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Article(id=1322506476480999551, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322506406058635943, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2024.12.548, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1733068800000, receivedDateStr=2024-12-02, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793239714974, onlineDateStr=2026-10-29, pubDate=1763136000000, pubDateStr=2025-11-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793239714974, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793239714974, creator=13701087609, updateTime=1793239714974, updator=13701087609, issue=Issue{id=1322506406058635943, tenantId=1146029695717560320, journalId=1281212831689347082, year='2025', volume='45', issue='11', pageStart='1101', pageEnd='1210', issueExtLink='null', onlineDate='null', pubDate='1763136000000', pubDateStr='2025-11-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793239698184, creator='13701087609', updateTime=1793239698184, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=1171, endPage=1179, ext={EN=ArticleExt(id=1322506476803960961, articleId=1322506476480999551, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=The Coupled Secondary Mode Decomposition and Optimized LightGBM Model for Dam Deformation Prediction, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

A dam deformation prediction model is proposed that integrates secondary mode decomposition with butterfly optimization algorithm(BOA)-optimized light gradient boosting machine(LightGBM). First, the training set data is decomposed using complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN), and the composite entropy of decomposed subsequences is calculated. Second, the K-means clustering algorithm is used to categorize the decomposed subsequences into high and low frequency components, and variational mode decomposition(VMD) is applied to high frequency signals. Finally, the BOA-optimized LightGBM model is employed for prediction. The case studies demonstrate that this method effectively processes deformation data and enhances data stationarity, achieving significant accuracy improvements compared with conventional approaches. The nMAPE, MSE, and MAE indexes improve 16.2%-22.5%, 16.8%-28.1%, and 16.2%-22.5%, respectively.

, authors=Hao KONG1, Yong DING1, *, Denghua LI2, 3, authorsList=Hao KONG, Yong DING, Denghua LI, authorCompany=null, correspAuthors=Yong DING, authorNote=

KONG Hao, postgraduate, majors in structural health monitoring, E-mail:

, correspAuthorsNote=null, copyrightStatement=All rights reserved. Unauthorized reproduction is prohibited., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322506483913306269, articleId=1322506476480999551, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=耦合二次模态分解和优化LightGBM的大坝变形预测模型, columnId=1322506197874356701, journalTitle=大地测量与地球动力学, columnName=地壳运动, runingTitle=null, highlight=null, articleAbstract=

提出一种结合二次模态分解与蝴蝶优化算法(BOA)优化轻量梯度提升机(LightGBM)的大坝变形预测模型。首先, 利用自适应噪声完备集合经验模态分解(CEEMDAN)对训练集数据进行分解并计算分解子序列的复合熵; 然后, 通过K-means聚类算法将分解子序列分为高、低频两类, 对高频信号数据进行变分模态分解(VMD); 最后, 使用BOA优化的LightGBM模型进行预测。实例表明, 该方法能有效处理变形数据, 提高数据平稳性, 且预测精度明显优于传统方法, nMAPE、MSE、MAE指标分别降低16.2%~22.5%、16.8%~28.1%、16.2%~22.5%。

, authors=孔颢1, 丁勇1, *, 李登华2, 3, authorsList=孔颢, 丁勇, 李登华, authorCompany=null, correspAuthors=丁勇, authorNote=

孔颢, 硕士生, 主要研究方向为结构健康监测, E-mail:

, correspAuthorsNote=

丁勇, 博士, 副教授, 主要研究方向为结构健康监测, E-mail:

DING Yong, PhD, associate professor, majors in structural health monitoring, E-mail:

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articleId=1322506476480999551, language=EN, label=Tab. 1, caption=

Entropy values of intrinsic mode functions

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熵值 PE SE CE
IMF1 1.787 0.374 0.292
IMF2 1.519 0.183 0.186
IMF3 1.142 0.246 0.190
IMF4 0.903 0.226 0.165
IMF5 0.733 0.032 0.064
IMF6 0.710 0.014 0.054
IMF7 0.703 0.006 0.050
), ArticleFig(id=1322506495405699295, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=表1, caption=

