基于WOA-RF的边坡稳定性预测模型

张建涛; 刘志祥; 张双侠; 郭腾飞; 袁丛祥

doi:10.11858/gywlxb.20230837

基于WOA-RF的边坡稳定性预测模型

doi: 10.11858/gywlxb.20230837

中南大学资源与安全工程学院, 湖南长沙　410083

基金项目: 国家重点研发计划项目（2022YFC2904101）；国家自然科学基金（52374107，51974359）

详细信息

作者简介:
张建涛（2000－），男，硕士研究生，主要从事机器学习与边坡稳定性研究. E-mail：215512079@csu.edu.cn

通讯作者:
刘志祥（1967－），男，博士，教授，主要从事采矿工程与岩石力学研究. E-mail：liulzx@csu.edu.cn

中图分类号: O347; TU457
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出版历程
- 收稿日期: 2023-12-25
- 修回日期: 2024-01-19
- 录用日期: 2024-01-26
- 刊出日期: 2024-06-03

Slope Stability Prediction Based on WOA-RF Hybrid Model

School of Resources and Safety Engineering, Central South University, Changsha 410083, Hunan, China

摘要

摘要: 为有效地预测边坡稳定性和预防边坡失稳事故的发生，提出了鲸鱼优化算法（whale optimization algorithm，WOA）和随机森林（random forest，RF）相结合的混合模型WOA-RF；基于所收集的边坡案例，采用混淆矩阵的分类性能指标和受试者工作特征曲线及线下面积评估混合模型WOA-RF的分类和泛化性能；使用WOA对4种广泛应用的机器学习模型进行优化，并将优化后的机器学习模型与WOA-RF模型进行对比分析。结果表明：WOA可以有效地优化超参数和提升模型性能；最优WOA-RF模型在训练集和测试集上的准确率分别为0.99和0.94，优化后，准确率、精确率、召回率、精确率和召回率的加权平均值分别提升了11.9%、19.0%、4.8%和11.9%；对比分析各个模型的预测性能后发现，WOA-RF模型的各项指标均优于其他模型；确定了特征重要性排序，发现容重是影响边坡稳定性的最敏感特征。WOA-RF模型可有效地预测边坡稳定性，预测结果可为防护措施的制定提供依据。
- 边坡稳定性预测 /
- 机器学习 /
- 鲸鱼优化算法 /
- 随机森林 /
- 特征重要性
Abstract: To effectively predict slope stability and prevent slope instability occurrence, a hybrid model WOA-RF, combining whale optimization algorithm (WOA) and random forest (RF) was proposed. Based on the collected slope cases, the classification and generalization performance of the model was evaluated according to the classification performance indicators given by the confusion matrix and the area under the receiver operating characteristic curve. Additionally, WOA was used to optimize four widely used machine learning models, and the optimized machine learning models were compared with WOA-RF. The results demonstrate that WOA is effective in optimizing hyperparameters and improving model performance. The optimal WOA-RF model achieves an accuracy of 0.99 on training set and of 0.94 on test set. After optimization, the accuracy, the precision, the recall, and the hamonic mean of the precision and recall are increased by 11.9%, 19.0%, 4.8%, and 11.9%, respectively. Comparative analysis reveals that the WOA-RF model is superior to the others in all indicators. Furthermore, the feature importance ranking was determined. Analysis of the feature importance indicates that unit weight is the most sensitive feature affecting slope stability. The established WOA-RF model is proved effective in predicting slope stability and facilitating the development of appropriate protective measures based on the predicted results.
- slope stability prediction /
- machine learning /
- whale optimization algorithm /
- random forest /
- feature importance

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图 1 边坡特征参数

Figure 1. Slope parameters

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图 2 特征散点分布和相关系数

Figure 2. Scatter distribution and correlation coefficient of dataset

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图 3 混淆矩阵

Figure 3. Confusion matrix

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图 4 交叉验证和适应度函数计算步骤

Figure 4. Cross validation and fitness function calculation process

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图 5 WOA-RF模型构建流程

Figure 5. WOA-RF model construction process

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图 6 不同种群数量下优化过程中适应度的变化曲线

Figure 6. Fitness variation for different population size during optimization process

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图 7 WOA-RF模型在训练集和测试集上的混淆矩阵和分类性能指标

Figure 7. Confusion matrix and classification performance of WOA-RF model for training and test sets

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图 8 WOA-RF模型在训练集和测试集上的ROC曲线

Figure 8. ROC curves of WOA-RF model for training and test sets

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图 9 各模型在测试集上的ROC曲线

Figure 9. ROC curves of different models for the test set

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图 10 各模型分类性能指标雷达图

Figure 10. Radar chart of performance indicators for different models

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图 11 特征重要性分值（重复次数：100）

Figure 11. Feature importance score (iteration: 100)

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表 1 数据集描述性统计

Table 1. Data set descriptive statistics

Feature	γ/(kN∙m⁻³)	c/kPa	ϕ/(°)	Φ/(°)	H/m	r_u/kPa	S
Max	31.30	300.00	45.00	59.00	511.00	0.50	1.0
Min	12.00	0	0	16.00	3.60	0	0
Mean	21.76	34.12	28.73	36.10	104.19	0.22	0.5
Median	20.96	19.96	30.24	35.00	50.00	0.25
Standard deviation	4.15	45.96	10.61	10.25	133.08	0.16

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表 2 WOA-RF模型参数设置

Table 2. Parameter settings in WOA-RF model

Title	n_estimators	N_{max_features}	D_{max_depth}	N_{min_samples_leaf}	N_{min_samples_split}	Criterion
Range	[1, 500]	[1, 6]	[1, 30]
Optimized value	167	3	11	1	2	Gini

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表 3 各模型优化前后的 $A_{\mathrm{cc}}$ 和 $F_{\mathrm{1\text{-}score}}$

Table 3. $A_{\mathrm{cc}}$ and $F_{\mathrm{1\text{-}score}}$ before and after optimization

Model	A_cc	F_1-score	Model	A_cc	F_1-score
KNN	0.76	0.76	WOA-KNN	0.82	0.82
SVM	0.80	0.80	WOA-SVM	0.85	0.84
ANN	0.53	0.52	WOA-ANN	0.80	0.79
DT	0.71	0.71	WOA-DT	0.75	0.75
RF	0.84	0.84	WOA-RF	0.94	0.94

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表 4 各模型优化后分类性能指标及排名

Table 4. Classification performance and ranking of models after optimization

Model	A_cc	A_cc rank	P_re	P_re rank	R_e	R_e rank	F_1-score	F_1-score rank	Total score
WOA-KNN	0.82	3	0.82	2	0.82	3	0.82	3	11
WOA-SVM	0.84	4	0.85	4	0.84	4	0.84	4	16
WOA-ANN	0.80	2	0.83	3	0.76	2	0.79	2	9
WOA-DT	0.75	1	0.75	1	0.72	1	0.73	1	4
WOA-RF	0.94	5	1.00	5	0.88	5	0.94	5	20

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