A Deformation Prediction Method Based on Dynamic Weighted Ensemble Learning

LI Jun-bao, WANG Rui-fang

Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (8) : 168-176.

PDF(7200 KB)
PDF(7200 KB)
Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (8) : 168-176. DOI: 10.11988/ckyyb.20250577
Engineering Safety and Disaster Prevention

A Deformation Prediction Method Based on Dynamic Weighted Ensemble Learning

Author information +
History +

Abstract

[Objective] The primary objective of this study is to develop a high-precision deformation prediction method capable of effectively handling the inherent nonlinearity and dynamic variations in monitoring data. Traditional single models and static ensemble methods often struggle to adapt to the shifting data distributions and sudden changes characteristic of real-world deformation scenarios, such as landslides and structural settlements. This research aims to overcome these limitations by proposing a Dynamic Weighted Ensemble Learning (DWEL) model that intelligently integrates multiple base learners and dynamically adjusts their contributions based on recent performance, thereby enhancing prediction accuracy, robustness, and generalization ability in complex environments. [Methods] The proposed DWEL model integrates four diverse and complementary base learners: Long Short-Term Memory (LSTM) networks, Support Vector Regression (SVR), Random Forest (RF), and XGBoost. This selection ensures comprehensive feature extraction from different perspectives. The core innovation of DWEL lies in its two-stage optimization mechanism: (1) Dynamic Weighting Mechanism. A sliding window is employed to continuously track the prediction error (absolute error) of each base learner over a recent period. (2) Two-Level Fusion Strategy. A novel “weight-then-regress” hybrid fusion strategy is implemented. Experiments were conducted on two real-world deformation monitoring datasets: a landslide monitoring dataset (Dataset A) characterized by high non-stationarity and abrupt changes, and a tunnel settlement dataset (Dataset B) with relatively stable long-term trends but periodic fluctuations. The model’s performance was evaluated against single models (LSTM, SVR, RF,XGBoost) and traditional ensemble methods (Averaging, Bagging, Static Stacking) using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the Coefficient of Determination (R2). Ablation studies were performed to validate the contribution of each core component. [Results] (1) Experimental results on both datasets demonstrated the superior performance of the proposed DWEL model.On the complex Landslide Dataset A, the complete DWEL model (DWEL-2) achieved the best results with an RMSE of 2.72 mm, MAE of 2.08 mm, and R2 of 0.951. This represented a significant improvement over the best single model (LSTM: RMSE=3.92 mm, R2=0.897), reducing the prediction error by approximately 30.6%. It also outperformed traditional ensemble methods like Static Stacking (RMSE=3.52 mm, R2=0.918). Similarly, on the Tunnel Settlement Dataset B, DWEL-2 attained an RMSE of 0.63 mm, MAE of 0.52 mm, and R2 of 0.951, again surpassing all competitors and reducing the error of the best single model (LSTM) by 32.3%.(2) Analysis of the dynamic weight changes revealed the model’s adaptive capability. For instance, during the accelerated deformation phase (hours 150-160) in Dataset A, the weights of LSTM andXGBoost increased significantly, indicating their stronger ability to capture nonlinear mutations, while RF and SVR maintained higher weights during stable periods. This visual analysis confirmed that the dynamic weighting mechanism effectively allocated influence based on temporal data characteristics.(3) The impact of the sliding window length (w) was systematically analyzed. For the highly dynamic Landslide Dataset A, a medium window length (w=16) yielded the optimal balance between responsiveness and stability (RMSE=2.72 mm), whereas shorter (w=8) or longer (w=24) windows led to increased errors due to noise sensitivity or delayed response, respectively. For the more stable Tunnel Dataset B, a longer window (w=24) performed best, demonstrating the method’s adaptability to different data dynamics. (4) Ablation studies conclusively proved the necessity of both innovative components. Using static weights instead of dynamic weighting increased the RMSE on Dataset A by 15.8% compared to the full DWEL-2 model. Using only the meta-learner without dynamic weights performed similarly to Static Stacking. Furthermore, the two-level fusion (DWEL-2) provided an 11.7% reduction in RMSE compared to using only dynamic weighted averaging (DWEL-1), highlighting the significant contribution of the regression-based residual correction in the second fusion layer. [Conclusions] This study successfully developed and validated a novel Dynamic Weighted Ensemble Learning (DWEL) model for deformation prediction. The key innovations include: 1) A dynamic weighting mechanism based on sliding window error feedback, which effectively addresses the lag issue of static ensemble methods during data distribution shifts, improving response speed at mutation points by over 60%; and 2) A two-level “weighted average followed by regression” fusion strategy that synergizes rapid dynamic adaptation with enhanced non-linear fitting capability, reducing prediction errors by an additional 11.7% compared to single-level fusion.The experimental results robustly demonstrate that the DWEL model significantly outperforms existing single and traditional ensemble models across different deformation scenarios (landslide and tunnel settlement). It exhibits remarkable accuracy, robustness, and generalization ability, particularly during critical periods of trend mutation. The method provides an effective, reliable, and high-precision prediction tool for geological hazard early warning and structural health monitoring. Future work will focus on the adaptive optimization of the weighting function and the integration of multi-physics field coupling modeling to further enhance prediction reliability in even more complex environments.

