
no
less
big
very big
(7) Geological structure
simple
general
complex
very complex
(8) Roof management situation
very good
good
general
bad
(9) Pressure relief situation
very good
good
general
bad
(10) Coal noise(shooting)
no
less
more
very more
Note: The strength refers to the uniaxial compressive strength.
According to the distribution characteristics of each effect factor of rock burst, here, we adopt the function of falling semi-trapezoid distribution and linear triangle distribution as shown in Fig. 1. The subordination degree of the continuous variables given in Table 1 can be directly determined by the formulation method. We established the function relation between the subordination degree and the effect factors of rock burst risk, which is the subordination function of rock burst effect factors. The analytic expression of subordination function for each rock burst risk grade can be expressed as follows (1) ~ (4):
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Membership degree
1
0.75 WA 0.5
WB
0.25
WC WD
0
S1
S4 S2 S3 Measured value x
Fig. 1. Subordination function of the effect factors
1 S −x WA = 2 S 2 − S1 0 0 x − S 2 WC = S3 − S 2 S −x 4 S 4 − S3
x < S1 S1 ≤ x < S2
(1)
x ≥ S2
x < S2
or
x ≥ S4
S 2 ≤ x < S3 S3 ≤ x < S 4
(3)
0 x − S1 WB = S 2 − S1 S −x 3 S3 − S2 0 x − S3 WD = S 4 − S3 1
x < S1
or
x ≥ S3
S1 ≤ x < S2
(2)
S 2 ≤ x < S3
x < S3 S3 ≤ x < S 4
(4)
x ≥ S4
In equations (1)~(4) above, WA , WB , WC and WD are the subordination degree of effect factors of rock burst that belonging to the four risk grades of rock burst, which can be obtained directly by inputting the actual measured value x . Otherwise, Si (i = 1, 2,3, 4) is the grading value of the effect factors of rock burst risk. According to the determination limit of effect factors given in Table 1, the continuous variables effect factors of rock burst risk can be fuzzied by using the fuzzy theory (effect factors (1)~(4) can be directly fuzzied by the determination limit). While the discrete variables effect factors (factors (5)~(10)), the subordination degree can be determined by applying expert evaluation method on the basis of the foundation principles of subordination degree. The calculated results of the subordination degree for the discrete variables (factors (5)~(10) of given in Table 1) is shown in Table 2. 2.2. Improved BP network An artificial neural network is a self-adapting, nonlinear dynamic system which has developed rapidly all over the world since the 1980s and is extensively used in many fields, such as image, speech and voice recognition, complex computations as well as trend prediction [6-13]. A back-propagation (BP) neural network is a kind of multi-layered and feed forward network, and changes the input/output of a group of specimens into a nonlinear optimization problem, which can be considered as mapping from a n-dimensional space to a p-dimensional space. The network model structure of risk prediction of rock burst presented here is shown in Fig. 2, with one input layer, one output layer and one or several hidden layers, each of which includes some neurons. An input signal first arrives at hidden nodes where it is processed by an excitation function and is then transferred into the output layer nodes to
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be processed, obtaining the final output results. In our prediction model, we adopt four-layer BP neural network, with the excitation function for each neural network being selected as a sigmoid function f ( x) = (1 + e− x )−1 [14]. The input layer includes 40 nodes, corresponding to the subordination degree of four different risk grades of 10 mainly effect factors of rock burst. And the output layer includes 4 nodes, corresponding to the four risk grades of without rock burst risk, weak rock burst risk, moderate rock burst risk, and strong rock burst risk. So, the input vector is a 40-dimensional vectors and a 4-dimensional vectors the output vector due to the risk grade of rock burst is regarded as the object vector (see Fig. 2). Table 2. Subordination degrees of the discrete variables of rock burst effect factors Effect factors of rock burst The risk of rock burst
Without rock burst risk (A)
Weak rock burst risk (B)
Moderate rock burst risk (C)
Strong rock burst risk (D)
Thickness change of coal seam (m)
Dip angle change of coal seam (o)
Geological structure
Roof management situation
Pressure relief situation
Coal (shooting)
WA = 0.65
WA = 0.70
WA = 0.70
WA = 0.60
WA = 0.65
WA = 0.60
WB = 0.20
WB = 0.15
WB = 0.15
WB = 0.25
WB = 0.20
WB = 0.25
WC = 0.10
WC = 0.10
WC = 0.10
WC = 0.10
WC = 0.10
WC = 0.10
WD = 0.05
WD = 0.05
WD = 0.05
WD = 0.05
WD = 0.05
WD = 0.05
WA = 0.15
WA = 0.10
WA = 0.10
WA = 0.15
WA = 0.15
WA = 0.15
WB = 0.60
WB = 0.65
WB = 0.65
WB = 0.55
WB = 0.60
WB = 0.55
