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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (12): 2275-2285    DOI: 10.3785/j.issn.1008-973X.2021.12.007
    
Prediction method of tunnel deformation based on time series and DEGWO-SVR model
Bao-qiang ZHU(),Shu-hong WANG*(),Ze ZHANG,Peng-yu WANG,Fu-rui DONG
School of Resource and Civil Engineering, Northeastern University, Shenyang 110819, China
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Abstract  

Combining time series analysis, differential evolution (DE), grey wolf optimizer (GWO), and support vector regression (SVR), a new prediction model of tunnel deformation was proposed, in order to accurately predict tunnel deformation has the characteristics of non-equidistant and complex nonlinear. Firstly, non-equidistant data was processed equidistantly by cubic-spline function interpolation. Then based on the time series principle, the deformation were decomposed into the trend terms and stationary random terms. The proposed model was used to predict the two terms. Finally, the displacement components were superimposed to realize the prediction of the tunnel cumulative deformation. Taking the measured vault settlement of Xinglong Tunnel in Chongqing as an example, the vault settlement of the front ZK37+900 and ZK37+910 section was predicted and compared with existing models. Results showed that the root-mean-square error were 0.193 7 mm and 0.086 9 mm, the mean-absolute-percent error were 1.21 % and 0.55 %, and the correlation coefficient were 0.997 1 and 0.992 8. Compared with the existing models, the proposed model has higher prediction accuracy and smaller error, it has better applicability and application prospects.

Key words： tunnel engineering      tunnel deformation prediction      time series      differential evolution (DE)      grey wolf optimizer (GWO)      support vector regression (SVR)     
Received: 07 January 2021      Published: 31 December 2021
CLC:  U 459  
Fund:  国家自然科学基金资助项目(U1602232)；中央高校基本科研业务专项资金资助项目(2101018)；辽宁省重点研发计划资助项目(2019JH2/10100035)
Corresponding Authors: Shu-hong WANG     E-mail: zbq2289675237@163.com;wangshuhong@mail.neu.edu.cn
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Bao-qiang ZHU
Shu-hong WANG
Ze ZHANG
Peng-yu WANG
Fu-rui DONG
Cite this article:

Bao-qiang ZHU,Shu-hong WANG,Ze ZHANG,Peng-yu WANG,Fu-rui DONG. Prediction method of tunnel deformation based on time series and DEGWO-SVR model. Journal of ZheJiang University (Engineering Science), 2021, 55(12): 2275-2285.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.12.007     OR     https://www.zjujournals.com/eng/Y2021/V55/I12/2275


基于时间序列与DEGWO-SVR模型的隧道变形预测方法

为了对准确预测隧道变形的非等距性及复杂非线性特征，结合时序分析理论、差分进化算法(DE)、灰狼优化算法(GWO)和支持向量回归机(SVR)模型，提出新的隧道变形预测模型. 利用3次样条函数插值法将非等距监测数据等距化；基于时间序列原理将变形分解为趋势项及平稳随机项，并采用所提模型分别对2个分解项进行预测；将各位移分量叠加，实现隧道累积变形的预测. 以重庆市兴隆隧道实测拱顶沉降为例，预测前方ZK37+900和ZK37+910断面拱顶沉降，并与已有模型进行对比. 结果表明：所提模型预测的均方根误差分别为0.193 7 、0.086 9 mm，平均绝对百分比误差分别为1.21%、0.55%，相关系数分别为0.997 1、0.992 8. 相比于已有模型，所提模型的预测精度更高、误差更小，具有更好的适用性及应用前景.