Key words

dynamic weighted ensemble learning / deformation prediction / time series prediction / model fusion / sliding window

Cite this article

Download Citations
LI Jun-bao , WANG Rui-fang. A Deformation Prediction Method Based on Dynamic Weighted Ensemble Learning[J]. Journal of Changjiang River Scientific Research Institute. 2026, 43(8): 168-176 https://doi.org/10.11988/ckyyb.20250577

References

[1]
朱小韦, 袁占良, 李宏超. 基于BP-PCA-WCA-SVM的混凝土大坝变形预测方法[J]. 长江科学院院报, 2024, 41(9): 138-145.
(Zhu Xiaowei, Yuan Zhanliang, Li Hongchao. A Method of Predicting Concrete Dam Deformation Based on BP-PCA-WCA-SVM[J]. Journal of Changjiang River Scientific Research Institute, 2024, 41(9): 138-145. (in Chinese))
[2]
赵奇. 基于GNSS和InSAR技术的矿区建筑物形变监测[J]. 测绘通报, 2024(11):126-132,166.
Abstract
矿区建筑物是煤矿生产的重要组成部分,一旦发生危险变形,会严重威胁到煤矿的正常生产,甚至造成安全事故。为了实现高精度的矿区建筑物形变监测,本文提出了融合GNSS和InSAR技术建筑物形变监测方法,以提高时序形变监测结果精度。以内蒙古锡林浩特市北郊矿区建筑物为例,采用30景Sentinel-1A卫星影像数据和35个站点GNSS数据,获取了地表时序形变。试验结果表明,GNSS-InSAR融合监测结果比InSAR监测结果精度高43.9%,能更好地为矿区建筑物形变监测与安全评估服务。结合降水量、温度数据分析表明,温度是矿区建筑形变的主要原因,周边采动对矿区建筑物的直接影响较小。此外,在监测周期内,矿区所有建筑物的各项变形阈值均小于允许变形值,未发生危险变形,可以继续安全运营。
(Zhao Qi. Monitoring of Deformation in Mining Buildings Based on GNSS and InSAR Technologies[J]. Bulletin of Surveying and Mapping, 2024(11): 126-132, 166. (in Chinese))
Mining area buildings are critical components of coal mining production. Dangerous deformations can severely threaten normal production and may even lead to safety incidents. In this study, the GNSS-InSAR fusion method is proposed to achieve high-precision deformation monitoring of mining area buildings. Taking the northern suburbs mining area of Xilinhot city,Inner Mongolia, as the study area, the dynamic deformation of mining buildings is obtained based on the GNSS,SBAS-InSAR, and GNSS-InSAR fusion methods with 30 scenes of Sentinel-1A image data and 35 sites GNSS data. The results show that the GNSS-InSAR fusion method is 43.9% more accurate than the SBAS-InSAR,which indicates that the proposed method provides better support for the deformation monitoring and safety assessment of mining area buildings. The combination of rainfall,temperature,and time-series deformation results inferred that temperature is the primary cause of building deformation,and the impact of surrounding mining activities on the buildings is negligible. Moreover,during the monitoring period, all deformation values of the mining area buildings are below the permissible deformation thresholds.The results indicate no dangerous deformations and confirm that the buildings can continue safe operations.
[3]
Shao P, Wang H, Long G, et al. A Novel Multi-step Ahead Prediction Method for Landslide Displacement Based on Autoregressive Integrated Moving Average and Intelligent Algorithm[J]. Engineering Applications of Artificial Intelligence, 2024, 137: 109107.
[4]
高如, 赵翌博, 曹文昱, 等. 城市更新深基坑工程动态监测及变形预测研究综述[J]. 水利水电技术(中英文), 2025, 56(增刊2): 15-17.
(Gao Ru, Zhao Yibo, Cao Wenyu, et al. Dynamic Monitoring and Deformation Prediction in Deep Foundation Pit Engineering for Urban Renewal Research Overview[J]. Water Resources and Hydropower Engineering, 2025, 56(S2): 15-17. (in Chinese))