WC = 0.20
WC = 0.20
WC = 0.20
WC = 0.20
WC = 0.20
WC = 0.20
WD = 0.05
WD = 0.05
WD = 0.05
WD = 0.10
WD = 0.05
WD = 0.10
WA = 0.05
WA = 0.05
WA = 0.05
WA = 0.10
WA = 0.05
WA = 0.10
WB = 0.20
WB = 0.20
WB = 0.20
WB = 0.20
WB = 0.20
WB = 0.20
WC = 0.60
WC = 0.65
WC = 0.65
WC = 0.55
WC = 0.60
WC = 0.55
WD = 0.15
WD = 0.10
WD = 0.10
WD = 0.15
WD = 0.15
WD = 0.15
WA = 0.05
WA = 0.05
WA = 0.05
WA = 0.05
WA = 0.05
WA = 0.05
WB = 0.10
WB = 0.10
WB = 0.10
WB = 0.10
WB = 0.10
WB = 0.10
WC = 0.20
WC = 0.15
WC = 0.15
WC = 0.25
WC = 0.20
WC = 0.25
WD = 0.65
WD = 0.70
WD = 0.70
WD = 0.60
WD = 0.65
WD = 0.60
x1
noise
y1
x2
y2 y3
x39
y4
x40 Input layer
Output layer Hidden layer
Fig. 2. Structure of the presented BP network
Standard BP algorithms are based on the standard steepest descent method, which can modify the gradient of network weights and threshold value by calculating the objective function [15]. The modified iterative process of weight and threshold value of the standard steepest descent method can be expressed by W (k +1) = W (k ) + α D(W (k )) ,
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where W (k ) is the weight, α is the learning rate and D(W (k )) is the gradient of objective function. In actual application, the algorithm of standard BP network is very simple. However, it also has inherent deficiencies, such as all too easily reaching local minimum, and a slow convergence speed. When D(W (k )) is very small, the modified weight is still small which shall lead to the decline of learning efficiency. Here, we adopt the improved fast training algorithm, namely the BP algorithm with variable learning rate [16]. By introducing the coefficient of self-adapting learning rate, the learning rate may change with the gradient of error curved surface, which can efficient pass over the local minimum value, and fast convergence. Therefore, the BP algorithm with variable learning rate can obtain an optimal learning rate in the local area to improve the convergence speed. The modified iterative process of weight and threshold value of the BP algorithm with variable learning rate can be expressed by W (k +1) = W (k ) + α (k ) D(W (k )) , where W (k ) is the vector of network weights and the threshold value, and α (k ) is the variable learning rate, where α (k ) = 2λα (k − 1) and λ = sign[ D(k ) D (k − 1)] . 2.3. Network training Neural network toolbox included in MATLAB has powerful and flexible function, and it does not require complex calculating programming, so we adopt the MATLAB 7.0 neural network toolbox as the training environment, and select 15-typical rock burst data (including both mining geological conditions and mining technical conditions) as the training sample as shown in Table 3. Table 3. Training samples
1 2 3 4 5 6 7 8 9 10
Mini ng dept h 463 552 520 574 558 392 478 452 713 582
Coal seam thickne ss 1.1 1.4 1.3 3.3 1.0 1.5 1.3 1.2 2.3 2.7
11
463
12
595
13
Coal strengt h
Roof stren gth
Thickness change of coal seam
Dip angle change of coal seam
9 6 12 8 13 12 16 17 19 16
12 18 10 16 23 35 40 28 56 48
no less no less less less big less less big
less less big less less big less big big big
6.4
20
40
less
big
1.5
18
52
big
very big
892
3.2
22
60
big
very big
14
982
1.7
26
65
big
big
15
912
2.2
19
68
big
very big
16
958
2.8
20
61
big
very big
Sam ples No.
Geologica l structure simple simple general simple general general simple general complex complex very complex complex Very complex Very complex complex Very complex
Roof managem ent situation very good very good good very good good good good good good bad
Pressure relief situation very good good very good very good good good bad good good bad
good
good
bad
bad
bad
bad
bad
good
good
bad
bad
bad
Coal noise (shooti ng) no no no less more less less less more more very more more Very more Very more more Very more
Risk grade without risk without risk without risk without risk weak risk weak risk weak risk weak risk moderate risk moderate risk moderate risk moderate risk strong risk strong risk strong risk strong risk
Due to the hidden layer nodes and output layer nodes of network model adopting the logarithmic type sigmoid function, the ideal output value of each neuron of output layer only tends to, but not reaches 1 and 0. So we assume that the four risk grades (without rock burst risk, weak rock burst risk, moderate rock burst risk, and strong rock burst risk) are corresponding to the four different vectors of network output: (0.9,0.1,0.1,0.1)T , (0.1,0.9,0.1,0.1)T , (0.1,0.9,0.1,0.1)T , and (0.1,0.1,0.1,0.9)T respectively.The data is processed by fuzzy theory to establish the BP network model. Under the condition of hidden layer nodes with 12, the error level of the improved BP network can reach the 0.0001 precision requirement, and its convergence curve is also shown in Fig. 3.