本征模态分量熵值

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熵值 PE SE CE
IMF1 1.787 0.374 0.292
IMF2 1.519 0.183 0.186
IMF3 1.142 0.246 0.190
IMF4 0.903 0.226 0.165
IMF5 0.733 0.032 0.064
IMF6 0.710 0.014 0.054
IMF7 0.703 0.006 0.050
), ArticleFig(id=1322506497104392417, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Tab. 2, caption=

Evaluation indexes of different models

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方法 R09 R29 J7-1 J17-1
r RMSE/mm NCC r RMSE/mm NCC r RMSE/mm NCC r RMSE/mm NCC
VMD 0.089 0.207 0.999 61 0.304 0.916 0.995 93 0.083 0.126 0.999 84 0.110 0.383 0.999 90
WT 0.096 0.198 0.999 64 0.252 1.269 0.994 90 0.090 0.092 0.999 88 0.107 0.371 0.999 91
GF 0.082 0.253 0.999 42 0.198 1.234 0.994 37 0.078 0.164 0.999 55 0.093 0.392 0.999 90
本文方法 0.102 0.138 0.999 77 0.405 0.759 0.997 94 0.091 0.072 0.999 94 0.125 0.284 0.999 94
), ArticleFig(id=1322506497205055714, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=表2, caption=

不同模型的评价指标

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方法 R09 R29 J7-1 J17-1
r RMSE/mm NCC r RMSE/mm NCC r RMSE/mm NCC r RMSE/mm NCC
VMD 0.089 0.207 0.999 61 0.304 0.916 0.995 93 0.083 0.126 0.999 84 0.110 0.383 0.999 90
WT 0.096 0.198 0.999 64 0.252 1.269 0.994 90 0.090 0.092 0.999 88 0.107 0.371 0.999 91
GF 0.082 0.253 0.999 42 0.198 1.234 0.994 37 0.078 0.164 0.999 55 0.093 0.392 0.999 90
本文方法 0.102 0.138 0.999 77 0.405 0.759 0.997 94 0.091 0.072 0.999 94 0.125 0.284 0.999 94
), ArticleFig(id=1322506497276358883, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Tab. 3, caption=

Prediction accuracy indexes of each algorithm

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测点 模型 精度指标
nMAPE MSE/mm MAE/mm R2
R09 CEEMDAN-VMD-XGBoost 0.047 0 0.601 1 0.605 9 0.969 9
CEEMDAN-VMD-LightGBM 0.044 5 0.529 9 0.574 1 0.975 7
VMD-BOA-LightGBM 0.043 4 0.580 7 0.560 2 0.973 4
GF-BOA-LightGBM 0.045 9 0.590 6 0.592 0 0.968 6
WT-BOA-LightGBM 0.046 2 0.612 7 0.596 3 0.970 9
CEEMDAN-VMD-BOA-LightGBM 0.036 4 0.440 6 0.469 5 0.979 7
R29 CEEMDAN-VMD-XGBoost 0.066 6 6.468 4 1.738 0 0.905 7
CEEMDAN-VMD-LightGBM 0.054 3 4.242 1 1.417 4 0.938 2
VMD-BOA-LightGBM 0.055 6 4.700 7 1.451 9 0.931 5
GF-BOA-LightGBM 0.063 6 5.789 7 1.660 8 0.915 6
WT-BOA-LightGBM 0.069 0 6.048 1 1.800 8 0.882 7
CEEMDAN-VMD-BOA-LightGBM 0.048 1 3.666 0 1.255 5 0.946 6
J7-1 CEEMDAN-VMD-XGBoost 0.039 6 0.632 4 0.550 5 0.971 4
CEEMDAN-VMD-LightGBM 0.035 6 0.396 1 0.494 7 0.982 1
VMD-BOA-LightGBM 0.033 2 0.403 4 0.462 3 0.981 8
GF-BOA-LightGBM 0.033 5 0.411 6 0.465 7 0.981 4
WT-BOA-LightGBM 0.032 8 0.415 7 0.456 5 0.981 2
CEEMDAN-VMD-BOA-LightGBM 0.031 7 0.379 7 0.440 7 0.982 9
J17-1 CEEMDAN-VMD-XGBoost 0.020 8 1.099 0 0.732 0 0.961 0
CEEMDAN-VMD-LightGBM 0.025 3 1.529 0 0.891 0 0.945 0
VMD-BOA-LightGBM 0.022 0 1.223 0 0.775 0 0.956 0
GF-BOA-LightGBM 0.021 7 1.036 0 0.766 0 0.963 0
WT-BOA-LightGBM 0.019 3 0.966 1 0.681 0 0.965 0
CEEMDAN-VMD-BOA-LightGBM 0.018 0 0.855 6 0.636 0 0.970 0
), ArticleFig(id=1322506497351856356, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=表3, caption=

