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Intelligent prediction of surrounding rock deformation of shallow buried highway tunnel and its engineering application
Tunnelling and Underground Space Technology 90 (2019) 1–11
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Intelligent prediction of surrounding rock deformation of shallow buried highway tunnel and its engineering application
T
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Shaoshuai Shi , Ruijie Zhao, Shucai Li, Xiaokun Xie, Liping Li, Zongqing Zhou1, Hongliang Liu Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China School of Qilu Transportation, Shandong University, Jinan 250061, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Shallow tunnel Support vector machine Information granulation Surrounding rock deformation Intelligent prediction Time series
The potential arch crown settlement is one of the most hazardous factors in shallow-buried tunnel excavations. Therefore, accurate prediction of arch crown settlement range is essential to minimize the possible risk of damage. Considering the time series regression characteristics of deformation of surrounding rock in shallowburied tunnels, the Support Vector Machine (SVM) information granulation method was newly applied in this study for deformation prediction of surrounding rock. First, obtain monitoring data of the tunnel arch crown settlement. Second, transform the data of three arch crown settlement into a triangular fuzzy particle. The three parameters, Low, R, and Up in the fuzzy particle represent the minimum, average and maximum value of the settlement of the arch crown in three days. Then, use the SVM to predict the Low, R, and Up values of the tunnel arch crown settlement. Finally, the established prediction model of surrounding rock with SVM information granulation method was applied to the Panlongshan tunnel on the line of the Qinglan expressway in China and prediction results agree well with practical situations, which means the method of SVM information granulation used in this study could provide relatively high accuracy when applied to deformation prediction of surrounding rock in shallow-buried tunnels. Meanwhile, the SVM information granulation method is simple, feasible and easy to implement. The presented method has been validated as an effective method of deformation prediction for surrounding rock, which also has good prospects for further engineering applications.
1. Introduction Prediction of deformation for surrounding rock in the tunnel has been a hot issue in the field of geotechnical engineering. The entrance and exit of the highway tunnel are mostly shallow buried section, where the surrounding rock weathering degree is high and the rock is broken, its obvious characteristic is that it can’t form an effective bearing arch, which is easy to collapse or cause a large ground subsidence. The surrounding rock deformation caused by the excavation is obvious, which will cause great influence or damage to the engineering structure and the surrounding environment. It is particularly important to predict the deformation of surrounding rock at the entrance and exit of the tunnel. At present, there are 3 kinds of methods to predict the deformation of the tunnel surrounding rock. They are mathematical model method or empirical formula method (Chou and Bobet, 2002; Janin et al., 2012; Suwansawat and Einstein, 2007), artificial intelligence and numerical simulation algorithm (Chakeri et al., 2011; Fargnoli et al., 2015; Talebinejad et al., 2014). The artificial intelligence algorithm is a hot
topic in recent years, for instance: neural network (Ahangari et al., 2015; Goh et al., 2018; Santos and Celestino, 2008), genetic algorithms, particle swarm optimization (Hasanipanah et al., 2016; Ninić and Meschke, 2015) and support vector machines. Goh and Hefney (2010) demonstrated that by coupling the trained neural network model to a spreadsheet optimization technique, the reliability assessment of the settlement serviceability limit state can be carried out using the firstorder reliability method. An alternate method of maximum ground surface settlement prediction, which is based on integration between wavelet theory and Artificial Neural Network (ANN), or wavelet network, is presented by Pourtaghi and Lotfollahi-Yaghin (2012). Ocak and Seker (2013) focused on surface settlement prediction using three different methods: artificial neural network, support vector machines, and Gaussian processes (GP). The success of the study has decreased the error rate to 13%, 12.8%, and 9%. In Moeinossadat’s et al. (2018) study, adaptive neuro-fuzzy inference system was adopted to predict the maximum surface settlement. The above studies greatly promote the research on deformation
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Corresponding author. E-mail addresses: [email protected] (S. Shi), [email protected] (Z. Zhou). 1 Co-corresponding author. https://doi.org/10.1016/j.tust.2019.04.013 Received 30 July 2018; Received in revised form 27 February 2019; Accepted 14 April 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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applications, so the input variables are nonlinear transformed. The main method is to map the data in the input space Rn into a feature space F through nonlinear mapping.
prediction for surrounding rock. However, the mathematical model method or empirical formula method is relatively simple, not suitable for complex time series, and it is difficult to find suitable mathematical models for different engineering conditions. The numerical simulation method has a high prediction accuracy for the surrounding rock deformation of the tunnel. However, in the process of modeling, it is necessary to consider the complex geological conditions, such as fault, joint fracture, groundwater and so on, so it is difficult to establish the model which accords with the actual situation of the tunnel. Artificial intelligence method has good regression prediction ability for nonlinear system, but it is easy to appear in the situation of undertraining or overtraining, and fall into the local optimal predicament, and the generalization ability is poor. Regression prediction analysis of complex time series has some limitations. Therefore, the generalization ability should be considered in the building of time series prediction model. In the present study, the information granulation time series regression model based on support vector machine is proposed. SVM has good generalization ability, obey the principle of structural risk minimization rather than empirical risk minimization. The SVM information granulation algorithm is mainly used to predict the stock opening index, urban water consumption and other fields, rarely used in engineering projects. In this paper, SVM information granulation is applied to tunnel surrounding rock deformation prediction. Compared with the tunnel surrounding rock deformation regression prediction model in the past can only predict a single numerical value, SVM-based information granulation algorithm can predict the change trend and space of time series. Which can not only improve the prediction of the time series regression of tunnel surrounding rock deformation, but also make an accurate prediction of the fluctuation range of the time series regression of the surrounding rock deformation. The established model was applied to Panlongshan tunnel on the line of Qinglan expressway in China. The study results show that the evaluation results agree well with practical situations. The presented method and selected results could provide scientific evidence for deformation prediction for surrounding rock in shallow buried tunnels.