An in-depth review of the current state of dynamic monitoring and deformation prediction technologies was offered for deep foundation pit engineering within the context of urban renewal. Various aspects were explored such as the evolution of monitoring technology, innovations in data processing method, the diversity of prediction models, and the challenges and solutions encountered in practical applications. By consolidating relevant research findings from both domestic and international sources, a theoretical foundation and technical support were provided for the safe execution of deep foundation pit engineering in future urban renewal projects, thereby fostering further advancements in this field's technology.

[5]
Xu Y, Zhao Y, Jiang Q, et al. Machine-learning-based Deformation Prediction Method for Deep Foundation-pit Enclosure Structure[J]. Applied Sciences, 2024, 14(3):1273.
[6]
Liu R, Zhang Q, Jiang F, et al. Research on Deformation Prediction of VMD-GRU Deep Foundation Pit Based on PSO Optimization Parameters[J]. Materials, 2024, 17(10): 2198.
[7]
王震豪, 聂闻, 许汉华, 等. 基于EEMD-Prophet-LSTM的滑坡位移预测[J]. 中国科学院大学学报, 2023, 40(4): 514-522.
(Wang Zhenhao, Nie Wen, Xu Hanhua, et al. Prediction of Landslide Displacement Based on EEMD-prophet-LSTM[J]. Journal of University of Chinese Academy of Sciences, 2023, 40(4): 514-522. (in Chinese))
[8]
王瑞婕, 包腾飞, 李扬涛, 等. 基于多因子融合和Stacking集成学习的大坝变形组合预测模型[J]. 水利学报, 2023, 54(4): 497-506.
(Wang Ruijie, Bao Tengfei, Li Yangtao, et al. Combined Prediction Model of Dam Deformation Based on Multi-factor Fusion and Stacking Ensemble Learning[J]. Journal of Hydraulic Engineering, 2023, 54(4): 497-506. (in Chinese))
[9]
冯子强, 李登华, 丁勇. 基于Blending-Clustering集成学习的大坝变形预测模型[J]. 水利水电技术(中英文), 2024, 55(4): 59-70.
(Feng Ziqiang, Li Denghua, Ding Yong. Dam Deformation Prediction Model Based on Blending-clustering Ensemble Learning[J]. Water Resources and Hydropower Engineering, 2024, 55(4): 59-70. (in Chinese))
[10]
Huang C, Zhou L, Liu F, et al. Deformation Prediction of Dam Based on Optimized Grey Verhulst Model[J]. Mathematics, 2023, 11(7): 1729.
[11]
郝泽嘉, 施玉群, 成博超, 等. 基于PSO-LSTM的大坝变形组合预测模型[J]. 长江科学院院报, 2025, 42(5):208-214,222.
Abstract
传统的大坝变形预测模型难以反映效应量与环境量之间存在的复杂非线性关系,预测效果常常不够理想。考虑到LSTM模型具有较强的非线性学习能力,PSO模型具有优越的全局寻优能力,将PSO应用于LSTM超参数全局寻优之中,建立基于PSO-LSTM的大坝变形组合预测模型,既可以解决传统预测模型在描述非线性特性方面的不足,又可以提高LSTM超参数取值的合理性,并为提升大坝变形预测精度提供一种新思路。运用所提出的方法,以某混凝土重力坝和某混凝土拱坝实测水平位移为例,进行了实例研究。研究结果表明,所提出的PSO-LSTM组合模型在模型的RMSE、MAE和R<sup>2</sup>等指标方面均优于单纯的LSTM模型和传统的监测统计模型,在3种预测模型中,PSO-LSTM组合模型的预测效果更优。
(Hao Zejia, Shi Yuqun, Cheng Bochao, et al. A Combined PSO-LSTM Prediction Model for Dam Deformation[J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(5): 208-214, 222. (in Chinese))
[12]
