Predicting Tunnel Squeezing Using the SVM-BP Combination Model 1

Rock squeezing has a large influence on tunnel construction safety; thus, when designing 11 and constructing tunnels it is highly important to use a reliable method for predicting tunnel squeezing 12 from incomplete data. In this study, a combination SVM-BP (support vector machine-back-propagation) 13 model is proposed to classify the deformation caused by surrounding rock squeezing. We designed 14 different characteristic parameters and three types of classifiers (an SVM model, a BP model, and the 15 proposed SVM-BP model) for the tunnel-squeezing prediction experiments and analysed the accuracy 16 of predictions by different models and the influences of characteristic parameters on the prediction 17 results. In contrast to other prediction methods, the proposed SVM-BP model is verified to be reliable. 18 The results show that four characteristics: tunnel diameter (D), tunnel buried depth (H), rock quality 19 index (Q) and support stiffness (K) reflect the effect of rock squeezing sufficiently for classification. 20 The SVM-BP model combines the advantages of both an SVM and a BP neural network. It possesses 21 flexible nonlinear modelling ability and the ability to perform parallel processing of large-scale 22 information. Therefore, the SVM-BP model achieves better classification performance than do the 23 2 SVM or BP models separately. Moreover, coupling D, H, and K has a significant impact on the 24 predicted results of tunnel squeezing. 25


Introduction 29
Tunnel-surrounding rock squeezing is a deformation based on a space-time relationship that usually 30 occurs in soft rock surrounding tunnels at large buried depths. Rock squeezing has a large impact on 31 the tunnel construction safety (Wang, 2020). The negative consequences of tunnel squeezing have been 32 reported repeatedly since it was first discovered during the construction of the Simplon Tunnel in 33 Switzerland (Yassaghi and Salari-Rad, 2005). Tunnel squeezing usually causes construction delays, 34 budget overruns, shield blockage and even possibly results in tunnel instability as well as casualties 35 (Sun, et al. 2018). Therefore, when designing and constructing tunnels it is very important to adopt a 36 reliable method for predicting rock squeezing surrounding the tunnel.

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However, the prediction ability of combination models based on machine learning still needs further 62 exploration.

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Among many machine learning methods, SVMs have strong generalization abilities and flexible 64 nonlinear modelling ability, applying to solving small sample, high dimensional and nonlinear 65 problems. Nevertheless , the SVM classifier is a binary classifier that cannot provide the posterior 66 probability for a given pattern and can lead to results with extremely poor accuracy (Shafiei, et al. 2012; 67 ability. The output of the model can be changed by altering the weight and threshold value of the model.

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However, the structure of the BP neural network is complex and changeable, and the gradient descent 71 method can cause the results to fall easily into a local minimum. Therefore, the BP neural network has 72 limited ability to solve small-sample problems (Ding, et al. 2011;Jin, et al. 2000). Thus, it seems to be 73 logical to try to combine the advantages of an SVM and a BP neural network to establish a new 74 combination model that could improve the accuracy of prediction results.

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The goals of this study are to develop a combined model of SVM and BP for large-scale 76 tunnel-squeezing prediction and to verify the robustness of the combined model by comparing it with 77 other machine learning methods. This paper mainly includes the selection process for prediction 78 parameters and statistical analyses, the construction of a prediction model, the analysis of the 79 prediction results, and a conclusion and discussion. During the selection of prediction parameters and 80 statistical analyses, the basis for the selection of surrounding rock parameters is analysed, a database 81 containing surrounding rock sample indexes is established. The data are pre-processed and analysed 82 statistically. In the section on prediction model construction, this paper introduces three different 83 classifiers: SVM, BP, and SVM-BP combination models. In the prediction results analysis, the 84 surrounding rock squeezing is classified and predicted according to the surrounding rock index data.

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The accuracy of the three models is compared, and the prediction results of other methods reported in 86 the literature are compared. The results show the robustness of the SVM-BP combination model.

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Finally, the accuracy of the three models under different combinations of surrounding rock indexes is 88 analysed. The conclusion and discussion section concludes the study and discusses the applicability of 89 5 the three models for rock-squeezing prediction.

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The tunnel parameters and surrounding rock indexes reflect the basic characteristics of the tunnel and 93 surrounding rock, respectively and are the most reliable parameters for predicting tunnel squeezing.