n ⎧ ϕ: R → F ⎨ ⎩ x → ϕ (x )
After mapping, the classification hyperplane becomes:
y = sign [(w·Φ (x )) + b]
yi sign [w·Φ (x ) + b] ⩾ 1 (i = 1, 2, ⋯, n)
min n, b
1 ∥w∥2 2
(7)
When the feature map is unknown, Eq. (4) cannot be solved directly, but it can be solved for the implicit feature mapping. For the quadratic programming problem, every constraint condition of Eq. (3) introduces Lagrange multiplier αi (αi ⩾ 0, i = 1, 2, ⋯, n) , and the Lagrange function is obtained as follows:
L (w, b, α ) =
1 ||w||2 − 2
n
∑ αi yi [(w·xi) + b − 1]
(8)
i=1
Tasks become αi maximization and w, b minimization. At its best, ac∂L ∂L cording to K-T condition, there are ∂b = 0 and ∂w = 0 . n ⎧ i = 1 αi yi = 0 n ⎨ ⎩ w = i = 1 αi yi Φ (x )
(9)
The dual quadratic programming problems can be obtained by substituting the Eq. (7) into the Eq. (4): n
n
1
⎧ max∑i = 1 αi − 2 ∑i, j = 1 αi αj yi yj (Φ (x i )·Φ (xj )) ⎪ s. t . αi ⩾ 0, i = 1, 2, ⋯, n ⎨ n ⎪∑i = 1 αi yi = 0 ⎩
Support vector machine, proposed by Cortes and Vapnik (1995), can be utilized to pattern classification and non-linear regression. The theoretical basis of SVM is statistical learning theory, more precisely, the approximate realization of structural risk minimization. The main idea is to establish a classification hyperplane as the decision surface, which maximizes the isolation margin between positive and negative examples. The principle is to learn the generalized error rate of the machine on the test data, bounded by the sum of the training error rate and a term of Vapnik-Chervonenkis dimension. In separable mode, the value of the SVM in the previous term is zero and the second term is minimized. Therefore, SVM has good generalization performance (Xue and Xiao, 2017). Suppose the training set is as follows:
(10)
From Eq. (10) we know that Φ(x i ) only interacts with the inner product. According to the Mercer theorem, the function k(u,v) satisfying the Mercer condition is called Mercer kernel function. Then there is a space H and a mapping Φ: Rn → H , then k(u,v) = Φ(u)·Φ(v ) . So, with kernel techniques, the inner product in eigenspace can be calculated directly from the data in input space. The coefficients αi (i = 1, 2, ⋯, n ) can be obtained by solving the dual problem. The vector xi corresponding to αi ≠ 0 is called the support vector, so a non-linear decision function is as follows: n
n
f (x ) = sign [ ∑ αi yi (Φ (x )·Φ (x i )) + b] = sign [ ∑ αi yi k (x , x i )+b] i=1
(1)
i=1
(11)
When dealing with the noise data, the slack variable ξi is introduced to relax the constraint:
Rn
where X is the input space vector, X ∈ , n is the number of training samples; Y is the model space, Y = {+1, −1} Separating hyperplane:
yi (w·Φ (x i ) + b) ⩾ 1 − ξi ξi ⩾ 0 i = 1, 2, ⋯, n
(12)
Eq. (12) allow a certain classification error. The sum of the upper bounds minimizing trial Eq. (7) and empirical error is as follows:
(2)
n
where w is the weight vector, x is the input vector, b is the threshold. For separable hyperplane classifiers, the classification conditions for no training errors are as follows:
yi [(w·xi ) + b] ⩾ 1 (i = 1, 2, ⋯, n)
(6)
The learning goal is to find the scalar b and w ∈ F to satisfy the expected minimum risk. According to VC theory, an upper bound of model complexity and minimization of empirical risk can be expressed by the following quadratic programming problem.
2.1. Support vector machine and algorithm structure
y = sign [(w· x ) + b]
(5)
The constraints of error-free classification in feature space are as follows:
2. Principle of support vector machine information granulation
(x1, y1), (x2 , y2 ), ⋯, (x n , yn ) ∈ X × Y
(4)
min n, b
1 ∥w∥2 + C ∑ ξi 2 i=1
(13)
where C is the penalty parameter, which determines a trade-off between model complexity and empirical error. This leads to dual problems:
(3)
The use of linear function classification is often not ideal in practical 2
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granulation problem for the first time in 1979. And a proposition of data granulation was given:
g ≜ (x is G ) is λ
where x is the variable of the value in the domain U; G is a fuzzy subset of U, which is characterized by the membership function μG ; λ represents the probability. It is generally assumed that U is a real set R (Rn ), G is a convex fuzzy subset of U, and λ is a fuzzy subset of unit intervals (Yin et al.,2017). Fuzzy information granule is a kind of information granule expressed in the form of fuzzy set, and fuzzy granulation of time series is carried out by fuzzy set method. It is divided into two steps: Dividing window and fuzzing. Dividing window is dividing the time series into several sub-sequences as operational window. Fuzzing is to fuzzy every window, and the fuzzy sets are called fuzzy information granulations. The combination of these two generalized modes is fuzzy information granulation, called f-granulation. In f-granulation, the most important thing is the process of fuzzification, that is, to build a reasonable fuzzy set in the given window, so that it can replace the data in the original window and represent the relevant information that people are concerned about. For a given time series, the problem of single window is considered, that is, the whole time series sequence X is considered as a window for fuzzification. The task of fuzzification is to establish a fuzzy particle P on X. That is, a fuzzy concept G, which can reasonably describe X , once G is determined, the fuzzy particle P is also determined:
Fig. 1. Support vector machine algorithm structure. n
1
n
⎧ max∑i = 1 αi − 2 ∑i, j = 1 αi αj yi yj (Φ (xi )·Φ (xj )) ⎪ s. t . 0 ⩽ α i ⩽ C, i = 1, 2, ⋯, n ⎨ n ⎪∑i = 1 αi yi = 0 ⎩
(14)
In general, the algorithm structure of SVM is shown in Fig. 1 Where K is a kernel function with the following types: Linear kernel function:
K (x , x i ) = xT x i
(15)
Polynomial kernel function:
K (x , x i ) = (γxT x i + r ) p , γ > 0
(16)
Radial basis kernel function:
K (x , x i ) = exp(−γ ∥x − x i ∥2 ), γ > 0
(17)
g ≜ x is G
Two-layer perceptron kernel function:
K (x , x i ) = tanh(γxT x i + r )
(19)
(18)
(20)
Therefore, the fuzzification process is essentially the process of determining a function A. A is the membership function of the fuzzy concept G (A = μG ). Generally, the basic form of the fuzzy concept is first determined when granulating. Then the specific membership function A is determined. The commonly used fuzzy particles are parabolic, Gaussian, trapezoid, triangular and other basic models. Due to simple formulas and computational efficiency, the study uses triangular fuzzy particles, the membership function is as follows, a case study is shown in Fig. 2.
In order to find the global optimal value instead of the local optimal value, and to ensure the good generalization ability of the unknown sample, a two-layer perceptron kernel function is used in this paper. 2.2. Information granulation basic knowledge and fuzzy model Information granulation mainly studies the formation, representation, thickness, semantic interpretation of information granules. The main aspects are word calculation and granulation calculation. The information granule divides the object set mainly through its function, similarity, function similarity and indistinguishability (Su et al., 2006). Information granulation, first proposed by Professor Zadeh (1968), is to decompose a whole into parts for research, each part is an information granule. These elements are combined because of indistinguishable, close to, or similar in function. Information granules are the collection of these elements (Aggarwal, 2017). There are three main models of information granulation: a model based on rough set theory, a model based on fuzzy set theory and a model based on quotient space theory. Fuzzy set theory describes the granularity by the degree of membership of the object with respect to the set. Which belongs to the same membership relationship of different objects. It focuses on the fuzziness of the set and emphasizes the degree of membership. The rough set theory describes the granularity by a set of up-and-down approximation of an available knowledge base, which reflects the set relationship of the objects in different classes, which focuses on the unresolvable degree between objects in the set and emphasizes the classification. The quotient space theory does not study the particle metrics because it discusses the change law of the particles from a macro perspective. Compared with rough set theory and quotient space theory, fuzzy set theory has a stronger function in optimizing, integrating and dealing with the uncertainty and incompleteness of knowledge. In this paper, the fuzziness of the set and its membership degree are studied, so the model based on fuzzy set theory is adopted. The model was proposed by the famous American scientist Professor Zadeh in the 1960s and discussed the fuzzy information
A (x , a, m , b) =
⎧ x − a 0, x < a ⎪ ,a ⩽x ⩽m m−a ⎨ ⎪ ⎩
b−x , b−m
m
0, x > b
(21)
Fig. 2. An example of membership function of a triangular fuzzy particle. 3
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Fig. 3. Panlongshan tunnel and geographical position of Tai’an city.
