Application of integrated model based on EEMD-CNN-LSTM for landslide-displacement prediction
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摘要: 滑坡位移预测是滑坡稳定性评价的重要环节。尽管基于深度学习范式的时间序列方法预测滑坡位移取得了一定的成果，但由于滑坡位移数据的非平稳性、周期性和趋势性变化特征，导致当前时间序列模型的滑坡位移的多变量预测容易过拟合。为解决这一问题，针对滑坡位移数据的波动性和由周期项与趋势项位移叠加组成的特性，提出一种基于孤立森林(Isolation Forest，IF)异常检测、集成经验模态分解(Ensemble Empirical Mode Decomposition，EEMD)、卷积神经网络（Convolutional Neural Networks，CNN）和长短期记忆神经网络(Long Short-Term Memory，LSTM) 相结合的滑坡位移预测模型。选择三峡库区以降雨为影响因子的阶跃型白家包滑坡为研究对象，引入IF算法对滑坡原始位移数据进行异常检测，使用EEMD方法提取滑坡趋势项和周期项位移，通过CNN捕捉局部周期项和趋势模式，并基于LSTM模型预测总体位移。结果表明，EEMD-CNN-LSTM在预测降雨情况时滑坡总体位移的均方根误差（RMSE）、平均绝对误差（MAE）、评价绝对百分比误差（MAPE）和决定系数（R2）4种指标分别为0.4190、0.3139、0.2379和0.9997，前3种精度评价指标较现有模型分别提升32.3%、25.1%、7.3%。相较于传统的LSTM模型、随机森林方法和EEMD-LSTM方法，EEMD-CNN-LSTM模型在有、无降雨这一外部影响因素下具有显著优势，能够较大地降低过拟合，提高预测的准确性。Abstract:
Objective Landslide-displacement prediction is critical when evaluating landslide stability. Despite the achievements of time-series methods based on deep-learning paradigms in predicting landslide displacement, the nonstationary, periodic, and trending characteristics of landslide displacement data cause multivariate predictions of current time-series models to easily overfit. Existing studies primarily focus on improving single models, whereas systematic studies pertaining to multimodel integration methods are scarce. This study aims to develop an integrated model that addresses these challenges and improves prediction accuracy. Methods Considering the volatility of landslide-displacement data and the combined characteristics of their periodic and trending displacement components, a landslide-displacement prediction model combining isolation forest (IF) anomaly detection, ensemble empirical mode decomposition (EEMD), convolutional neural networks (CNNs), and long short-term memory (LSTM) neural networks is proposed. The stepped Baijiabao landslide in the Three Gorges Reservoir area, which is affected by rainfall, is investigated in this study. First, the IF algorithm is introduced to detect anomalies in the original landslide-displacement data. This enables outliers, which can distort the prediction results, to be identified and excluded. Subsequently, EEMD is adopted to decompose the displacement data into intrinsic mode functions (IMFs), which represent the underlying periodic and trend components. This decomposition allows one to analyze the inherent characteristics of the data more comprehensively. Next, a CNN is employed to capture local periodic and trend patterns within the IMFs. CNNs are particularly effective in recognizing spatial patterns and features, thus rendering them suitable for identifying complex patterns in the displacement data. Finally, the overall displacement is predicted using the LSTM model, which is suitable for accommodating sequential data and capturing long-term dependencies. These techniques are integrated to leverage their respective strengths, thereby improving the prediction accuracy. Result The results indicate that the root-mean-square error（RMSE）, mean absolute error（MAE）, absolute percentage error in evaluation (MAPE), and determination coefficient（R2）indices of the EEMD-CNN-LSTM model for predicting the overall landslide displacement under rainfall conditions are 0.4190, 0.3139, 0.2379, and 0.9997, respectively, which signify improvements in the accuracy of the first three evaluation indices by 32.3%, 25.1%, and 7.3%, respectively, compared with those of existing models. This significant improvement demonstrates the model’s robustness in accommodating the complexities of landslide-displacement data under varying conditions. For predictions without rainfall, the RMSE, MAE, MAPE, and R2 indices are 0.4302, 0.2908, 0.2431, and 0.9996, respectively, which signify improvements in the accuracy of the first three indices by 31.2%, 31.7%, and 8.7%, respectively, compared with those of existing models. These results highlight the model’s high generalizability across different scenarios, as it can maintain high prediction accuracies regardless of external influencing factors such as rainfall. Compared with conventional LSTM, random forest, and EEMD-LSTM models, the EEMD-CNN-LSTM model offers significant advantages under the influence of rainfall and without rainfall, thus significantly reducing overfitting and improving the prediction accuracy. The hybrid approach effectively captures the intricate patterns in the data, which cannot be achieved by single models. Conclusion In summary, the multimodel integration method based on IF anomaly detection, EEMD decomposition, local-feature capturing by the CNN, and overall prediction by LSTM significantly improves the accuracy of landslide-displacement prediction, particularly under the influence of rainfall. The integrated model not only addresses the overfitting issues typically encountered in time-series prediction models but also enhances the model’s robustness and reliability. The combination of IF for anomaly detection ensures that outliers do not skew the prediction results, whereas EEMD facilitates the decomposition of data into meaningful components. The CNN’s ability to capture local patterns, coupled with the LSTM’s strength in modeling long-term dependencies, enables the establishment of a comprehensive framework that can effectively accommodate the complexities of landslide displacement data.[ Significance ]This study provides an effective multimodel integration method for landslide-displacement prediction, which addresses the overfitting issues in existing models as well as offers substantial scientific significance and practical value. The proposed model’s ability to accurately predict landslide displacement under varying conditions is extremely beneficial to the stability evaluation of landslide-prone areas, thereby contributing to disaster prevention and mitigation efforts. The innovation is based on the systematic integration of anomaly detection, data decomposition, and advanced neural-network techniques, which results in a robust framework that outperforms conventional methods. The findings of this study are applicable to real-world scenarios, thereby enhancing the accuracy and reliability of landslide monitoring systems and supporting informed decision-making in hazard management and infrastructure development. -
图 2 LSTM网络结构
注：ht-1—上一时刻的输出；ht—当前时刻的输出；ct-1—上一时刻状态；ct—当前状态；xt—当前输入；it—输入门；ft—遗忘门；ot—输出门
Figure 2. LSTM network architecture
Note：ht-1−output of previous moment; ht−output of current moment; ct-1−previous-moment-status; ct−current status; xt−current input; it−input gate; ft−forget gate; ot−output gate.