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Based on of a literature review, the previously published methods for predicting tunnel squeezing are 95 summarized, as shown in Table 1. We can clearly see that many scholars have mainly adopted features 96 such as the tunnel buried depth (H), rock quality index (Q), tunnel diameter (D), support stiffness (K), 97 and stress intensity ratio (SSR) as prediction parameters, but these prior studies seldom considered the 98 vertical in situ stress and surrounding rock classification index (GC) based on the BQ system. Some of 99 the above parameters are difficult to adopt as prediction parameters for various reasons, such as the 100 vertical in situ stress and GC, which are often difficult to obtain in the early stages of a project. The

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SSR is often difficult to obtain from engineering; consequently, much of the existing literature omits 102 data regarding the SSR. Therefore, this study adopts four easy-to-obtain parameters (H, Q, D, and K) as 103 input variables to predict tunnel squeezing.

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deformation threshold for squeezing is  = 1% (  is the percentage strain), that is, when  ＞ 1%, 115 the tunnel-surrounding rock will be squeezed. Among the 180 collected data samples, 112 were 116 non-squeezing samples and 68 were squeezing samples. In this paper, the code for the non-squeezing 117 condition is 0 and the code for the squeezing condition is 1.

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To obtain the relationships between the parameters, a parameter interaction matrix was constructed, as 120 shown in Fig. 1(a). The graph on the diagonal in Fig. 1(a) shows the distribution of each individual 121 parameter (considering both squeezing and non-squeezing cases), while the graph not on the diagonal 122 shows their pairing relationship. Some outliers exist in Fig 1(a) that may lead to a lower classification 123 accuracy. Therefore, it is necessary to detect these outliers and perform denoising. Fig 1(b) shows the 124 correlation between the four parameters (D, H, Q, K) of the tunnel sample case after noise reduction.

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The red lines in the non-diagonal graph below the diagonal are the nonlinear fitting lines for each 126 parameter pair.
are undetermined and satisfy the following conditions (Chang and Lin, 2011): (1)

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Here, , where the sample that satisfies the equation (2) 174

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we can obtain partial derivatives of w and b: 187 (7)

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Step 2: introduce the relaxation variable  , which allows a small number of samples to be incorrectly (9)

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The classification function can be obtained by finding the optimal values for * w and * b : 194 (10)   respectively, and the learning rate  is set. 228 Step 2: Calculate the output value and the error value of the output layer.

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Step 3: Adjust the connection weight and threshold.

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Based on the principle of gradient descent, the relevant parameters are adjusted in the backward 239 direction. The adjustment formula for any related parameter  is (Zhou, 2016): 241 The weights and thresholds are adjusted as follows (Wang and Shi, 2013) [28] : (18)

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Step 4: Repeat the above steps during the training process of the neural network, which can be 247 considered as a process searching for the optimal parameter solutions-that is, minimize e by finding a

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However, some studies show that the performance of multi-classifier fusion methods is better than that 265 of single classifiers. For example, (Zhao and Liu, 2020) reported that the advantage of using a 266 combination method involving multiple classifiers is that it results in a more stable performance on 267 different data sets. This advantage is also significant for improving the overall system performance.             Table 3.

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(2) In classifying surrounding rock squeezing, through a comparison of three classifiers, this study 422 24 concludes that the SVM-BP model combines the advantages of an SVM and a BP neural network; and 423 that the combined model has flexible nonlinear modelling and parallel processing capabilities for 424 large-scale data. Thus, the SVM-BP model achieves better classification performances than do the 425 SVM and BP models. Simultaneously, however, the combined model may also reflect the shortcomings 426 of both because its effect is not good on some classification problems. This aspect of the results is 427 worth further study and mining.

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(3) In this study, three classifiers (SVM, BP, SVM-BP) were used to classify tunnel-surrounding rock 429 squeezing. Because this is a two classification problem, the accuracy of all three tested classifiers is 430 high. At present, most of the methods classify their results into two categories; however, in the future,

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predicting the probability of tunnel-surrounding rock squeezing has more practical significance.

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(4) By combining different characteristic parameters and using different models to classify the 433 surrounding rock squeezing, it can be concluded that the coupling of D, H and K has a large influence 434 on the prediction of surrounding rock squeezing under different models.

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(5) In future work, we plan to further study how to select the optimal feature subset by using 436 optimization techniques to improve the performance of multi-classifier combinations.

Conflicts of Interest 438
The authors declare that there are no conflict of interest.