基于WMA-SVM的边坡稳定性预测模型

孙华芬; 饶辉; 侯克鹏; 汪洪林; 王泽奇

doi:10.11858/gywlxb.20251241

基于WMA-SVM的边坡稳定性预测模型

doi: 10.11858/gywlxb.20251241

孙华芬^{1, 2,},
饶辉^{1, 2},
侯克鹏^{1, 2,*, ,},
汪洪林^{1, 2},
王泽奇^{1, 2}

1.
昆明理工大学国土资源工程学院, 云南昆明　650093
2.
云南省中-德蓝色矿山与特殊地下空间开发利用重点实验室, 云南昆明　650093

基金项目: 云南省基础研究计划面上项目（202001AT070205）；云南省“兴滇英才支持计划”青年人才专项（CG25111F287A）

详细信息

作者简介:
孙华芬（1984－），女，博士，副教授，主要从事地质灾害研究. E-mail：154221644@qq.com

通讯作者:
侯克鹏（1966－），男，博士，教授，博士生导师，主要从事安全工程、采矿工程和岩土工程研究. E-mail：1912864323@qq.com

中图分类号: TU470; TP18; O521.9
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出版历程
- 收稿日期: 2025-10-27
- 修回日期: 2026-01-22
- 录用日期: 2026-07-16
- 网络出版日期: 2026-01-27

A WMA-SVM Model for Slope Stability Prediction

SUN Huafen^{1, 2
,},
RAO Hui^{1, 2},
HOU Kepeng^{1, 2,*
, ,},
WANG Honglin^{1, 2},
WANG Zeqi^{1, 2}

1.
Faculty of Land and Resources Engineering, Kunming University of Science and Technology, Kunming 650093, Yunnan, China
2.
Yunnan Key Laboratory of Sino-German Blue Mining and Special Underground Space Development and Utilization, Kunming 650093, Yunnan, China

摘要

摘要: 为了提升数据驱动模型在边坡稳定性分类任务中的预测精度，提出了一种融合新型鲸鱼迁徙优化算法（whale migration algorithm, WMA）与支持向量机（support vector machine, SVM）的混合智能模型WMA-SVM。首先，构建了一个涵盖多种工程背景的异构边坡案例数据集。针对其显著的类别不平衡问题，采用合成少数类过采样技术（synthetic minority over-sampling technique, SMOTE）与局部异常因子（local outlier factor, LOF）算法相结合的策略，生成了高质量平衡数据集。然后，利用经8个基准测试函数验证的具有优越寻优性能的WMA算法，对SVM的超参数进行自适应寻优。模型评估结果表明，WMA-SVM在各项性能指标上均显著优于对比模型。此外，基于置换特征重要性（permutation feature importance, PFI）算法分析得出，容重、边坡角和内摩擦角是影响该数据集分类结果的关键敏感性特征。最后，通过8组独立的工程案例测试，进一步验证了模型的泛化能力，结果显示，预测与实际状态高度吻合。研究结果为边坡稳定性的智能分析提供了一种具备较好泛化潜力的建模框架。
- 边坡稳定性 /
- 机器学习 /
- 鲸鱼迁徙算法 /
- 支持向量机 /
- 不均衡数据 /
- 泛化能力
Abstract: To enhance the prediction accuracy of data-driven models in slope stability classification, this study proposes a hybrid intelligent model (WMA-SVM) that integrates a novel whale migration algorithm (WMA) with a support vector machine (SVM). First, a heterogeneous dataset of slope cases from diverse engineering backgrounds was constructed. To address its significant class imbalance, a combined strategy using the synthetic minority over-sampling technique (SMOTE) and the local outlier factor (LOF) algorithm was adopted to generate a high-quality balanced dataset. Subsequently, the WMA algorithm, which demonstrated superior optimization performance on eight benchmark test functions, was employed to optimize the hyperparameters of the SVM adaptively. Evaluation results show that the proposed WMA-SVM model significantly outperforms all benchmark models across various performance metrics. Moreover, based on the permutation feature importance (PFI) method, the unit weight, slope angle, and internal friction angle were identified as the most critical features influencing the classification outcomes for this dataset. Finally, the model’s generalization capability was further validated through eight independent engineering case studies, revealing a high consistency between the predictions and the actual stability states. This research provides a modeling framework with considerable generalization potential for the intelligent analysis of slope stability.
- slope stability /
- machine learning /
- whale migration algorithm /
- support vector machine /
- imbalanced data /
- generalization capability

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图 1 特征参数相关性分析矩阵

Figure 1. Correlation matrix of the characteristic parameters

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图 2 SVM最优超平面示意图

Figure 2. Optimal hyperplane of the SVM

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图 3 合作迁徙系统和算法优化过程

Figure 3. Cooperative migration system and its optimization

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图 4 算法收敛曲线

Figure 4. Convergence curve of the algorithm

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图 5 WMA-SVM模型的构建流程

Figure 5. Workflow of the WMA-SVM model

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图 6 WMA-SVM模型混淆矩阵

Figure 6. Confusion matrix of the WMA-SVM model

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图 7 WMA-SVM模型ROC曲线

Figure 7. ROC curves of the WMA-SVM model

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图 8 特征重要性分析

Figure 8. Feature importance analysis

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图 9 各模型混淆矩阵结果

Figure 9. Confusion matrices of the model

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表 1 边坡案例数据库

Table 1. Slope case database

No.	H/m	β/(°)	γ/(kN∙m⁻³)	c/kPa	φ/(°)	r_u	Slope state
1	10	45.0	22.4	10.0	35.0	0.40	F
2	110	41.0	27.3	14.0	31.0	0.25	S
3	115	40.0	16.0	10.0	35.0	0.35	F
4	115	40.0	16.0	70.9	20.0	0.40	F
5	135	41.0	27.3	31.5	29.7	0.25	S
6	220	30.0	26.0	150.0	45.0	0.29	S
7	289	42.0	27.0	32.0	33.0	0.25	S
8	305	47.0	31.3	68.6	37.0	0.25	F
$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\vdots $
339	320	42.6	27.0	32.0	33.0	0.29	F
340	359	42.0	27.0	35.0	35.0	0.25	S
341	420	43.0	27.0	40.0	35.0	0.25	F