图 3 基于EEMD-CNN-LSTM模型的滑坡位移预测流程图
Figure 3. Flow chart of landslide-displacement prediction based on EEMD-CNN-LSTM model
图 4 白家包滑坡及布设点位示意图
Figure 4. Schematic illustration of Baijiabao landslide and laying point
图 6 数据预处理
a—异常值检测；b—异常值剔除
Figure 6. Data preprocessing:
(a) Outlier detection; (b) Outlier culling
图 7 EMD与EEMD模型的分解结果对比
a—EMD模型；b—EEMD模型
Figure 7. Comparison of decomposition results between EMD and EEMD:
(a) EMD model; (b) EEMD model
图 8 EEMD-CNN-LSTM模型对滑坡位移趋势项的预测结果
a—降雨情况下；b—无降雨情况下
Figure 8. Prediction results of EEMD-CNN-LSTM model for displacement-trend terms of landslide:
(a) With rainfall; (b) Without rainfall
图 9 EEMD-CNN-LSTM模型对滑坡位移周期项的预测结果
a—降雨情况下；b—无降雨情况下
Figure 9. Prediction results of EEMD-CNN-LSTM model for landslide-periodic displacement:
(a) With rainfall; (b) Without rainfall
图 10 EEMD-CNN-LSTM模型与EEMD-LSTM模型对滑坡位移趋势项预测结果对比
a—EEMD-CNN-LSTM模型；b—EEMD-LSTM模型
Figure 10. Prediction results of EEMD-CNN-LSTM and EEMD-LSTM models for displacement-trend terms of landslide:
(a) EEMD-CNN-LSTM model; (b) EEMD-LSTM model
图 11 EEMD-CNN-LSTM模型与EEMD-LSTM模型对滑坡位移周期项预测结果对比
a—EEMD-CNN-LSTM模型；b—EEMD-LSTM模型
Figure 11. Prediction results of EEMD-CNN-LSTM and EEMD-LSTM models for landslide periodic displacement
(a) EEMD-CNN-LSTM model; (b) EEMD-LSTM model
图 12 EEMD-CNN-LSTM模型对白家包滑坡位移预测结果
Figure 12. Landslide-displacement prediction results of EEMD-LSTM model
图 13 EEMD-CNN-LSTM模型、EEMD-LSTM模型和LSTM模型以及随机森林模型对滑坡位移预测结果与真实值的对比（ZD1监测点）
a—有降雨情况下；b—无降雨情况下
Figure 13. Prediction results of EEMD-CNN-LSTM, EEMD-LSTM, LSTM, and random-forest models for ZD1
(a) With rainfall; (b) Without rainfall
图 14 EEMD-CNN-LSTM模型、EEMD-LSTM模型、LSTM模型和随机森林模型对滑坡位移预测结果与真实值的对比（ZD2监测点）
a—有降雨情况下；b—无降雨情况下
Figure 14. Prediction results of EEMD-CNN-LSTM, EEMD-LSTM, LSTM, and random-forest models for ZD2
(a) With rainfall; (b) Without rainfall
表 1 ZD2监测点EEMD-CNN-LSTM模型、EEMD-LSTM模型、LSTM模型和随机森林模型对滑坡位移预测结果的性能评价
Table 1. Performance evaluation of ZD2 prediction results for EEMD-CNN-LSTM, EEMD-LSTM, LSTM, and random-forest models (with/without rainfall)
模型类型 RMSE/mm MAE/mm MAPE/% R2 EEMD-CNN-LSTM 0.4302/0.4190 0.2908/0.3139 0.2431/0.2379 0.9996/0.9997 EEMD-LSTM 0.6249/0.6187 0.4259/0.4193 0.2642/0.2567 0.9983/0.9983 LSTM 1.9925/3.4102 1.3365/2.7297 0.7888/1.5778 0.9812/0.9449 随机森林 0.8391/1.0329 0.6365/0.7316 0.5078/0.5762 0.9890/0.9885 注：“/”前为降雨下的结果；“/”后为无降雨下的结果 
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