Prediction of landslide displacement based on improved grey wolf optimizer and support vector regression

doi:10.11772/j.issn.1001-9081.2023030331

Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (3): 972-982.DOI: 10.11772/j.issn.1001-9081.2023030331

Special Issue: 前沿与综合应用

• Frontier and comprehensive applications • Previous Articles Next Articles

Prediction of landslide displacement based on improved grey wolf optimizer and support vector regression

Shuai REN¹^,²^,³, Yuanfa JI¹^,²^,³(), Xiyan SUN¹^,²^,³^,⁴, Zhaochuan WEI¹^,²^,³, Zian LIN¹^,³

^1.Guangxi Key Laboratory of Precision Navigation Technology and Application （Guilin University of Electronic Technology），Guilin Guangxi 541004，China
^2.School of Information and Communication，Guilin University of Electronic Technology，Guilin Guangxi 541004，China
^3.National & Local Joint Engineering Research Center of Satellite Navigation Positioning and Location Service，Guilin University of Electronic Technology，Guilin Guangxi 541004，China
^4.GUET-Nanning E-Tech Research Institute Company Limited，Nanning Guangxi 530031，China

Received:2023-03-29 Revised:2023-04-27 Accepted:2023-05-11 Online:2023-05-24 Published:2024-03-10
Contact: Yuanfa JI
About author:REN Shuai， born in 2000， M. S. candidate. His research interests include landslide disaster warning system.
SUN Xiyan， born in 1973， Ph. D.， professor. Her research interests include satellite navigation.
WEI Zhaochuan， born in 1973， M. S.， associate professor. His research interests include signal processing.
LIN Zian， born in 1991， Ph. D. candidate. His research interests include computer graphics.
Supported by:
National Natural Science Foundation of China(62061010);Guangxi Science and Technology Department Project(Gui Ke AA20302022)

基于改进灰狼优化与支持向量回归的滑坡位移预测

任帅¹^,²^,³, 纪元法¹^,²^,³(), 孙希延¹^,²^,³^,⁴, 韦照川¹^,²^,³, 林子安¹^,³

^1.广西精密导航技术与应用重点实验室(桂林电子科技大学), 广西桂林 541004
^2.桂林电子科技大学信息与通信学院, 广西桂林 541004
^3.桂林电子科技大学卫星导航定位与位置服务国家地方联合工程研究中心, 广西桂林 541004
^4.南宁桂电电子科技研究院有限公司, 南宁 530031

通讯作者: 纪元法
作者简介:任帅（2000—），男，陕西渭南人，硕士研究生，主要研究方向：滑坡灾害预警系统
孙希延（1973—），女，山东潍坊人，教授，博士，主要研究方向：卫星导航
韦照川（1973—），男，广西河池人，副教授，硕士，主要研究方向：信号处理
林子安（1991—），男，广西梧州人，博士研究生，主要研究方向：计算机图形学。
基金资助:
国家自然科学基金资助项目(62061010);广西科技厅项目(桂科AD20302022)

Abstract

Abstract:

To address the issues of difficult prediction of landslide displacement and difficulty in selecting influencing factors， a model combining Double Moving Average （DMA）， Variational Modal Decomposition （VMD）， Improved Gray Wolf Optimizer （IGWO） algorithm and Support Vector Regression （SVR） was proposed for landslide displacement prediction. Firstly， DMA was used to extract the trend and periodic terms of landslide displacement， and polynomial fitting was used to predict the trend term. Secondly， the influencing factors of the landslide periodic term were classified， and VMD was used to decompose the original factor sequence to obtain the optimal sequence. Then， a grey wolf optimizer algorithm combining SVR with an improved Circle-based multi-tactic， called CTGWO-SVR （Circle Tactics Grey Wolf Optimizer with SVR）， was proposed to predict the landslide periodic term. Finally， the cumulative displacement prediction sequence was obtained using a time series additive model， and the model was evaluated using post validation difference verification and small probability error in grey prediction. Experimental results show that compared with GA （Genetic Algorithm）-SVR and GWO-SVR models， CTGWO-SVR has higher prediction accuracy with a fitting degree of 0.979， and the Root Mean Square Error （RMSE） reduces by 51.47% and 59.25%， respectively. The model evaluation accuracy is level one， which can meet the real-time and accuracy requirements of landslide prediction.