各算法预测精度指标

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测点 模型 精度指标
nMAPE MSE/mm MAE/mm R2
R09 CEEMDAN-VMD-XGBoost 0.047 0 0.601 1 0.605 9 0.969 9
CEEMDAN-VMD-LightGBM 0.044 5 0.529 9 0.574 1 0.975 7
VMD-BOA-LightGBM 0.043 4 0.580 7 0.560 2 0.973 4
GF-BOA-LightGBM 0.045 9 0.590 6 0.592 0 0.968 6
WT-BOA-LightGBM 0.046 2 0.612 7 0.596 3 0.970 9
CEEMDAN-VMD-BOA-LightGBM 0.036 4 0.440 6 0.469 5 0.979 7
R29 CEEMDAN-VMD-XGBoost 0.066 6 6.468 4 1.738 0 0.905 7
CEEMDAN-VMD-LightGBM 0.054 3 4.242 1 1.417 4 0.938 2
VMD-BOA-LightGBM 0.055 6 4.700 7 1.451 9 0.931 5
GF-BOA-LightGBM 0.063 6 5.789 7 1.660 8 0.915 6
WT-BOA-LightGBM 0.069 0 6.048 1 1.800 8 0.882 7
CEEMDAN-VMD-BOA-LightGBM 0.048 1 3.666 0 1.255 5 0.946 6
J7-1 CEEMDAN-VMD-XGBoost 0.039 6 0.632 4 0.550 5 0.971 4
CEEMDAN-VMD-LightGBM 0.035 6 0.396 1 0.494 7 0.982 1
VMD-BOA-LightGBM 0.033 2 0.403 4 0.462 3 0.981 8
GF-BOA-LightGBM 0.033 5 0.411 6 0.465 7 0.981 4
WT-BOA-LightGBM 0.032 8 0.415 7 0.456 5 0.981 2
CEEMDAN-VMD-BOA-LightGBM 0.031 7 0.379 7 0.440 7 0.982 9
J17-1 CEEMDAN-VMD-XGBoost 0.020 8 1.099 0 0.732 0 0.961 0
CEEMDAN-VMD-LightGBM 0.025 3 1.529 0 0.891 0 0.945 0
VMD-BOA-LightGBM 0.022 0 1.223 0 0.775 0 0.956 0
GF-BOA-LightGBM 0.021 7 1.036 0 0.766 0 0.963 0
WT-BOA-LightGBM 0.019 3 0.966 1 0.681 0 0.965 0
CEEMDAN-VMD-BOA-LightGBM 0.018 0 0.855 6 0.636 0 0.970 0
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耦合二次模态分解和优化LightGBM的大坝变形预测模型
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孔颢 1 , 丁勇 1, * , 李登华 2, 3
大地测量与地球动力学 | 地壳运动 2025,45(11): 1171-1179
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大地测量与地球动力学 |地壳运动 2025 , 45 (11) : 1171 -1179
耦合二次模态分解和优化LightGBM的大坝变形预测模型
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孔颢1 , 丁勇1, * , 李登华2, 3
作者信息
  • 1 南京理工大学安全科学与工程学院, 南京市孝陵卫街200号, 210094
  • 2 南京水利科学研究院, 南京市虎踞关34号, 210029
  • 3 水利部水库大坝安全重点实验室, 南京市虎踞关34号, 210029
通讯作者:

丁勇, 博士, 副教授, 主要研究方向为结构健康监测, E-mail:

DING Yong, PhD, associate professor, majors in structural health monitoring, E-mail:

作者简介:

孔颢, 硕士生, 主要研究方向为结构健康监测, E-mail:

The Coupled Secondary Mode Decomposition and Optimized LightGBM Model for Dam Deformation Prediction
Hao KONG1 , Yong DING1, * , Denghua LI2, 3
Affiliations
  • 1 School of Safety Science and Engineering, Nanjing University of Science and Technology, 200 Xiaolingwei Street, Nanjing 210094, China
  • 2 Nanjing Hydraulic Research Institute, 34 Hujuguan, Nanjing 210029, China
  • 3 Key Laboratory of Reservoir and Dam Safety, MWR, 34 Hujuguan, Nanjing 210029, China

    • KONG Hao, postgraduate, majors in structural health monitoring, E-mail:

出版时间: 2025-11-15 doi: 10.14075/j.jgg.2024.12.548
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摘要
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提出一种结合二次模态分解与蝴蝶优化算法(BOA)优化轻量梯度提升机(LightGBM)的大坝变形预测模型。首先, 利用自适应噪声完备集合经验模态分解(CEEMDAN)对训练集数据进行分解并计算分解子序列的复合熵; 然后, 通过K-means聚类算法将分解子序列分为高、低频两类, 对高频信号数据进行变分模态分解(VMD); 最后, 使用BOA优化的LightGBM模型进行预测。实例表明, 该方法能有效处理变形数据, 提高数据平稳性, 且预测精度明显优于传统方法, nMAPE、MSE、MAE指标分别降低16.2%~22.5%、16.8%~28.1%、16.2%~22.5%。

二次模态分解  /  高低频信号划分  /  蝴蝶优化算法  /  轻量梯度提升机  /  变形预测

A dam deformation prediction model is proposed that integrates secondary mode decomposition with butterfly optimization algorithm(BOA)-optimized light gradient boosting machine(LightGBM). First, the training set data is decomposed using complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN), and the composite entropy of decomposed subsequences is calculated. Second, the K-means clustering algorithm is used to categorize the decomposed subsequences into high and low frequency components, and variational mode decomposition(VMD) is applied to high frequency signals. Finally, the BOA-optimized LightGBM model is employed for prediction. The case studies demonstrate that this method effectively processes deformation data and enhances data stationarity, achieving significant accuracy improvements compared with conventional approaches. The nMAPE, MSE, and MAE indexes improve 16.2%-22.5%, 16.8%-28.1%, and 16.2%-22.5%, respectively.