3. Engineering application
strike and the hole axis oblique line, there is no fracture structure in the entrance, the joints and fractures are developed, and the local dissolution fractures are developed. Drilling reveals that the local development of small-scale filling caverns, dissolution fractures and erosion of the pores see muddy filling, poor stability. The rock uniaxial saturated compressive strength is 13.2–18.6 MPa, rock mass basic quality value is 195, rock longitudinal wave velocity mass is 500(m/s), rock mass classification is V grade. Because of the poor surrounding rock quality of the entrance section, the tunnel entrance section is excavated by Center Cross Diagram (CRD) method.
3.1. Engineering background To further validate the established model, a practical project named the Panlongshan tunnel was selected as the investigated object and investigated with the present method for deformation prediction of surrounding rock. Panlongshan tunnel is located in Tai'an City, Shandong Province, China. The tunnel is 2885 m in length with a bidirectional 6 lanes. The entrance of Panlongshan tunnel is about 100 m, and the entrance and geographical position of the Panlongshan tunnel is shown in Fig. 3. The entrance of the tunnel located at the foot of the mountain with a gentle slope of about 5–12°, and the Quaternary soil thickness varies from 0.40 m to 1.20 m. Engineering geological profile of Panlongshan tunnel is shown in Fig. 4, the YK78+410 tunnel face is shown in Fig. 5, it can be seen that the exposed sections of the entrance section are dominated by Late Cambrian limestone, partially framed thin-layered marls, bedded structure, small strata inclination, rock
3.2. Monitoring data In this paper, the arch crown settlement monitoring data of the YK78+410 section for 75 days is taken as the model sample. Fig. 6 shows the time-dependent curve of arch crown settlement. It can be seen from Fig. 6 that the arch crown settlement data has changed greatly in the first 20 days, and after 20 days, the tunnel arch crown
Fig. 4. Engineering geological profile of Panlongshan tunnel. 4
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Fig. 5. Photo of the tunnel face of YK78+410 section.
change of the arch crown settlement value. 3.4. Parameters optimization The penalty parameter c and the parameter g of kernel function of support vector machine need to be optimized, which can improve the precision of the model (Patwari et al., 2010). The commonly used parameter optimization algorithms are genetic algorithms (Phan et al., 2017), particle swarm optimization (Jia et al., 2017) and grid optimization. Grid optimization algorithm is a practical data search method, which is suitable for searching multi-dimensional arrays in parallel from different growth directions. The grid optimization algorithm traverses all the parameter combinations in the search range and can search for the optimal parameters, so it has the advantage to predict the small data samples. Therefore, the grid optimization algorithm is adopted in this study for parameter optimization. The parameter determination method based on grid optimization algorithm is realized as follows: the original data is randomly divided into two groups, and each subset data is separately used as a verification set, and the remaining K − 1 subset data is used as a training set, so the K models can be obtained. The model sets the selection range and search step size of the penalty parameter c and the kernel function parameter g. According to the cross-validation method, the MeanSquare Error (MSE) of the training set and the MSE of the test set after traversing the combination (c, g) are calculated. Finally, the optimal parameter combination (c, g) is determined under the premise of ensuring the minimum of sum of MSE of training set and test set. Then, the MSE of each group (c, g) value is drawn by contour line, and the contour map of parameter optimization is obtained. As shown in Figs. 9–14, the x axis represents the logarithmic value of c at the base of 2, the y axis represents the logarithmic value of g at the base of 2, and the contour line represents the MSE of c and g. The SVM parameter optimization method is as follows: First, rough optimization, the range of c and g is 2−10 to 210, and the change value of c and g is: 2−10, 2−9, … 210, MSE change interval is 0.1, and the results are shown in Figs. 9, 11, 13. Then, from the rough optimization results, it can be seen that the value range of c can be reduced to 2−2 ∼ 28, and the range of g can be reduced to 2−8 ∼ 22, the change value of c is: 2−2, 2−1.5, … 28, the change value of g is: 2−8, 2−7.5… 22. The parameter selection result shows the change interval of MSE is 0.05, so that the precision of the optimization result is higher of the fine optimization and the change of MSE can be seen more clearly.
Fig. 6. Curve of arch crown settlement of YK78+410 section.
settlement is approximately stable. 3.3. SVM information granulation method and fuzzy granulation Model Objective: Based on the daily arch crown settlement values of the YK78+410 section of Panlongshan Tunnel from February 18, 2018 to May 3, 2018. The original data of each arch crown settlement value is granulated with fuzzy information for 3 days as a window, which is used as training data, predict the variation trend and range space of the arch crown settlement on May 4–6, 2018. In the deformation prediction processes, we assumed that the settlement value of YK78+410 cross-section is time-dependent and time is taken as an independent variable that affects the settlement of the tunnel vault. The algorithm flow chart is shown in Fig. 7. The results of three days of arch crown settlement monitoring data are taken as one information granulation and divided into 25 windows. The result of granulation of the original data is presented in Fig. 8. The Low parameter describes the minimum change of the arch crown settlement value, the R parameter describes the average change of the arch crown settlement value, the Up parameter describes the maximum 5
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Fig. 7. Prediction flowchart based on the model of SVM information granulation method.
3.5. Prediction results and analysis Figs. 15–20 show the fitting result and error histogram of the SVM information granulation of Low, R, Up, from which the following conclusions can be drawn: (1) From a single figure analysis: Low fitted curve for 1–3 days, 7–9 days, R fitted curve for 1–3 days, Up fitted curve for 1–6 days have a larger fitting error. According to the analysis of comparison of each figure, the error of the fitted curve is larger in 1–9 days, especially 1–3 days of excavation of YK78+410 section. The reason is that the arch crown settlement has a large change in the time range within 1–3 days, and there is no support from the training data before, so it is impossible to obtain a more accurate prediction result by SVM training. (2) From Figs. 15–20, it can be seen that the information granulation fitting curves of Low, R, Up are better after 9 days. One reason is that the support of pre-training data, the second is that the time series fluctuation after 9 days is small, so it has good prediction effect.
Fig. 8. Granulation results.
Table 1 shows the comparison between the measured data and the predicted data, and it can be seen from the table that the variation range of the arch crown settlement on May 4, 5 and 6 is accurate, which indicates that the SVM – based information granulating time series regression prediction model has a good prediction effect and can reflect the fluctuation range of the arch crown settlement and has a certain reference value.
The best parameter of low curve is obtained by rough optimization and fine optimization: c = 90.5097, g = 0.015625, the best parameter of the R curve: c = 90.5097, g = 0.015625, the best parameter of the Up curve: c = 181.019, g = 0.0110485. The optimal parameters c and g were used to train the SVM. Then, the arch crown settlement was regressed and predicted, and the comparison chart and the error diagram between the original data and the predicted data were obtained.
