Rockburst Prediction Model Based on Entropy Weight Integrated with Grey Relational BP Neural Network

A rockburst prediction model of the entropy weight grey relational backpropagation (BP) neural network is developed.-emodel needs to select the evaluation factors according to the engineering practice and establish the sample library. -e entropy weight method is used to calculate the objective weight of the characteristic factors, and the similarity between the samples is calculated by the combination of grey relational theory and the entropy method. -e training sample of the BP neural network is selected by threshold determination. Finally, we use the trained neural network to estimate the rockburst intensity grade of samples to be tested. -is model is applied to the rockburst prediction of Qamchiq tunnel project, and the prediction results are in good agreement with the actual conditions of the subsequent construction, thus verifying the feasibility and effectiveness of themodel in the rockburst prediction.


Introduction
e increase of cover depth leads to high ground stress and rockburst [1][2][3].Rockburst is sudden damage in tunnel excavation because of the transient release of elastic strain energy.Besides, there are many reasons causing rockburst, and the mechanism of rockburst is complex [4][5][6].At present, scholars have explained rockburst from the view of energy.However, they focus on partial factors.Due to the limitations of data, some studies cannot get the important information accurately, i.e., in situ stress, geological structure, and rock mechanics parameters [7][8][9].e complete rockburst analysis and prediction system are limited in engineering field [10][11][12].In the study, the researchers use the help of experimental tunnel to collect data and predict potential rockburst for the constructing tunnel.In order to analyze the large amount of data, the artificial intelligence is employed.
At present, artificial intelligence is widely used to solve nonlinear problems.Backpropagation (BP) neural network, which can learn independently and has good adaptability and antiinterference, has been used to predict the rockburst [13,14].However, the defect of BP neural network is that the sample has a great influence on its accuracy.It is easy to cause the weight threshold calculation to fall into local minimum [15,16].In order to improve the prediction accuracy, genetic algorithm (GA) [17] and particle swarm optimization (PSO) [18] are applied in the BP neural network to optimize the weight threshold in rockburst prediction.
In order to improve the quality of samples, a prediction model of rockburst intensity is proposed in this study.
at is, on the basis of traditional BP neural network, the entropy weight method and grey relational analysis (GRA) are used to optimize the training samples, so as to improve the network generalization accuracy.Further, in the study, the researchers verified the accuracy of this rockburst prediction model through practical engineering application.
Rockburst is influenced by many factors, and the relationship between these factors and rockburst is complicated.It is difficult to find an accurate index to evaluate rockburst.A large amount of field data has proved that there is a certain correlation among the rockbursts [19][20][21].
e rockburst with the same intensity would occur at conditions with similar factors.So, we filter out some similar series from the field data.It is possible to predict rockbursts at other similar conditions.In order to filter these similar data, we can use the grey relational theory to calculate the correlation of series.
e traditional grey relational theory assumes that when the contribution rate of each factor is the same, the weights of each factor would be equal in the calculation of correlation degree [22].In fact, the influence of different factors on the analysis object is quite different.In order to reflect the influence degree of different evaluation factors, the entropy weight method is used to determine the weight of each factor.Compared with the traditional method, the entropy weight method would make the result more objective and real.Furthermore, we use the BP neural network to predict rockburst intensity in other similar conditions.As a tool of nonlinear multivariate decision making, BP neural network can learn the rules of training samples independently and avoid the interference of human factors.To sum up, it is a feasible way to use the entropy weight method combined with GRA to filter out similar series and predict possible rockburst by BP neural network.