Key words: landslide displacement prediction, displacement decomposition, time series, Variational Modal Decomposition (VMD), grey correlation analysis, Gray Wolf Optimizer (GWO) algorithm, Support Vector Regression (SVR)

摘要：

针对滑坡位移难以预测、影响因素难以选择等问题，提出一种结合了二次移动平均（DMA）法、变分模态分解（VMD）、改进灰狼优化（IGWO）算法与支持向量回归（SVR）的模型进行滑坡位移预测。首先，利用DMA提取滑坡位移趋势项和周期项，采用多项式拟合对趋势项进行预测；其次，对滑坡周期项的影响因素进行分类，采用VMD对原始影响因子序列进行分解获得最优序列；再次，提出一种结合SVR与基于改进Circle多策略的灰狼优化算法CTGWO-SVR（Circle Tactics Grey Wolf Optimizer with SVR）对滑坡周期项进行预测；最后采用时间序列加法模型求出累计位移预测序列，并采用灰色预测的后验证差校验和小概率误差对模型进行评价。实验结果表明，与GA-SVR和GWO-SVR模型相比，CTGWO-SVR的预测精度更高，拟合度达到0.979，均方根误差分别减小了51.47%与59.25%，预测精度等级为一级，可满足滑坡预测的实时性和准确性要求。

关键词: 滑坡位移预测, 位移分解, 时间序列, 变分模态分解, 灰色关联分析, 灰狼优化算法, 支持向量回归

CLC Number:

TP183

Shuai REN, Yuanfa JI, Xiyan SUN, Zhaochuan WEI, Zian LIN. Prediction of landslide displacement based on improved grey wolf optimizer and support vector regression[J]. Journal of Computer Applications, 2024, 44(3): 972-982.

任帅, 纪元法, 孙希延, 韦照川, 林子安. 基于改进灰狼优化与支持向量回归的滑坡位移预测[J]. 《计算机应用》唯一官方网站, 2024, 44(3): 972-982.

Figures/Tables 26

Fig. 1 Grey wolf hierarchy

Fig. 2 Circle mapping and its improvement

Fig. 3 Comparison of convergence factors

Fig. 4 Flow of CTGWO-SVR prediction model

Fig. 5 Monitoring data of ZG111， a landslide monitoring site in Bazimen

Fig. 6 Flow of displacement prediction

Tab. 1 Test functions

函数名	函数表达式	维数	搜索范围
Sphere	$F 1 x = ∑ i = 1 n x i 2$	30	［-100，100］
Schwefel 2.22	$F 2 x = ∑ i = 1 n x i + ∏ i = 1 n x i$	30	［-10，10］
Schwefel 1.2	$F 3 x = ∑ i = 1 n ∑ j = 1 i x j 2$	30	［-100，100］
Schwefel 2.21	$F 4 x = m a x i x i, 1 ≤ i ≤ n$	30	［-100，100］
Quartic	$F 5 x = ∑ i = 1 n i x i 4 + r a n d o m 0,1$	30	［-1.28，1.28］
Rastrigin	$F 6 x = ∑ i = 1 n x i 2 - 10 c o s 2 π x i + 10$	30	［-5.12，5.12］
Ackley	$F 7 x = - 20 e x p - 0.2 1 n ∑ i = 1 n x i 2 - e x p 1 n ∑ i = 1 n 2 π x i + 20 + e$	30	［-32，32］
Griewank	$F 8 x = 1 4 000 ∑ i = 1 n x i 2 - ∏ i = 1 n c o s x i i + 1$	30	［-600，600］