关键词： 隧道工程,  隧道变形预测,  时间序列,  差分进化(DE),  灰狼优化(GWO),  支持向量回归(SVR) 
Fig.7 Prediction results of trend terms displacement of different models
函数 算法 vOS vW vAVG vSTD
f1(x) DE 8.21×10?4 1.83×10?3 1.25×10?3 2.26×10?4
f1(x) GWO 1.11×10?7 2.50×10?6 7.04×10?7 5.21×10?7
f1(x) DEGWO 0 6.21×10?7 1.77×10?7 1.68×10?7
f2(x) DE 6.41×10 8.51×10 7.57×10 6.41
f2(x) GWO 5.68×10?14 1.00×10 2.09 3.57
f2(x) DEGWO 0 7.16×10?12 1.07×10?12 2.31×10?12
Tab.1 Effects comparison of test function
Fig.1 Flowchart of prediction based on DEGWO-SVR
Fig.2 Deformation monitoring point layout of each section
Fig.3 Location plan of deformation monitoring point
Fig.4 Engineering geological section
Fig.5 Equidistant time series data of different sections
Fig.6 Displacement of trend terms and stationary random terms of different sections
监测断面 p/10?2 H
1% 5% 10%
ZK37+950 1.28 0 1 1
ZK37+940 1.48 0 1 1
ZK37+930 0.87 1 1 1
ZK37+920 0.38 1 1 1
ZK37+910 0.32 1 1 1
ZK37+900 0.30 1 1 1
Tab.2 Result evaluation of ADF test of random terms displacement
模型 监测断面 位移分量 c g
DEGWO-SVR ZK37+900 趋势项 9.999 0.010
DEGWO-SVR ZK37+900 平稳随机项 7.185 2.707
DEGWO-SVR ZK37+910 趋势项 6.080 0.010
DEGWO-SVR ZK37+910 平稳随机项 28.350 1.669
SVM信息粒化 ZK37+900 趋势项 51.874 0.150
SVM信息粒化 ZK37+900 平稳随机项 26.164 0.713
SVM信息粒化 ZK37+910 趋势项 82.852 0.150
SVM信息粒化 ZK37+910 平稳随机项 12.170 0.315
SVM ZK37+900 趋势项 1.000 0.125
SVM ZK37+900 平稳随机项 1.000 0.125
SVM ZK37+910 趋势项 1.516 0.125
SVM ZK37+910 平稳随机项 8.000 0.125
Tab.3 Optimal parameters of different prediction models
模型 R RMSE/ mm MAPE/ %
ZK37+900 ZK37+910 ZK37+900 ZK37+910 ZK37+900 ZK37+910
DEGWO-SVR 0.999 6 0.999 7 0.187 0 0.057 6 1.25 0.39
SVM信息粒化 0.979 6 0.939 6 0.645 7 0.765 0 4.06 4.85
SVM 0.982 1 0.976 4 1.002 3 0.841 6 6.71 5.57
Tab.4 Prediction accuracy and error of trend terms displacement of different models
Fig.8 Prediction results of stationary random terms displacement of  differentmodels
模型 R RMSE/mm MAPE/%
ZK37+900 ZK37+910 ZK37+900 ZK37+910 ZK37+900 ZK37+910
DEGWO-SVR 0.957 4 0.918 6 0.079 5 0.084 4 26.51 77.04
SVM信息粒化 0.979 9 0.923 9 0.148 6 0.118 9 122.56 85.76
SVM 0.972 9 0.978 3 0.214 8 0.121 3 179.07 88.54
Tab.5 Prediction accuracy and error of stationary random terms displacement of  different models
Fig.9 Prediction results of cumulative displacement of different models
模型 R RMSE/mm MAPE/%
ZK37+900 ZK37+910 ZK37+900 ZK37+910 ZK37+900 ZK37+910
DEGWO-SVR 0.997 1 0.992 8 0.193 7 0.086 9 1.21 0.55
SVM信息粒化 0.987 9 0.903 4 0.505 0 0.878 9 4.52 6.70
SVM 0.982 9 0.982 5 0.791 8 0.726 7 5.89 5.32
Tab.6 Prediction accuracy and error of cumulative displacement of different models
Fig.10 Initial deformation prediction results of ZK37+910 section
模型 R RMSE/mm MAPE/%
DEGWO-SVR 0.997 4 0.185 4 1.57
SVM信息粒化 0.993 1 0.704 9 6.53
SVM 0.997 1 0.792 7 7.02
Tab.7 Prediction accuracy and error of initial deformation of ZK37+910 section
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