secondary mode decomposition  /  high and low frequency signal classification  /  butterfly optimization algorithm  /  light gradient boosting machine  /  deformation prediction
孔颢, 丁勇, 李登华. 耦合二次模态分解和优化LightGBM的大坝变形预测模型. 大地测量与地球动力学, 2025 , 45 (11) : 1171 -1179 . DOI: 10.14075/j.jgg.2024.12.548
Hao KONG, Yong DING, Denghua LI. The Coupled Secondary Mode Decomposition and Optimized LightGBM Model for Dam Deformation Prediction[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (11) : 1171 -1179 . DOI: 10.14075/j.jgg.2024.12.548
正文
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大坝作为水资源管理的核心设施，在防洪调控中具有关键作用。大坝安全运行依赖持续变形监测，通过数据分析和预测可及时预警安全隐患[1]。然而，原始监测数据常受到各种噪声和干扰的影响，直接使用这些数据进行分析可能导致结果不准确，因此，对历史监测数据进行有效处理是提高预测精度的关键[2]。数据重构是数据处理的重要技术之一，通过数据分解、去噪、重构，可以提升数据质量，揭示更为本质的规律和特征。
在大坝变形监测中，常用的数据重构方法有经验模态分解(empirical mode decomposition，EMD)[3]、变分模态分解(variational mode decomposition，VMD)[4]和自适应噪声完备集合经验模态分解(complete ensemble empirical mode decomposition with adaptive noise，CEEMDAN)[5]等。石佳晨等[6]提出的改进小波阈值去噪方法主要侧重于整体信号的去噪处理，而在处理高频信号时，可能会导致微小但重要的特征信息被削弱，进而影响预测精度；柳磊等[7]提出一种结合VMD和K-奇异值分解(K-singular value decomposition，KSVD)的降噪算法，通过对VMD分解后的信号分量进行KSVD去噪处理，提高了数据的平稳性；杨孟等[8]提出一种完备集合经验模态分解(complete ensemble empirical mode decomposition，CEEMD)与粒子滤波法相结合的方法对大坝数据进行处理，虽然在应对噪声和非线性特征方面具有一定优势，但同样无法对高频信号进行细致处理，可能会丢失部分关键细节。
随着对机器学习研究的深入，许多学者开始使用机器学习构建模型。模型参数的选取对模型精度具有显著影响。为确定最优参数组合，张孟昕等[9]使用麻雀搜索算法(sparrow search algorithm，SSA)优化极限梯度提升(extreme gradient boosting，XGBoost)，得到最优参数组合，提高了计算效率；Liu等[10]使用鲸鱼优化算法(whale optimization algorithm，WOA)对随机森林(random forest，RF)进行优化，寻优后的模型在精度上优于其他模型；Zhang等[11]通过粒子群优化算法(particle swarm optimization，PSO)优化最小二乘支持向量回归(least squares support vector regression，LSSVR)模型，在提高精度的同时提高了模型运算速度。轻量梯度提升机(light gradient boosting machine，LightGBM)采用基于直方图的决策树算法，相较于XGBoost减少了内存使用，加快了训练速度，在大数据集、高维数据中训练速度更快，但如何选取LightGBM算法的参数仍是一个问题。
基于以上问题，本文提出一种基于二次模态分解和优化LightGBM的预测方法，该方法主要包括数据重构和优化预测2个部分。首先，将训练集数据通过CEEMDAN算法进行分解，计算分解后信号的复合熵；然后，使用K-means聚类算法对分解子序列进行特征聚类，将信号分成高、低频信号，采用VMD算法对高频信号进行二次分解，通过分解后的信号与高频信号之间的Pearson相关系数确定VMD分解层数，将重构后的高频信号和低频信号进行叠加得到最终的重构数据；最后，使用蝴蝶优化算法(butterfly optimization algorithm，BOA)优化的LightGBM模型对重构后的数据进行预测，得到最终的预测结果。经工程实例验证，本文所提方法能够有效提升预测精度。