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Fig. 9. Rough optimization results of parameters of Low.
4. Conclusions
settlement at the shallow buried section of Panlongshan tunnel, the experimental results show that:
In view of the time series regression of the arch crown settlement in shallow buried tunnels, a prediction model based on SVM information granulation is proposed. Based on the measured data of the arch crown
(1) SVM has a strong learning ability in simulating the regression trend of the time series of the arch crown settlement. Using grid
Fig. 10. Fine optimization results of parameters of Low. 7
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Fig. 11. Rough optimization results of parameters of R.
space of nonlinear system compared with the traditional prediction model. The engineering application in this paper shows that the variation range of arch crown settlement predicted by this model for the next three days in May 4, 5, 6 days is accurate, and has good
optimization algorithm to optimize SVM parameters can avoid the blindness and inefficiency of trial calculation. (2) The time series regression prediction model based on SVM information granulation can predict the change trend and change
Fig. 12. Fine optimization results of parameters of R. 8
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Fig. 13. Rough optimization results of parameters of Up.
Fig. 14. Fine optimization results of parameters of Up. 9
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Fig. 18. Fitting error of R.
Fig. 15. Fitting result of Low.
Fig. 19. Fitting result of Up.
Fig. 16. Fitting error of Low.
Fig. 20. Fitting error of Up.
Fig. 17. Fitting result of R.
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Table 1 Prediction of variation trend and range of YK78+410 section. Date
The actual range of change [Low,R,Up]
Predict the range of change [Low,R,Up]
February 21st–23rd May 1st −3rd May 4th–6th
[6.87,7.50,8.05] [8.98,8.99,9.01] [8.97,8.98,9.00]
[6.057,7.538,7.632] [8.877,8.938,9.013] [8.750,8.893,9.010]
Cortes, C., Vapnik, V., 1995. Support-vector networks. Mach. Learn. 20, 273–297. Chou, W., Bobet, A., 2002. Predictions of ground deformations in shallow tunnels in clay. Tunnel. Undergr. Space Technol. 17 (1), 3–19. Fargnoli, V., Boldini, D., Amorosi, A., 2015. Twin tunnel excavation in coarse grained soils: observations and numerical back-predictions under free field conditions and in presence of a surface structure. Tunnel. Undergr. Space Technol. 49, 454–469. Goh, A.T.C., Hefney, A.M., 2010. Reliability assessment of EPB tunnel-related settlement. Geomech. Eng. 2 (1), 57–69. Goh, A.T.C., Zhang, W., Zhang, Y., Xiao, Y., Xiang, Y., 2018. Determination of earth pressure balance tunnel-related maximum surface settlement: a multivariate adaptive regression splines approach. Bull. Eng. Geol. Environ. 77 (2), 489–500. Hasanipanah, M., Noorian-Bidgoli, M., Jahed Armaghani, D., Khamesi, H., 2016. Feasibility of PSO-ANN model for predicting surface settlement caused by tunneling. Eng. Comput. 32 (4), 705–715. Janin, J., et al., 2012. Settlement monitoring and tunnelling process adaptation—case of South Toulon tunnel. Geotech. Aspect. Undergr. Constr. Soft Ground 205–212. Jia, S., Qian, X., Yuan, X., 2017. Optimal design for dividing wall column using support vector machine and particle swarm optimization. Chem. Eng. Res. Des. 125, 422–432. Moeinossadat, S.R., Ahangari, K., Shahriar, K., 2018. Control of ground settlements caused by EPBS tunneling using an intelligent predictive model. Ind. Geotech. J. 48 (3), 420–429. Ninić, J., Meschke, G., 2015. Model update and real-time steering of tunnel boring machines using simulation-based meta models. Tunnel. Undergr. Space Technol. 45, 138–152. Ocak, I., Seker, S.E., 2013. Calculation of surface settlements caused by EPBM tunneling using artificial neural network, SVM, and Gaussian processes. Environ. Earth Sci. 70 (3), 1263–1276. Patwari, N., Croft, J., Jana, S., Kasera, S.K., 2010. High-rate uncorrelated bit extraction for shared secret key generation from channel measurements. IEEE Trans. Mobile Comput. 9 (1), 17–30. Phan, A.V., Nguyen, M.L., Bui, L.T., 2017. Feature weighting and SVM parameters optimization based on genetic algorithms for classification problems. Appl. Intell. 46 (2), 455–469. Pourtaghi, A., Lotfollahi-Yaghin, M.A., 2012. Wavenet ability assessment in comparison to ANN for predicting the maximum surface settlement caused by tunneling. Tunnel. Undergr. Space Technol. 28, 257–271. Santos, O.J., Celestino, T.B., 2008. Artificial neural networks analysis of São Paulo subway tunnel settlement data. Tunnel. Undergr. Space Technol. 23 (5), 481–491. Su, C., Chen, L., Yih, Y., 2006. Knowledge acquisition through information granulation for imbalanced data. Expert Syst. Appl. 31 (3), 531–541. Suwansawat, S., Einstein, H.H., 2007. Describing settlement troughs over twin tunnels using a superposition technique, 133(4), 445–468. Talebinejad, A., et al., 2014. Investigation of surface and subsurface displacements due to multiple tunnels excavation in urban area. Arab. J. Geosci. 7 (9), 3913–3923. Xue, X., Xiao, M., 2017. Deformation evaluation on surrounding rocks of underground caverns based on PSO-LSSVM. Tunnel. Undergr. Space Technol. 69, 171–181. Yin, S., Jiang, Y., Tian, Y., Kaynak, O., 2017. A data-driven fuzzy information granulation approach for freight volume forecasting. IEEE Trans. Indus. Electron. 64 (2), 1447–1456. Zadeh, L.A., 1968. Fuzzy algorithms. Inform. Control 12 (2), 94–102.
prediction effect. It can reflect the time series fluctuation range of arch crown settlement and has certain reference value. (3) The information granulation time series regression prediction model based on SVM provides a new method for nonlinear time series regression for the arch crown settlement of shallow buried tunnels. This method is also applicable to other fields of timevarying nonlinear systems. Acknowledgements This research was funded by National Natural Science Foundation of China (Grant No. 51609129, 51709159, 51679131), State key laboratory for Mine disaster prevention and control, cultivation base co-built by province and ministry of Shandong university of science and technology (Grant No. MDPC201707, MDPC201802), Shandong postdoctoral innovation project special Foundation (Grant No. 201502025, 201702014), China Postdoctoral Science Foundation (Grant No. 2017T100492, 2017M612273). Declarations of interest None. References Aggarwal, M., 2017. Representation of uncertainty with information and probabilistic information granules. Int. J. Fuzzy Syst. 19 (5), 1617–1634. Ahangari, K., Moeinossadat, S.R., Behnia, D., 2015. Estimation of tunnelling-induced settlement by modern intelligent methods. Soils Foundat. 55 (4), 737–748. Chakeri, H., Hasanpour, R., Hindistan, M.A., Ünver, B., 2011. Analysis of interaction between tunnels in soft ground by 3D numerical modeling. Bull. Eng. Geol. Environ. 70 (3), 439–448.