Similarity Calculation Method Based on GRA.
e GRA is a systematic analysis method which can describe the relation degree between individuals [23].A grey system means that a system in which part of the information is known and part of the information is unknown.In this system, the attributes of samples expressed are quantified as indexes.We can judge the similarity degree of two samples based on the change trend of these index values.
e GRA method is widely used and convenient.Assume that the system consists of M known series and 1 unknown series and each series has n attribute indexes.So, the unknown series can be expressed as sequence r 0 � {r 0 (k) | k � 1, 2, . .., n}, and the j-th known series can be expressed as sequence r j � {r j (k) | k � 1, 2, . .., n}. e details of using GRA to calculate similarity are presented as follows: Step 1: the dimensions of attribute indexes are not unified; in order to eliminate the influence of dimension, the value of the index is standardized to get its eigenvalue: where r jk ′ is the value of the k-th attribute of the j-th series and max j (r jk ′ ) and min j (r jk ′ ) are the maximum and minimum values of the k-th attribute in all series, respectively.
Step 2: GRA is used to calculate the relation coefficient ξ jk of an attribute between the unknown series r 0 and known series r j : where ρ is the distinguishing coefficient, ρ ∈ [0, 1], and generally, ρ takes 0.5.
Step 3: the similarity degree s j between the unknown series and the j-th known series is calculated: where w k is the weight of each attribute index.It is determined by the entropy weight method.e value of s j reflects the relation degree between known series and unknown series.

Weight Method Based on Information Entropy.
Shannon develops the concept of information entropy to express the randomness [24].e information entropy describes the reliability, importance, and the weight of an influential factor [25].In order to avoid the interference of human factors, we use entropy to weight attributes.e entropy of the k-th attribute can be expressed as where m is the amount of known series.And then, the weight of each attribute can be expressed as

Forecasting Method Based on BP Neural Network. BP neural network, which was proposed by Rumelhart and
McCelland in 1986, is a multilayer feedforward network trained by error backpropagation algorithm.BP neural network is good at finding out the complex relationship between the factors [26].BP neural network includes an input layer, an output layer, and one or more hidden layers.BP algorithm is composed of forwarding propagation and backward propagation.If the output layer gets the expected output and the error reaches the expected value, the learning algorithm is finished.Otherwise, the backpropagation is carried out, and it will continue to output after adjusting the weight thresholds between the layers until the output error meets the condition.e standard 3-layer BP neural network model structure is shown in Figure 1.

Application in Rockburst Prediction
e researchers applied the proposed prediction model to the Qamchiq tunnel project.e sample library was built 2 Advances in Civil Engineering from the rockburst intensity of the earlier excavated tunnel.e similar sample sequence is filtered out by using the GRA method, and then, the BP neural network is used to infer the rockburst intensity grade of the unexcavated tunnel section.Finally, the results of the calculation will be compared with the actual situation to verify the validity of the model.