Tab. 1 Test functions

函数名	函数表达式	维数	搜索范围
Sphere	$F 1 x = ∑ i = 1 n x i 2$	30	［-100，100］
Schwefel 2.22	$F 2 x = ∑ i = 1 n x i + ∏ i = 1 n x i$	30	［-10，10］
Schwefel 1.2	$F 3 x = ∑ i = 1 n ∑ j = 1 i x j 2$	30	［-100，100］
Schwefel 2.21	$F 4 x = m a x i x i, 1 ≤ i ≤ n$	30	［-100，100］
Quartic	$F 5 x = ∑ i = 1 n i x i 4 + r a n d o m 0,1$	30	［-1.28，1.28］
Rastrigin	$F 6 x = ∑ i = 1 n x i 2 - 10 c o s 2 π x i + 10$	30	［-5.12，5.12］
Ackley	$F 7 x = - 20 e x p - 0.2 1 n ∑ i = 1 n x i 2 - e x p 1 n ∑ i = 1 n 2 π x i + 20 + e$	30	［-32，32］
Griewank	$F 8 x = 1 4 000 ∑ i = 1 n x i 2 - ∏ i = 1 n c o s x i i + 1$	30	［-600，600］

Tab. 2 Comparison of performance test results of GWO algorithms improved by different strategies

函数	IGWO-1		IGWO-2		EGWO		HGWO		CTGWO
函数	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差
F₁	0	0	3.15E-14	4.38E-14	3.32E-50	5.32E-50	1.12E-32	2.32E-32	0	0
F₂	1.46E-180	0	1.70E-24	1.00E-24	6.93E-30	9.33E-30	9.33E-20	6.92E-20	0	0
F₃	0	0	4.58E-09	4.17E-09	2.83E-12	7.53E-12	3.18E-08	6.55E-08	0	0
F₄	2.97E-173	0	2.50E-10	1.08E-10	1.68E-13	2.37E-13	4.17E-08	4.56E-08	0	0
F₅	0.000 326 7	1.21E-04	0.001 548	0.001 706	1.71E-04	1.91E-04	1.49E-03	7.53E-04	4.88E-05	6.88E-05
F₆	0	3.066 8	3.593 496	1.14E-14	0	0	2.27E-01	9.20E-01	0	0
F₇	4.44E-15	0	1.87E-14	1.65E-14	-4.40E-16	0	4.27E-14	4.37E-15	8.88E-16	8.882E-16
F₈	0	0.052 3	0.003 629	0	4.99E-04	2.69E-03	1.37E-03	5.82E-03	0	0

Tab. 3 Comparison of performance test results of four algorithms

函数	PSO		SSA		GWO		CTGWO
函数	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差
F₁	2.435 352	2.378 911	6.940 00E-67	9.28E-56	1.292 00E-27	1.60E-27	0	0
F₂	4.491 009	4.181 337	7.669 76E-28	3.74E-31	8.390 54E-17	7.28E-17	0	0
F₃	212.093 600	174.288 900	1.005 92E-30	4.13E-25	2.474 11E-05	0.000 665 000	0	0
F₄	1.906 436	2.060 081	7.325 47E-27	1.33E-30	7.154 11E-07	9.38E-07	0	0
F₅	14.435 840	14.752 670	0.001 295 708	0.001 653	0.001 732 140	0.001 818 027	4.88E-05	6.88E-05
F₆	163.087 900	156.233 300	0	0	2.753 117 129	2.500 410 916	0	0
F₇	2.718 287	2.653 917	8.881 78E-16	8.88E-16	1.004 83E-13	1.002 46E-13	8.88E-16	8.88E-16
F₈	0.116 163	0.140 406	0	0	0.004 924 486	0.004 041 731	0	0

Fig. 7 Iteration effect comparison among different optimizer algorithms on F1 to F8 test functions

Fig. 8 Results of secondary moving average decomposition for Bazimen landslide displacement

Tab. 4 Correlation between each influence factor and landslide periodic term

项目	关联度	项目	关联度
$R 1$	0.693 7	$W 1$	0.611 3
$R 2$	0.692 1	$W 2$	0.646 8
$R 3$	0.649 1	$W 3$	0.763 3
$R 4$	0.651 5	$W 4$	0.733 8
$R 5$	0.749 3	$W 5$	0.643 3
$R 6$	0.715 0	$W 6$	0.607 1
$R 7$	0.710 9	$W 7$	0.611 9
$L 1$	0.726 1	$L 2$	0.780 4