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Intelligent prediction of surrounding rock deformation of shallow buried highway tunnel and its engineering application
T
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Shaoshuai Shi , Ruijie Zhao, Shucai Li, Xiaokun Xie, Liping Li, Zongqing Zhou1, Hongliang Liu Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China School of Qilu Transportation, Shandong University, Jinan 250061, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Shallow tunnel Support vector machine Information granulation Surrounding rock deformation Intelligent prediction Time series
The potential arch crown settlement is one of the most hazardous factors in shallow-buried tunnel excavations. Therefore, accurate prediction of arch crown settlement range is essential to minimize the possible risk of damage. Considering the time series regression characteristics of deformation of surrounding rock in shallowburied tunnels, the Support Vector Machine (SVM) information granulation method was newly applied in this study for deformation prediction of surrounding rock. First, obtain monitoring data of the tunnel arch crown settlement. Second, transform the data of three arch crown settlement into a triangular fuzzy particle. The three parameters, Low, R, and Up in the fuzzy particle represent the minimum, average and maximum value of the settlement of the arch crown in three days. Then, use the SVM to predict the Low, R, and Up values of the tunnel arch crown settlement. Finally, the established prediction model of surrounding rock with SVM information granulation method was applied to the Panlongshan tunnel on the line of the Qinglan expressway in China and prediction results agree well with practical situations, which means the method of SVM information granulation used in this study could provide relatively high accuracy when applied to deformation prediction of surrounding rock in shallow-buried tunnels. Meanwhile, the SVM information granulation method is simple, feasible and easy to implement. The presented method has been validated as an effective method of deformation prediction for surrounding rock, which also has good prospects for further engineering applications.
1. Introduction Prediction of deformation for surrounding rock in the tunnel has been a hot issue in the field of geotechnical engineering. The entrance and exit of the highway tunnel are mostly shallow buried section, where the surrounding rock weathering degree is high and the rock is broken, its obvious characteristic is that it can’t form an effective bearing arch, which is easy to collapse or cause a large ground subsidence. The surrounding rock deformation caused by the excavation is obvious, which will cause great influence or damage to the engineering structure and the surrounding environment. It is particularly important to predict the deformation of surrounding rock at the entrance and exit of the tunnel. At present, there are 3 kinds of methods to predict the deformation of the tunnel surrounding rock. They are mathematical model method or empirical formula method (Chou and Bobet, 2002; Janin et al., 2012; Suwansawat and Einstein, 2007), artificial intelligence and numerical simulation algorithm (Chakeri et al., 2011; Fargnoli et al., 2015; Talebinejad et al., 2014). The artificial intelligence algorithm is a hot
topic in recent years, for instance: neural network (Ahangari et al., 2015; Goh et al., 2018; Santos and Celestino, 2008), genetic algorithms, particle swarm optimization (Hasanipanah et al., 2016; Ninić and Meschke, 2015) and support vector machines. Goh and Hefney (2010) demonstrated that by coupling the trained neural network model to a spreadsheet optimization technique, the reliability assessment of the settlement serviceability limit state can be carried out using the firstorder reliability method. An alternate method of maximum ground surface settlement prediction, which is based on integration between wavelet theory and Artificial Neural Network (ANN), or wavelet network, is presented by Pourtaghi and Lotfollahi-Yaghin (2012). Ocak and Seker (2013) focused on surface settlement prediction using three different methods: artificial neural network, support vector machines, and Gaussian processes (GP). The success of the study has decreased the error rate to 13%, 12.8%, and 9%. In Moeinossadat’s et al. (2018) study, adaptive neuro-fuzzy inference system was adopted to predict the maximum surface settlement. The above studies greatly promote the research on deformation
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Corresponding author. E-mail addresses: [email protected] (S. Shi), [email protected] (Z. Zhou). 1 Co-corresponding author. https://doi.org/10.1016/j.tust.2019.04.013 Received 30 July 2018; Received in revised form 27 February 2019; Accepted 14 April 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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applications, so the input variables are nonlinear transformed. The main method is to map the data in the input space Rn into a feature space F through nonlinear mapping.
prediction for surrounding rock. However, the mathematical model method or empirical formula method is relatively simple, not suitable for complex time series, and it is difficult to find suitable mathematical models for different engineering conditions. The numerical simulation method has a high prediction accuracy for the surrounding rock deformation of the tunnel. However, in the process of modeling, it is necessary to consider the complex geological conditions, such as fault, joint fracture, groundwater and so on, so it is difficult to establish the model which accords with the actual situation of the tunnel. Artificial intelligence method has good regression prediction ability for nonlinear system, but it is easy to appear in the situation of undertraining or overtraining, and fall into the local optimal predicament, and the generalization ability is poor. Regression prediction analysis of complex time series has some limitations. Therefore, the generalization ability should be considered in the building of time series prediction model. In the present study, the information granulation time series regression model based on support vector machine is proposed. SVM has good generalization ability, obey the principle of structural risk minimization rather than empirical risk minimization. The SVM information granulation algorithm is mainly used to predict the stock opening index, urban water consumption and other fields, rarely used in engineering projects. In this paper, SVM information granulation is applied to tunnel surrounding rock deformation prediction. Compared with the tunnel surrounding rock deformation regression prediction model in the past can only predict a single numerical value, SVM-based information granulation algorithm can predict the change trend and space of time series. Which can not only improve the prediction of the time series regression of tunnel surrounding rock deformation, but also make an accurate prediction of the fluctuation range of the time series regression of the surrounding rock deformation. The established model was applied to Panlongshan tunnel on the line of Qinglan expressway in China. The study results show that the evaluation results agree well with practical situations. The presented method and selected results could provide scientific evidence for deformation prediction for surrounding rock in shallow buried tunnels.