Overview of Qamchiq Tunnel Project. Located in Batisco,
Namangan Province, the Federal Republic of Uzbekistan, the Qamchiq tunnel crosses the Kurami Mountains and Kuyinid and Sani Salak Sai River valley.Qamchiq tunnel is a superlong and super-deep buried tunnel with an elevation of 1364 m for entry, 1480 m for the exit; the length of the tunnel is 19.268 km, and the maximum buried depth is about 1275 m. e geography and longitudinal profile is presented in Figure 2. e main lithology of the tunnel site is granite, granodiorite, granite porphyry, syenite porphyry, etc. e surrounding rock is integrated and strong.e groundwater in this area mainly consists of bedrock fissure water, structural fault water, and pore water of quaternary loose rock.e maximum runoff modulus of groundwater is 864 m 3 /d•km 2 .
e rockburst is a very serious problem during the construction.And, the Qamchiq tunnel is the key project of Anwa electrified railway project.erefore, it is very necessary to study rockburst prediction in the tunnel site.
e occurrence conditions of rockburst are complex, which are mainly divided into internal causes and external causes.e hard and brittle rock mass under the condition of high geostress accumulates more energy in the geological tectonic movement, and its stress is close to the strength of rock mass, which is the internal cause of rockburst.And, the excavation of the tunnel will disturb the original equilibrium state of surrounding rock, causing the stress redistribution of surrounding rock and the strong stress differentiation of surrounding rock.After the secondary stress concentration reaches the strength of rock mass, the rock mass will collapse and spall. is is the external cause of rockburst.In addition, the development of rock mass structural planes and groundwater will also affect the properties of rock mass energy storage.
Based on the literature investigation and on-the-spot measurement of tunnel, the following indexes are selected to describe a tunnel section [27][28][29][30][31][32][33]: the Russian criterion value C 1 (C 1 � σ θmax /σ C , i.e., the ratio of maximum tangential stress of chamber σ θmax to rock uniaxial compressive strength σ C ), rock brittleness coefficient C 2 (C 2 � σ C /σ t , i.e., ratio of uniaxial compressive strength σ C to uniaxial tensile strength of rock σ t ), the grade of groundwater condition C 3 and rock integrity coefficient C 4 (Kv value).e above indexes reflect the different attributes of the tunnel section, respectively.C 1 reflects the characteristics of the secondary stress field in the chamber, which is calculated by numerical simulation based on the initial geostress data.C 2 reflects the hardness and brittleness degree of rocks.C 3 reflects the hydrogeological characteristics of the tunnel site, and C 4 reflects the development of the structural plane of the surrounding rock.C 3 , the grade of groundwater condition, is evaluated according to the results of a site investigation in tunnel site, and its quantitative results are shown in Table 1.e grade of groundwater condition is negatively correlated with rockburst intensity.When the other conditions are the same, the higher the grade of the groundwater condition, the lower the rockburst intensity.
e rockburst intensity of Qamchiq tunnel was described in four grades: no rockburst (0 grade), slight (1 grade), moderate (2 grade), and severe (3 grade) rockburst.No rockburst means no loosening, breaking of rockburst, or the phenomenon of silent emission.e other main characteristics of the 3 kinds of rockburst are detailed in document [34].
During the tunnel construction, 20 groups of rockburst data were obtained from the tunnel which was constructed earlier.e values of the indexes of the tunnel section are shown in Table 2.

Calculation of the Weight of Index.
e index values are standardized according to formula (1), and then, the weights of each feature attribute are calculated according to formulae (4) and ( 5). e results are shown in Table 3.

Calculation of the Similarity Degree of Series.
Taking the unexcavated tunnel section MK41 + 425 as an example to show the process of forecasting with this model in detail, the index values of the section are as follows: C 1 is 0.223, C 2 is 8.2, C 3 is 2, and C 4 is 0.75.en, GRA is used to calculate the similarity between the unknown series and known series 1∼20.e similarity degree is calculated by using formulae (2) and ( 3). e results are shown in Table 4.
As mentioned earlier, the prediction accuracy of BP neural network depends largely on the selection of training samples.If the sample size is too large, the calculation of BP neural network will be trapped in a local minimum, resulting in slow convergence and poor network quality.If the sample size is too small, it cannot fully reflect the impact of indexes on research objective.erefore, we can consider using fewer high-quality training samples for good model training and finally achieve a higher network generalization accuracy.In this project, the threshold of similarity degree is 0.73 to select a series of BP neural network training samples, which can ensure the fewer number and the high quality of selected samples.e numbers of the selected series are 1, 4, 10, 14, 15, and 20.