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表 2 相关测试函数信息

Table 2. Specifications of the related test functions

Function name	Type	Range	Dimension	Theoretical optimum
Shifted sphere, f₁	Unimodal	[–100, 100]	30	–450
Shifted Schwefel’s 1.2, f₂	Unimodal	[–100, 100]	30	–450
Shifted rotated Elliptic, f₃	Unimodal	[–100, 100]	30	–450
Shifted Schwefel’s 1.2 with noise, f₄	Unimodal	[–100, 100]	30	–450
Shifted Rastrigin’s, f₉	Multimodal	[–5.12, 5.12]	30	–330
Shifted rotated Ackley’s, f₁₀	Multimodal	[–32, 32]	30	–140
Shifted rotated Griewank’s, f₁₁	Multimodal	[–600, 600]	30	–130
Shifted penalized function 2, f₁₃	Multimodal	[–50, 50]	30	–130

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表 3 各算法性能参数的对比

Table 3. Performance comparison of the algorithms

Model	f₁		f₂		f₃		f₄
Model	Mean	Std.	Mean	Std.	Mean	Std.	Mean	Std.
WMA	−450	5.99×10^–14	−449.964	0.062 3	−450	5.99×10^–14	4.02×10³	1.21×10³
WOA	−202.68	180.249	8.32×10⁴	1.93×10⁴	8.01×10⁷	4.15×10⁷	1.64×10⁵	6.00×10⁴
BA	−449.998	2.79×10^–4	−423.848	44.102	1.07×10⁶	7.13×10⁵	1.38×10⁵	3.71×10⁴
GWO	1.26×10³	2.40×10^–13	1.76×10⁴	3.83×10^–12	3.44×10⁷	7.85×10^–9	2.28×10⁴	0
DBO	−415.204	15.172	9.08×10³	8.35×10³	1.08×10⁷	6.50×10⁶	2.25×10⁴	7.13×10³
PSO	2.88×10³	1.87×10³	448.438	947.171	1.38×10⁷	2.70×10⁷	4.10×10³	2.16×10³

Model	f₉		f₁₀		f₁₁		f₁₃
Model	Mean	Std.	Mean	Std.	Mean	Std.	Mean	Std.
WMA	−258.493	28.566	−327.475	1.291	90.051	0.057	−129.535	0.598
WOA	−89.812	59.854	−311.632	0.767	91.910	0.466	−129.957	0.048
BA	−65.402	47.599	−310.755	0.213	802.914	71.429	−58.940	5.538
GWO	−254.179	0	−324.633	0	92.851	1.50×10^–14	−129.904	3.00×10^–14
DBO	−167.004	28.376	−324.773	3.330	91.377	0.232	−129.979	0.045
PSO	−270.576	15.705	−327.277	4.415	133.516	45.777	−129.991	0.015

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表 4 不同分类模型的性能对比

Table 4. Performance comparison of different classification models

Model	A	P	R	F_1-Score	S_AUC
WMA-SVM	0.955 8	0.955 9	0.956 3	0.955 9	0.976 6
WOA-SVM	0.897 1	0.897 1	0.897 4	0.897 0	0.931 0
SSA-SVM	0.911 8	0.913 7	0.910 8	0.911 5	0.939 0
PSO-SVM	0.867 6	0.871 1	0.866 2	0.866 9	0.886 0
GWO-SVM	0.882 4	0.893 0	0.884 8	0.881 9	0.919 0
DBO-SVM	0.838 2	0.875 0	0.842 9	0.835 4	0.869 0
BA-SVM	0.852 9	0.794 9	0.939 4	0.861 1	0.923 0

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表 5 工程实例

Table 5. Engineering examples

No.	Project name	γ/(kN∙m⁻³)	c/kPa	φ/(°)	β/(°)	H/m	r_u	Slope type	Actual state of the slope
1	Sujiaping Landslide	20.0	30	36.00	45.0	50.0	0.29	Soil	F
2	Jipaizi Landslide	27.0	35	35.00	42.0	359.0	0.29	Rock	F
3	Sichuan Kualiangzi Slope	21.0	10	30.34	30.0	30.0	0.29	Soil	S
4	Touzhai Slope in Yunnan	21.5	15	29.00	41.5	123.6	0.36	Rock	S
5	Zhongyan Village Landslide	12.0	0	30.00	45.0	8.0	0.29	Soil	F
6	Songshan Ancient Landslide	27.0	43	35.00	43.0	420.0	0.29	Rock	F
7	Huanglashi Landslide	22.0	0	40.00	33.0	8.0	0.30	Soil	S
8	Liu JiaWu Slope	27.0	32	33.00	42.2	239.0	0.29	Rock	S

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