柳磊, 李登华, 丁勇. 基于VMD-KSVD字典学习降噪的大坝变形预测[J]. 大地测量与地球动力学, 2024, 44(9):951-958,984.
(Liu Lei, Li Denghua, Ding Yong. Dam Deformation Prediction Based on VMD and KSVD Dictionary Learning Noise Reduction[J]. Journal of Geodesy and Geodynamics, 2024, 44(9):951-958,984. (in Chinese))
[13]
刘天翼, 艾星星, 张九丹. 基于MLR-DE-LSTM的大坝变形串联组合预测模型[J]. 中国农村水利水电, 2025(2):207-212.
(Liu Tianyi, Ai Xingxing, Zhang Jiudan. Dam Deformation Serial Combined Prediction Model Based on MLR-DE-LSTM[J]. China Rural Water and Hydropower, 2025(2): 207-212. (in Chinese))
[14]
Wu Y, Kang F, Zhu S, et al. Data-driven Deformation Prediction Model for Super High Arch Dams Based on a Hybrid Deep Learning Approach and Feature Selection[J]. Engineering Structures, 2025, 325:119483.
[15]
Chen S, Gu C, Lin C, et al. Prediction of Arch Dam Deformation via Correlated Multi-target Stacking[J]. Applied Mathematical Modelling, 2021, 91: 1175-1193.
[16]
邓思源, 周兰庭, 王飞, 等. 大坝变形的XGBoost-LSTM变权组合预测模型及应用[J]. 长江科学院院报, 2022, 39(10): 72-79.
Abstract
为了实现更高精度的大坝变形预报,提出了一种大坝变形的XGBoost-LSTM变权组合预测模型,即首先引入XGBoost模型和LSTM模型对大坝变形分别进行分析预测,然后采用变权组合方法将二者的分析预测结果进行有机融合,进而得到最终预测结果。以某混凝土重力坝为例,首先通过与随机森林、ELMAN以及逐步回归分析各模型的对比研究,论证了XGBoost与LSTM应用于大坝变形预测的优越性;进一步地,XGBoost与LSTM的变权组合预测效果相较于各单一模型取得了较大程度的提升,且相较于二者的等值赋权组合提升优势更加显著,变形预测结果与工程实际情况更加吻合,具有较好的适用性和可推广价值。
(Deng Siyuan, Zhou Lanting, Wang Fei, et al. XGBoost-LSTM Combinatorial Model with Variable Weight for Dam Deformation Prediction and Its Application[J]. Journal of Yangtze River Scientific Research Institute, 2022, 39(10): 72-79. (in Chinese))
A XGBoost-LSTM combinatorial model with variable weight is proposed to more accurately predict dam deformation. First,the XGBoost (eXtreme Gradient Boosting) model and LSTM (Long Short-Term Memory) model are introduced to analyze and predict the dam deformation respectively,and then the results of the two models are combined by using variable weight combination method to obtain the final prediction result. With a concrete gravity dam as a case study,the advantages of XGBoost and LSTM models in dam deformation prediction are demonstrated respectively through comparison with those of random forest,ELMAN and stepwise regression analysis models;furthermore,the prediction effect of the combinatorial model is verified to have enhanced remarkably compared with each of the single model and the equivalent-weighted XGBoost-LSTM combinatarial model. The deformation prediction results are more consistent with the actual engineering situation,thus is well applicable and popularizable.
[17]
Liu L, Cao X, Wang H, et al. Optimization of Model Parameters and Hyperparameters in Deep Learning Models for Spatial Interaction Prediction[J]. Expert Systems with Applications, 2025, 266: 126160.
PDF(7200 KB)

Accesses

Citation

Detail

Sections
Recommended

/