Input layer
Hidden layer Output layer Advances in Civil Engineering

Simulation Prediction Using BP Neural Network Model.
According to Kosmogorov's theory [35], three-layer feedforward network can approximate any continuous function under the rational conditions, so the network structure of single hidden layer is adopted in this model, which is divided into three layers: a hidden layer, an input layer, and an output layer.e number of hidden layer nodes can be determined by the following empirical formula [36]: where n is the number of input layer nodes.When the number of input layer node takes 4, the number of hidden layers is 9 by formula (6).Using the neural network toolbox function in MATLAB R2016a to train and simulate the network, the BP neural network model is constructed as shown in Figure 3.
In terms of parameter settings, the premnmx function is used to normalize input data, Tansig activation function is used in the process from the input layer to hidden layer, Pureline activation function is used in the process from hidden layer to the output layer, and traingdm function with variable rate gradient descent is used for network training.
e initial learning rate is set to 0.01, the training step size is set to 15000, and the global error threshold is set as 1 × 10 −5 .For the output layer data, the rockburst grade is expressed by means of unit vector: no rockburst is (1, 0, 0, 0), slight rockburst is (0, 1, 0, 0), medium rockburst is (0, 0, 1, 0), and strong rockburst is (0, 0, 0, 1).Series 1, series 4, series 10, series 14, series 15, and series 20 selected by the GRA method are used as training samples.e variation of global error in the training process is shown in Figure 4.It can be seen from the graph that the neural network achieves convergence after 8637 iterations.
e index value of MK41 + 425 tunnel section is input and predicted by the network trained.e result is (0.000, 0.001, 0.999, −0.014).e output data of this section is consistent with the results of 2-grade rockburst.
e prediction results determined that the MK41 + 425 tunnel section is grade 2 rockburst.
Referring to the above calculation process of MK41 + 425 tunnel section, we use entropy weight grey relational BP neural network model and traditional BP neural network  model to predict the rockburst intensity grade of the tunnel, respectively, and verify and compare the prediction accuracy of the two methods through follow-up construction.en, the prediction accuracy of the two methods is compared with the actual situation of subsequent construction.e predicted results corresponding to typical sections of rockburst in actual situations are shown in Table 5. e variation of global error of traditional BP network in the training process is also shown in Figure 5.It can be seen from the graph that the traditional BP network achieves convergence after 28341 iterations.e traditional BP neural network model picks all the 20 groups of rockburst data in the training process without selection.So, it achieves a slower convergence than entropy weight grey relational BP neural network model.
Table 5 shows that the accuracy rate of entropy weight grey relational BP neural network model is 90% while the traditional BP neural network model is only 70%.So, the entropy weight grey relational BP neural network model is more effective than the traditional BP neural network model.It confirms that the filtered high-quality samples can improve the generalization accuracy of BP neural network [37,38].Moreover, the prediction results of this model are in good agreement with the actual situation, which basically meets the accuracy requirement of rockburst prediction.A few of the predicted results deviate from the actual situation, which may be due to the complexity and diversity of rockburst genesis in the tunnel site [39,40].Besides the four selected indexes, the occurrence of rockburst may also be related to the construction situation, the special structure of the tunnel section, and other reasons, which leads to the deviation between the actual rockburst situation and the law presented by the sample.It shows that the prediction of rockburst should be combined with the monitoring of the construction site.It is necessary to know the dynamic trend of rockburst in time and then formulate corresponding prevention measures [41][42][43][44], so as to minimize the loss caused by rockburst.

Figure 1 :
Figure 1: Schematic diagram of BP neural network model.

Figure 2 :
Figure 2: Geography and longitudinal profile of the Qamchiq tunnel.

Table 1 :
Grade of groundwater condition.

Table 2 :
Index information in the sample library.

Table 3 :
Entropy weight calculation results.

Table 4 :
Similarity degree calculation results.Series Similarity degree Series Similarity degree Series Similarity degree Series Similarity degree Series Similarity degree ) e entropy weight grey relational BP neural network model is applied to rockburst prediction for the first time, which provides a new idea and method for tunnel rockburst prediction.(2) Compared with the traditional BP neural network model, the accuracy of the prediction results of entropy weight grey relational BP neural network model is obviously improved, which confirms that the filtered high-quality samples can effectively improve the generalization accuracy of BP neural network.e whole prediction process is not disturbed by external subjective factors.(3) e prediction results of the entropy weight grey relational BP neural network model are in good agreement with the actual situation.It met the requirements of rockburst prediction accuracy.After actual engineering verification, the model can be used as a prediction method for rockburst intensity grade.

Table 5 :
Comparison between simulation prediction results and the actual situation.