S. Jian et al. / Procedia Earth and Planetary Science 1 (2009) 536–543
Error
10
541
0
10
-1
10
-2
Training curve 10
-3
10
-4
objective curve
0
400
1200
800
1600
2000
Iteration times
Fig. 3. Network train convergence curve
3. Example analysis Sanhejian Coal Mine of Xuzhou Mining Group is a new mine that has been mined at the end of the 1980s, which is designed mine with the capacity of 1.2 Mt/a, and now 1.6 Mt/a. Primary mineable coal seam in Sanhejian Coal Mine are Shanxi Formation 7-coal and 9-coal and their buried depth is below -420 m, now the mining depth of Sanhejian Coal Mine reaches below -980 m. With the increase of mining depth, the stress in coal and rock mass becomes increasingly great, and the coal and rock dynamical disasters becomes increasingly great, so the risk of rock burst becomes increasingly frequent. Therefore, rock burst is one of the main dynamical disasters in Sanhejian Coal Mine. Table 4 shows the mining geological coditions and mining technical conditions of part working face of Sanhejian Coal Mine. Table 5 shows the comparison between the practical rock burst conditions and the predicted results of rock burst by the improved BP algorithms. We can know from Table 5 that the forecast results calculated by the fuzzy neural network are quite close to the practical conditions, indicating that this method can be well applied to the relevant engineering with satisfactory results. Table 4. Effect factors of rock burst of Sanhejian Coal Mines
No.
Worki ng face
Ming depth
1 2 3 4 5 6 7 8 9 10
7109 7110 7125 7141 7202 7204 9101 9108 9112 9202
621 625 668 722 784 820 830 836 840 850
Coal seam thickne ss 1.2 1.4 0.8 2.5 1.6 2.4 1.6 0.8 2.6 2.2
Coal stren gth
Roof strengt h
Thickness change of coal seam
Dip angle change of coal seam
Geological structure
13 15 5 24 16 17 82 8 34 28
28 34 13 63 24 72 41 12 65 12
less big no very big big big very big no big very big
less very big no very big less big very big big very big big
complex complex general very complex very complex complex very complex simple complex very complex
Roof managem ent situation general bad good bad good bag general good bad general
Pressure relief situation
Coal noise (shooting)
general general good bad good bad bad very good general general
more very more less very more very more more very more less very more very more
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Table 5. Comparison between predicted results and practical conditions No.
Working face
Predicted risk of rock burst
Actual risk of rock burst
1 2 3 4 5 6 7 8 9 10
7109 working face 7110 working face 7125 working face 7141 working face 7202 working face 7204 working face 9101 working face 9108 working face 9112 working face 9202 working face
moderate rock burst(0.099, 0.098, 0.897, 0.101) moderate rock burst(0.103, 0.099, 0.899, 0.102) weak rock burst(0.098, 0.901, 0.097, 0.101) strong rock burst(0.102, 0.098, 0.097, 0.901) moderate rock burst(0.097, 0.099, 0.899, 0.103) strong rock burst(0.099, 0.098, 0.097, 0.903) strong rock burst(0.102, 0.099, 0.098, 0.899) without rock burst(0.902, 0.098, 0.097, 0.101) strong rock burst(0.099, 0.097, 0.098, 0.903) strong rock burst(0.102, 0.098, 0.097, 0.901)
moderate rock burst moderate rock burst weak rock burst strong rock burst moderate rock burst strong rock burst strong rock burst without rock burst strong rock burst strong rock burst
4. Conclusions In this paper, we propose a fuzzy neural network risk prediction model of rock burst using the knowledge of fuzzy mathematics and neural network. This risk prediction model selects typical rock burst data as the training samples with the improved BP algorithm. This method is an improvement of comprehensive index judgment and multi-index judgment with fuzzy mathematics. Practical engineering applications in Sanhejian Coal Mines indicate that this method is not only precise and simple, but also intelligent, with the predicted results well agreeing with the practical conditions. Therefore, this method can be applied to the relevant engineering projects with satisfactory results.
Acknowledgements Financial support for this work, provided by the National Natural Science Foundation of China (50874103), the Natural Science Foundation of Jiangsu Province (KB2008135) and the National Basic Research Program of China (2006CB202210), as well as by the Qing-lan Project of Jiangsu Province, is gratefully acknowledged.
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