n ⎧ ϕ: R → F ⎨ ⎩ x → ϕ (x )
After mapping, the classification hyperplane becomes:
y = sign [(w·Φ (x )) + b]
yi sign [w·Φ (x ) + b] ⩾ 1 (i = 1, 2, ⋯, n)
min n, b
1 ∥w∥2 2
(7)
When the feature map is unknown, Eq. (4) cannot be solved directly, but it can be solved for the implicit feature mapping. For the quadratic programming problem, every constraint condition of Eq. (3) introduces Lagrange multiplier αi (αi ⩾ 0, i = 1, 2, ⋯, n) , and the Lagrange function is obtained as follows:
L (w, b, α ) =
1 ||w||2 − 2
n
∑ αi yi [(w·xi) + b − 1]
(8)
i=1
Tasks become αi maximization and w, b minimization. At its best, ac∂L ∂L cording to K-T condition, there are ∂b = 0 and ∂w = 0 . n ⎧ i = 1 αi yi = 0 n ⎨ ⎩ w = i = 1 αi yi Φ (x )
(9)
The dual quadratic programming problems can be obtained by substituting the Eq. (7) into the Eq. (4): n
n
1
⎧ max∑i = 1 αi − 2 ∑i, j = 1 αi αj yi yj (Φ (x i )·Φ (xj )) ⎪ s. t . αi ⩾ 0, i = 1, 2, ⋯, n ⎨ n ⎪∑i = 1 αi yi = 0 ⎩
Support vector machine, proposed by Cortes and Vapnik (1995), can be utilized to pattern classification and non-linear regression. The theoretical basis of SVM is statistical learning theory, more precisely, the approximate realization of structural risk minimization. The main idea is to establish a classification hyperplane as the decision surface, which maximizes the isolation margin between positive and negative examples. The principle is to learn the generalized error rate of the machine on the test data, bounded by the sum of the training error rate and a term of Vapnik-Chervonenkis dimension. In separable mode, the value of the SVM in the previous term is zero and the second term is minimized. Therefore, SVM has good generalization performance (Xue and Xiao, 2017). Suppose the training set is as follows:
(10)
From Eq. (10) we know that Φ(x i ) only interacts with the inner product. According to the Mercer theorem, the function k(u,v) satisfying the Mercer condition is called Mercer kernel function. Then there is a space H and a mapping Φ: Rn → H , then k(u,v) = Φ(u)·Φ(v ) . So, with kernel techniques, the inner product in eigenspace can be calculated directly from the data in input space. The coefficients αi (i = 1, 2, ⋯, n ) can be obtained by solving the dual problem. The vector xi corresponding to αi ≠ 0 is called the support vector, so a non-linear decision function is as follows: n
n
f (x ) = sign [ ∑ αi yi (Φ (x )·Φ (x i )) + b] = sign [ ∑ αi yi k (x , x i )+b] i=1
(1)
i=1
(11)
When dealing with the noise data, the slack variable ξi is introduced to relax the constraint:
Rn
where X is the input space vector, X ∈ , n is the number of training samples; Y is the model space, Y = {+1, −1} Separating hyperplane:
yi (w·Φ (x i ) + b) ⩾ 1 − ξi ξi ⩾ 0 i = 1, 2, ⋯, n
(12)
Eq. (12) allow a certain classification error. The sum of the upper bounds minimizing trial Eq. (7) and empirical error is as follows:
(2)
n
where w is the weight vector, x is the input vector, b is the threshold. For separable hyperplane classifiers, the classification conditions for no training errors are as follows:
yi [(w·xi ) + b] ⩾ 1 (i = 1, 2, ⋯, n)
(6)
The learning goal is to find the scalar b and w ∈ F to satisfy the expected minimum risk. According to VC theory, an upper bound of model complexity and minimization of empirical risk can be expressed by the following quadratic programming problem.
2.1. Support vector machine and algorithm structure
y = sign [(w· x ) + b]
(5)
The constraints of error-free classification in feature space are as follows:
2. Principle of support vector machine information granulation
(x1, y1), (x2 , y2 ), ⋯, (x n , yn ) ∈ X × Y
(4)
min n, b
1 ∥w∥2 + C ∑ ξi 2 i=1
(13)
where C is the penalty parameter, which determines a trade-off between model complexity and empirical error. This leads to dual problems:
(3)
The use of linear function classification is often not ideal in practical 2
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granulation problem for the first time in 1979. And a proposition of data granulation was given:
g ≜ (x is G ) is λ
where x is the variable of the value in the domain U; G is a fuzzy subset of U, which is characterized by the membership function μG ; λ represents the probability. It is generally assumed that U is a real set R (Rn ), G is a convex fuzzy subset of U, and λ is a fuzzy subset of unit intervals (Yin et al.,2017). Fuzzy information granule is a kind of information granule expressed in the form of fuzzy set, and fuzzy granulation of time series is carried out by fuzzy set method. It is divided into two steps: Dividing window and fuzzing. Dividing window is dividing the time series into several sub-sequences as operational window. Fuzzing is to fuzzy every window, and the fuzzy sets are called fuzzy information granulations. The combination of these two generalized modes is fuzzy information granulation, called f-granulation. In f-granulation, the most important thing is the process of fuzzification, that is, to build a reasonable fuzzy set in the given window, so that it can replace the data in the original window and represent the relevant information that people are concerned about. For a given time series, the problem of single window is considered, that is, the whole time series sequence X is considered as a window for fuzzification. The task of fuzzification is to establish a fuzzy particle P on X. That is, a fuzzy concept G, which can reasonably describe X , once G is determined, the fuzzy particle P is also determined:
Fig. 1. Support vector machine algorithm structure. n
1
n
⎧ max∑i = 1 αi − 2 ∑i, j = 1 αi αj yi yj (Φ (xi )·Φ (xj )) ⎪ s. t . 0 ⩽ α i ⩽ C, i = 1, 2, ⋯, n ⎨ n ⎪∑i = 1 αi yi = 0 ⎩
(14)
In general, the algorithm structure of SVM is shown in Fig. 1 Where K is a kernel function with the following types: Linear kernel function:
K (x , x i ) = xT x i
(15)
Polynomial kernel function:
K (x , x i ) = (γxT x i + r ) p , γ > 0
(16)
Radial basis kernel function:
K (x , x i ) = exp(−γ ∥x − x i ∥2 ), γ > 0
(17)
g ≜ x is G
Two-layer perceptron kernel function:
K (x , x i ) = tanh(γxT x i + r )
(19)
(18)
(20)
Therefore, the fuzzification process is essentially the process of determining a function A. A is the membership function of the fuzzy concept G (A = μG ). Generally, the basic form of the fuzzy concept is first determined when granulating. Then the specific membership function A is determined. The commonly used fuzzy particles are parabolic, Gaussian, trapezoid, triangular and other basic models. Due to simple formulas and computational efficiency, the study uses triangular fuzzy particles, the membership function is as follows, a case study is shown in Fig. 2.
In order to find the global optimal value instead of the local optimal value, and to ensure the good generalization ability of the unknown sample, a two-layer perceptron kernel function is used in this paper. 2.2. Information granulation basic knowledge and fuzzy model Information granulation mainly studies the formation, representation, thickness, semantic interpretation of information granules. The main aspects are word calculation and granulation calculation. The information granule divides the object set mainly through its function, similarity, function similarity and indistinguishability (Su et al., 2006). Information granulation, first proposed by Professor Zadeh (1968), is to decompose a whole into parts for research, each part is an information granule. These elements are combined because of indistinguishable, close to, or similar in function. Information granules are the collection of these elements (Aggarwal, 2017). There are three main models of information granulation: a model based on rough set theory, a model based on fuzzy set theory and a model based on quotient space theory. Fuzzy set theory describes the granularity by the degree of membership of the object with respect to the set. Which belongs to the same membership relationship of different objects. It focuses on the fuzziness of the set and emphasizes the degree of membership. The rough set theory describes the granularity by a set of up-and-down approximation of an available knowledge base, which reflects the set relationship of the objects in different classes, which focuses on the unresolvable degree between objects in the set and emphasizes the classification. The quotient space theory does not study the particle metrics because it discusses the change law of the particles from a macro perspective. Compared with rough set theory and quotient space theory, fuzzy set theory has a stronger function in optimizing, integrating and dealing with the uncertainty and incompleteness of knowledge. In this paper, the fuzziness of the set and its membership degree are studied, so the model based on fuzzy set theory is adopted. The model was proposed by the famous American scientist Professor Zadeh in the 1960s and discussed the fuzzy information
A (x , a, m , b) =
⎧ x − a 0, x < a ⎪ ,a ⩽x ⩽m m−a ⎨ ⎪ ⎩
b−x , b−m
m
0, x > b
(21)
Fig. 2. An example of membership function of a triangular fuzzy particle. 3
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Fig. 3. Panlongshan tunnel and geographical position of Tai’an city.
