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
计量
- 文章访问数: 63
- HTML全文浏览量: 24
- PDF下载量: 15
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

HTML全文

图 1 边坡特征参数

Figure 1. Slope parameters

下载: 全尺寸图片幻灯片

图 2 特征散点分布和相关系数

Figure 2. Scatter distribution and correlation coefficient of dataset

下载: 全尺寸图片幻灯片

图 3 混淆矩阵

Figure 3. Confusion matrix

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

图 5 WOA-RF模型构建流程

Figure 5. WOA-RF model construction process

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

图 10 各模型分类性能指标雷达图

Figure 10. Radar chart of performance indicators for different models

下载: 全尺寸图片幻灯片

图 11 特征重要性分值（重复次数：100）

Figure 11. Feature importance score (iteration: 100)

下载: 全尺寸图片幻灯片

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

参考文献(25)

[1]	陈昌富, 李伟, 张嘉睿, 等. 山区公路边坡工程智能分析与设计研究进展 [J]. 湖南大学学报 (自然科学版), 2022, 49(7): 15–31. CHEN C F, LI W, ZHANG J R, et al. State-of-the-art of intelligent analysis and design in slope engineering of highways in mountainous areas [J]. Journal of Hunan University (Natural Sciences), 2022, 49(7): 15–31.
[2]	何丽平, 汪晓俊, 郭剑雄, 等. 砂泥岩互层岩质边坡爆破振动衰减规律现场试验研究 [J]. 高压物理学报, 2023, 37(5): 055301. HE L P, WANG X J, GUO J X, et al. Field experimental research on blasting vibration attenuation law of sand-mudstone interbedded rock slope [J]. Chinese Journal of High Pressure Physics, 2023, 37(5): 055301.
[3]	LIN Y, ZHOU K P, LI J L. Prediction of slope stability using four supervised learning methods [J]. IEEE Access, 2018, 6: 31169–31179. doi: 10.1109/ACCESS.2018.2843787
[4]	KURTZ W, LAPIN A, SCHILLING O S, et al. Integrating hydrological modelling, data assimilation and cloud computing for real-time management of water resources [J]. Environmental Modelling & Software, 2017, 93: 418–435.
[5]	杨杰, 马春辉, 程琳, 等. 高陡边坡变形及其对坝体安全稳定影响研究进展 [J]. 岩土力学, 2019, 40(6): 2341–2353, 2368. YANG J, MA C H, CHENG L, et al. Research advances in the deformation of high-steep slopes and its influence on dam safety [J]. Rock and Soil Mechanics, 2019, 40(6): 2341–2353, 2368.
[6]	DONG L J, WESSELOO J, POTVIN Y, et al. Discrimination of mine seismic events and blasts using the Fisher classifier, naive Bayesian classifier and logistic regression [J]. Rock Mechanics and Rock Engineering, 2016, 49(1): 183–211. doi: 10.1007/s00603-015-0733-y
[7]	QI C C, TANG X L. A hybrid ensemble method for improved prediction of slope stability [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2018, 42(15): 1823–1839. doi: 10.1002/nag.2834
[8]	张凯, 张科. 基于LightGBM算法的边坡稳定性预测研究 [J]. 中国安全科学学报, 2022, 32(7): 113–120. ZHANG K, ZHANG K. Prediction study on slope stability based on LightGBM algorithm [J]. China Safety Science Journal, 2022, 32(7): 113–120.
[9]	武梦婷, 陈秋松, 齐冲冲. 基于机器学习的边坡安全稳定性评价及防护措施 [J]. 工程科学学报, 2022, 44(2): 180–188. WU M T, CHEN Q S, QI C C. Slope safety, stability evaluation, and protective measures based on machine learning [J]. Chinese Journal of Engineering, 2022, 44(2): 180–188.
[10]	LIN S, ZHENG H, HAN B, et al. Comparative performance of eight ensemble learning approaches for the development of models of slope stability prediction [J]. Acta Geotechnica, 2022, 17(4): 1477–1502. doi: 10.1007/s11440-021-01440-1
[11]	KARIR D, RAY A, KUMAR BHARATI A, et al. Stability prediction of a natural and man-made slope using various machine learning algorithms [J]. Transportation Geotechnics, 2022, 34: 100745. doi: 10.1016/j.trgeo.2022.100745
[12]	陈光耀, 汪明武, 金菊良. 基于CMFOA-SVM的边坡稳定性评价模型 [J]. 长江科学院院报, 2023, 40(2): 95–101. CHEN G Y, WANG M W, JIN J L. CMFOA-SVM model for evaluating slope stability [J]. Journal of Changjiang River Scientific Research Institute, 2023, 40(2): 95–101.
[13]	QI C C, TANG X L. Slope stability prediction using integrated metaheuristic and machine learning approaches: a comparative study [J]. Computers & Industrial Engineering, 2018, 118: 112–122.
[14]	BREIMAN L. Random forests [J]. Machine Learning, 2001, 45(1): 5–32. doi: 10.1023/A:1010933404324
[15]	MIRJALILI S, LEWIS A. The whale optimization algorithm [J]. Advances in Engineering Software, 2016, 95: 51–67. doi: 10.1016/j.advengsoft.2016.01.008
[16]	LIN S, ZHENG H, HAN C, et al. Evaluation and prediction of slope stability using machine learning approaches [J]. Frontiers of Structural and Civil Engineering, 2021, 15(4): 821–833. doi: 10.1007/s11709-021-0742-8
[17]	KHAJEHZADEH M, KEAWSAWASVONG S. Predicting slope safety using an optimized machine learning model [J]. Heliyon, 2023, 9(12): e23012. doi: 10.1016/j.heliyon.2023.e23012
[18]	LU P, ROSENBAUM M S. Artificial neural networks and grey systems for the prediction of slope stability [J]. Natural Hazards, 2003, 30(3): 383–398. doi: 10.1023/B:NHAZ.0000007168.00673.27
[19]	SUN J L, WU S C, ZHANG H J, et al. Based on multi-algorithm hybrid method to predict the slope safety factor-stacking ensemble learning with Bayesian optimization [J]. Journal of Computational Science, 2022, 59: 101587.
[20]	YAN X M, LI X B. Bayes discriminant analysis method for predicting the stability of open pit slope [C]//2011 International Conference on Electric Technology and Civil Engineering (ICETCE). Lushan: IEEE, 2011: 147–150.
[21]	HOANG N D, PHAM A D. Hybrid artificial intelligence approach based on metaheuristic and machine learning for slope stability assessment: a multinational data analysis [J]. Expert Systems with Applications, 2016, 46: 60–68. doi: 10.1016/j.eswa.2015.10.020
[22]	SAH N K, SHEOREY P R, UPADHYAYA L N. Maximum likelihood estimation of slope stability [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1994, 31(1): 47–53.
[23]	STONE M. Cross-validatory choice and assessment of statistical predictions [J]. Journal of the Royal Statistical Society: Series B (Methodological), 1974, 36(2): 111–133. doi: 10.1111/j.2517-6161.1974.tb00994.x
[24]	LIU Z D, LI D Y. Intelligent hybrid model to classify failure modes of overstressed rock masses in deep engineering [J]. Journal of Central South University, 2023, 30(1): 156–174. doi: 10.1007/s11771-022-5208-1
[25]	GUYON I, GUNN S, NIKRAVESH M, et al. Feature extraction: foundations and applications (studies in fuzziness & soft computing) [M]. Berlin, Heidelberg: Springer-Verlag, 2006.