Tab. 4 Correlation between each influence factor and landslide periodic term

项目	关联度	项目	关联度
$R 1$	0.693 7	$W 1$	0.611 3
$R 2$	0.692 1	$W 2$	0.646 8
$R 3$	0.649 1	$W 3$	0.763 3
$R 4$	0.651 5	$W 4$	0.733 8
$R 5$	0.749 3	$W 5$	0.643 3
$R 6$	0.715 0	$W 6$	0.607 1
$R 7$	0.710 9	$W 7$	0.611 9
$L 1$	0.726 1	$L 2$	0.780 4

Tab. 5 Correlation between L2 decomposition and landslide periodic term

影响因子	关联度
上月周期项滑坡（ $L 2$ ）	0.780 4
上月周期项滑坡高频	0.737 5
上月周期项滑坡低频	0.745 0

Tab. 5 Correlation between L2 decomposition and landslide periodic term

影响因子	关联度
上月周期项滑坡（ $L 2$ ）	0.780 4
上月周期项滑坡高频	0.737 5
上月周期项滑坡低频	0.745 0

Tab. 6 Correlation between L1 decomposition and landslide periodic term

影响因子	关联度
上月滑坡（ $L 1$ ）	0.726 1
上月滑坡高频	0.819 1
上月滑坡低频	0.767 4

Tab. 6 Correlation between L1 decomposition and landslide periodic term

影响因子	关联度
上月滑坡（ $L 1$ ）	0.726 1
上月滑坡高频	0.819 1
上月滑坡低频	0.767 4

Tab. 7 Correlation between L1 high frequency after decomposition and landslide periodic term

影响因子	关联度
上月滑坡高频	0.819 1
上月滑坡高频-高频	0.810 9
上月滑坡高频-低频	0.809 4

Fig. 9 Grey correlation analysis for landslide classes

Tab. 8 Correlation between decomposed inter-month variation of reservoir water level and landslide periodic term

影响因子	关联度
库水位月间变化	0.763 3
库水位月间变化-高频	0.668 7
库水位月间变化-低频	0.689 0

Fig. 10 Grey correlation analysis of reservoir water level classes

Tab. 9 Correlation between decomposed cumulative rainfall in the first two months and landslide cycle term

影响因子	关联度
前两月累计降雨	0.749 3
前两月累计降雨-高频	0.762 4
前两月累计降雨-低频	0.724 1

Tab. 10 Correlation between high frequency decomposition of accumulated rainfall in first two months and landslide periodic term

影响因子	关联度
前两月累计降雨高频	0.762 4
前两月累计降雨高频-高频	0.756 9
前两月累计降雨高频-低频	0.736 1

Fig. 11 Grey correlation analysis of rainfall classes

Tab. 11 Optimization and training results of different models

模型	C	ε	γ	$R 2$	RMSE
GA-SVR	69.14	6.05	0.13	0.884	9.89
GWO-SVR	2 368.84	0.52	0.11	0.836	11.78
CTGWO-SVR	2 024.57	0.10	0.96	0.979	4.80

Tab. 11 Optimization and training results of different models

模型	C	ε	γ	$R 2$	RMSE
GA-SVR	69.14	6.05	0.13	0.884	9.89
GWO-SVR	2 368.84	0.52	0.11	0.836	11.78
CTGWO-SVR	2 024.57	0.10	0.96	0.979	4.80

Fig. 12 Period term predictions by different optimization algorithms

Fig. 13 Iterative optimization of CTGWO

Tab. 12 Accuracy grade

等级	后验证差比值	小概率误差	精度结果
1	<0.35	>0.95	好
2	<0.50	>0.80	合格
3	<0.65	>0.70	勉强
4	≥0.65	≤0.70	不合格

Fig. 14 Bazimen prediction of landslide trend term

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Prediction of landslide displacement based on improved grey wolf optimizer and support vector regression

基于改进灰狼优化与支持向量回归的滑坡位移预测

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