3. Engineering application
strike and the hole axis oblique line, there is no fracture structure in the entrance, the joints and fractures are developed, and the local dissolution fractures are developed. Drilling reveals that the local development of small-scale filling caverns, dissolution fractures and erosion of the pores see muddy filling, poor stability. The rock uniaxial saturated compressive strength is 13.2–18.6 MPa, rock mass basic quality value is 195, rock longitudinal wave velocity mass is 500(m/s), rock mass classification is V grade. Because of the poor surrounding rock quality of the entrance section, the tunnel entrance section is excavated by Center Cross Diagram (CRD) method.
3.1. Engineering background To further validate the established model, a practical project named the Panlongshan tunnel was selected as the investigated object and investigated with the present method for deformation prediction of surrounding rock. Panlongshan tunnel is located in Tai'an City, Shandong Province, China. The tunnel is 2885 m in length with a bidirectional 6 lanes. The entrance of Panlongshan tunnel is about 100 m, and the entrance and geographical position of the Panlongshan tunnel is shown in Fig. 3. The entrance of the tunnel located at the foot of the mountain with a gentle slope of about 5–12°, and the Quaternary soil thickness varies from 0.40 m to 1.20 m. Engineering geological profile of Panlongshan tunnel is shown in Fig. 4, the YK78+410 tunnel face is shown in Fig. 5, it can be seen that the exposed sections of the entrance section are dominated by Late Cambrian limestone, partially framed thin-layered marls, bedded structure, small strata inclination, rock
3.2. Monitoring data In this paper, the arch crown settlement monitoring data of the YK78+410 section for 75 days is taken as the model sample. Fig. 6 shows the time-dependent curve of arch crown settlement. It can be seen from Fig. 6 that the arch crown settlement data has changed greatly in the first 20 days, and after 20 days, the tunnel arch crown
Fig. 4. Engineering geological profile of Panlongshan tunnel. 4
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Fig. 5. Photo of the tunnel face of YK78+410 section.
change of the arch crown settlement value. 3.4. Parameters optimization The penalty parameter c and the parameter g of kernel function of support vector machine need to be optimized, which can improve the precision of the model (Patwari et al., 2010). The commonly used parameter optimization algorithms are genetic algorithms (Phan et al., 2017), particle swarm optimization (Jia et al., 2017) and grid optimization. Grid optimization algorithm is a practical data search method, which is suitable for searching multi-dimensional arrays in parallel from different growth directions. The grid optimization algorithm traverses all the parameter combinations in the search range and can search for the optimal parameters, so it has the advantage to predict the small data samples. Therefore, the grid optimization algorithm is adopted in this study for parameter optimization. The parameter determination method based on grid optimization algorithm is realized as follows: the original data is randomly divided into two groups, and each subset data is separately used as a verification set, and the remaining K − 1 subset data is used as a training set, so the K models can be obtained. The model sets the selection range and search step size of the penalty parameter c and the kernel function parameter g. According to the cross-validation method, the MeanSquare Error (MSE) of the training set and the MSE of the test set after traversing the combination (c, g) are calculated. Finally, the optimal parameter combination (c, g) is determined under the premise of ensuring the minimum of sum of MSE of training set and test set. Then, the MSE of each group (c, g) value is drawn by contour line, and the contour map of parameter optimization is obtained. As shown in Figs. 9–14, the x axis represents the logarithmic value of c at the base of 2, the y axis represents the logarithmic value of g at the base of 2, and the contour line represents the MSE of c and g. The SVM parameter optimization method is as follows: First, rough optimization, the range of c and g is 2−10 to 210, and the change value of c and g is: 2−10, 2−9, … 210, MSE change interval is 0.1, and the results are shown in Figs. 9, 11, 13. Then, from the rough optimization results, it can be seen that the value range of c can be reduced to 2−2 ∼ 28, and the range of g can be reduced to 2−8 ∼ 22, the change value of c is: 2−2, 2−1.5, … 28, the change value of g is: 2−8, 2−7.5… 22. The parameter selection result shows the change interval of MSE is 0.05, so that the precision of the optimization result is higher of the fine optimization and the change of MSE can be seen more clearly.
Fig. 6. Curve of arch crown settlement of YK78+410 section.
settlement is approximately stable. 3.3. SVM information granulation method and fuzzy granulation Model Objective: Based on the daily arch crown settlement values of the YK78+410 section of Panlongshan Tunnel from February 18, 2018 to May 3, 2018. The original data of each arch crown settlement value is granulated with fuzzy information for 3 days as a window, which is used as training data, predict the variation trend and range space of the arch crown settlement on May 4–6, 2018. In the deformation prediction processes, we assumed that the settlement value of YK78+410 cross-section is time-dependent and time is taken as an independent variable that affects the settlement of the tunnel vault. The algorithm flow chart is shown in Fig. 7. The results of three days of arch crown settlement monitoring data are taken as one information granulation and divided into 25 windows. The result of granulation of the original data is presented in Fig. 8. The Low parameter describes the minimum change of the arch crown settlement value, the R parameter describes the average change of the arch crown settlement value, the Up parameter describes the maximum 5
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Fig. 7. Prediction flowchart based on the model of SVM information granulation method.
3.5. Prediction results and analysis Figs. 15–20 show the fitting result and error histogram of the SVM information granulation of Low, R, Up, from which the following conclusions can be drawn: (1) From a single figure analysis: Low fitted curve for 1–3 days, 7–9 days, R fitted curve for 1–3 days, Up fitted curve for 1–6 days have a larger fitting error. According to the analysis of comparison of each figure, the error of the fitted curve is larger in 1–9 days, especially 1–3 days of excavation of YK78+410 section. The reason is that the arch crown settlement has a large change in the time range within 1–3 days, and there is no support from the training data before, so it is impossible to obtain a more accurate prediction result by SVM training. (2) From Figs. 15–20, it can be seen that the information granulation fitting curves of Low, R, Up are better after 9 days. One reason is that the support of pre-training data, the second is that the time series fluctuation after 9 days is small, so it has good prediction effect.
Fig. 8. Granulation results.
Table 1 shows the comparison between the measured data and the predicted data, and it can be seen from the table that the variation range of the arch crown settlement on May 4, 5 and 6 is accurate, which indicates that the SVM – based information granulating time series regression prediction model has a good prediction effect and can reflect the fluctuation range of the arch crown settlement and has a certain reference value.
The best parameter of low curve is obtained by rough optimization and fine optimization: c = 90.5097, g = 0.015625, the best parameter of the R curve: c = 90.5097, g = 0.015625, the best parameter of the Up curve: c = 181.019, g = 0.0110485. The optimal parameters c and g were used to train the SVM. Then, the arch crown settlement was regressed and predicted, and the comparison chart and the error diagram between the original data and the predicted data were obtained.
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Fig. 9. Rough optimization results of parameters of Low.
4. Conclusions
settlement at the shallow buried section of Panlongshan tunnel, the experimental results show that:
In view of the time series regression of the arch crown settlement in shallow buried tunnels, a prediction model based on SVM information granulation is proposed. Based on the measured data of the arch crown
(1) SVM has a strong learning ability in simulating the regression trend of the time series of the arch crown settlement. Using grid
Fig. 10. Fine optimization results of parameters of Low. 7
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Fig. 11. Rough optimization results of parameters of R.
space of nonlinear system compared with the traditional prediction model. The engineering application in this paper shows that the variation range of arch crown settlement predicted by this model for the next three days in May 4, 5, 6 days is accurate, and has good
optimization algorithm to optimize SVM parameters can avoid the blindness and inefficiency of trial calculation. (2) The time series regression prediction model based on SVM information granulation can predict the change trend and change
Fig. 12. Fine optimization results of parameters of R. 8
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Fig. 13. Rough optimization results of parameters of Up.
Fig. 14. Fine optimization results of parameters of Up. 9
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Fig. 18. Fitting error of R.
Fig. 15. Fitting result of Low.
Fig. 19. Fitting result of Up.
Fig. 16. Fitting error of Low.
Fig. 20. Fitting error of Up.
Fig. 17. Fitting result of R.
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Table 1 Prediction of variation trend and range of YK78+410 section. Date
The actual range of change [Low,R,Up]
Predict the range of change [Low,R,Up]
February 21st–23rd May 1st −3rd May 4th–6th
[6.87,7.50,8.05] [8.98,8.99,9.01] [8.97,8.98,9.00]
[6.057,7.538,7.632] [8.877,8.938,9.013] [8.750,8.893,9.010]
Cortes, C., Vapnik, V., 1995. Support-vector networks. Mach. Learn. 20, 273–297. Chou, W., Bobet, A., 2002. Predictions of ground deformations in shallow tunnels in clay. Tunnel. Undergr. Space Technol. 17 (1), 3–19. Fargnoli, V., Boldini, D., Amorosi, A., 2015. Twin tunnel excavation in coarse grained soils: observations and numerical back-predictions under free field conditions and in presence of a surface structure. Tunnel. Undergr. Space Technol. 49, 454–469. Goh, A.T.C., Hefney, A.M., 2010. Reliability assessment of EPB tunnel-related settlement. Geomech. Eng. 2 (1), 57–69. Goh, A.T.C., Zhang, W., Zhang, Y., Xiao, Y., Xiang, Y., 2018. Determination of earth pressure balance tunnel-related maximum surface settlement: a multivariate adaptive regression splines approach. Bull. Eng. Geol. Environ. 77 (2), 489–500. Hasanipanah, M., Noorian-Bidgoli, M., Jahed Armaghani, D., Khamesi, H., 2016. Feasibility of PSO-ANN model for predicting surface settlement caused by tunneling. Eng. Comput. 32 (4), 705–715. Janin, J., et al., 2012. Settlement monitoring and tunnelling process adaptation—case of South Toulon tunnel. Geotech. Aspect. Undergr. Constr. Soft Ground 205–212. Jia, S., Qian, X., Yuan, X., 2017. Optimal design for dividing wall column using support vector machine and particle swarm optimization. Chem. Eng. Res. Des. 125, 422–432. Moeinossadat, S.R., Ahangari, K., Shahriar, K., 2018. Control of ground settlements caused by EPBS tunneling using an intelligent predictive model. Ind. Geotech. J. 48 (3), 420–429. Ninić, J., Meschke, G., 2015. Model update and real-time steering of tunnel boring machines using simulation-based meta models. Tunnel. Undergr. Space Technol. 45, 138–152. Ocak, I., Seker, S.E., 2013. Calculation of surface settlements caused by EPBM tunneling using artificial neural network, SVM, and Gaussian processes. Environ. Earth Sci. 70 (3), 1263–1276. Patwari, N., Croft, J., Jana, S., Kasera, S.K., 2010. High-rate uncorrelated bit extraction for shared secret key generation from channel measurements. IEEE Trans. Mobile Comput. 9 (1), 17–30. Phan, A.V., Nguyen, M.L., Bui, L.T., 2017. Feature weighting and SVM parameters optimization based on genetic algorithms for classification problems. Appl. Intell. 46 (2), 455–469. Pourtaghi, A., Lotfollahi-Yaghin, M.A., 2012. Wavenet ability assessment in comparison to ANN for predicting the maximum surface settlement caused by tunneling. Tunnel. Undergr. Space Technol. 28, 257–271. Santos, O.J., Celestino, T.B., 2008. Artificial neural networks analysis of São Paulo subway tunnel settlement data. Tunnel. Undergr. Space Technol. 23 (5), 481–491. Su, C., Chen, L., Yih, Y., 2006. Knowledge acquisition through information granulation for imbalanced data. Expert Syst. Appl. 31 (3), 531–541. Suwansawat, S., Einstein, H.H., 2007. Describing settlement troughs over twin tunnels using a superposition technique, 133(4), 445–468. Talebinejad, A., et al., 2014. Investigation of surface and subsurface displacements due to multiple tunnels excavation in urban area. Arab. J. Geosci. 7 (9), 3913–3923. Xue, X., Xiao, M., 2017. Deformation evaluation on surrounding rocks of underground caverns based on PSO-LSSVM. Tunnel. Undergr. Space Technol. 69, 171–181. Yin, S., Jiang, Y., Tian, Y., Kaynak, O., 2017. A data-driven fuzzy information granulation approach for freight volume forecasting. IEEE Trans. Indus. Electron. 64 (2), 1447–1456. Zadeh, L.A., 1968. Fuzzy algorithms. Inform. Control 12 (2), 94–102.
prediction effect. It can reflect the time series fluctuation range of arch crown settlement and has certain reference value. (3) The information granulation time series regression prediction model based on SVM provides a new method for nonlinear time series regression for the arch crown settlement of shallow buried tunnels. This method is also applicable to other fields of timevarying nonlinear systems. Acknowledgements This research was funded by National Natural Science Foundation of China (Grant No. 51609129, 51709159, 51679131), State key laboratory for Mine disaster prevention and control, cultivation base co-built by province and ministry of Shandong university of science and technology (Grant No. MDPC201707, MDPC201802), Shandong postdoctoral innovation project special Foundation (Grant No. 201502025, 201702014), China Postdoctoral Science Foundation (Grant No. 2017T100492, 2017M612273). Declarations of interest None. References Aggarwal, M., 2017. Representation of uncertainty with information and probabilistic information granules. Int. J. Fuzzy Syst. 19 (5), 1617–1634. Ahangari, K., Moeinossadat, S.R., Behnia, D., 2015. Estimation of tunnelling-induced settlement by modern intelligent methods. Soils Foundat. 55 (4), 737–748. Chakeri, H., Hasanpour, R., Hindistan, M.A., Ünver, B., 2011. Analysis of interaction between tunnels in soft ground by 3D numerical modeling. Bull. Eng. Geol. Environ. 70 (3), 439–448.
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