1 方法理论
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1.1 基于HST模型的大坝变形监测理论
根据坝工原理[12]，大坝位移受到水压力、温度荷载的影响，大坝任意一点的位移(δ)可由3个部分组成，分别为水压分量(δH)、温度分量(δT)和时效分量(δθ)：
$\delta=\delta_H+\delta_T+\delta_\theta$
HST因子模型数学表达式如下：
$\begin{gathered}\delta=a_0+\sum\limits_{i=1}^n a_i H^i+ \\\sum\limits_{j=1}^2\left[b_{1 j} \sin \frac{2 \pi j t}{365}+b_{2 j} \cos \frac{2 \pi j t}{365}\right]+c_1 \theta+c_2 \ln \theta\end{gathered}$
式中，a0为常数项；H为上游库水位；n为多项式阶数；ai、b1j、b2j、c1和c2为回归系数；t为大坝初始观测日期到当前观测日期的天数；θ为t/100。
1.2 复合熵计算
本文提出基于CEEMDAN和VMD算法的二次模态分解方法，CEEMDAN算法是对EMD算法的改进，通过在分解的本征模态函数(IMFs)中添加高斯白噪声，减少模态混合问题。VMD算法则是一种自适应信号分解方法，能够有效处理高频非平稳、非线性信号，同时避免模态混叠。CEEMDAN算法分解的IMF中包含高频信号、低频信号和残差信号，正确区分高、低频信号可以有效保留数据特征，降低噪声。基于此，本文提出一种在排列熵(permutation entropy，PE)[13]和样本熵(sample entropy，SE)[14]基础上进行改进的复合熵(composite entropy，CE)，计算步骤如下：
1) 首先计算除残差外的各个本征模态分量的排列熵和样本熵，表示式为：
$\begin{aligned}& E_P=-\sum P(\pi) \ln P(\pi) \\& E_S=-\ln \left(\frac{B(m+1, r)}{A(m, r)}\right)\end{aligned}$
式中，EP为排列熵；ES为样本熵；P(π)为概率分布；B(m+1, r)表示长度为m+1的嵌入向量对数量；A(m, r)表示长度为m的嵌入向量对数量。
2) 计算出每个本征模态分量的排列熵和样本熵后，根据这些熵值计算复合熵，为避免单一熵值可能过大而影响整体结果的稳定性，对排列熵和样本熵进行加权处理。
计算单一本征模态分量的排列熵和样本熵在所有信号中的占比：
$\left\{\begin{array}{l}E_{P_{\text {total }}}=\sum\limits_i^{n-1} E_{P_i} \\E_{S_{\text {total }}}=\sum\limits_i^{n-1} E_{S_i} \\P_{E_{P_i}}=\frac{E_{P_i}}{E_{P_{\text {total }}}} \\P_{E_{S_i}}=\frac{E_{S_i}}{E_{S_{\text {total }}}}\end{array}\right.$
式中，n为本征模态分量数量。
对排列熵占比和样本熵占比进行加权计算，得到复合熵ECi：
$E_{C_i}=a \cdot P_{E_{P_i}}+b \cdot P_{E_{S_i}}$
式中，a和b为权重系数，取a+b=1。
1.3 BOA-LightGBM预测模型
蝴蝶优化算法(BOA)[15]是一种受自然界蝴蝶行为启发而提出的全局优化算法，其优化过程为：1)初始化种群，随机生成一组候选解；2)通过计算每只蝴蝶的适应度来评估其在解空间中的优劣；3)通过模拟蝴蝶在自然界中的迁移行为来寻找更优位置。BOA凭借其较强的全局搜索能力和跳出局部最优解的能力，在多种优化问题中表现出色。
LightGBM算法是基于梯度提升决策树(gradient boosting decision tree，GBDT)而改进的算法。LightGBM利用直方图算法来加速计算，并在数据分布较为稀疏的情况下跳过不必要的计算，从而大幅减少内存使用量。但该算法在训练过程中受弱学习器数量、学习率和每棵树的最大深度等关键参数的影响较大。为进一步提高模型的精度与稳定性，本文引入BOA算法对LightGBM模型的3个关键参数进行寻优。
2 数据重构和预测模型建立
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本文提出的重构方法和预测模型流程(图 1)如下：
1) 使用CEEMDAN算法对大坝变形数据进行初步分解，获得若干本征模态函数(IMFs)。
2) 计算IMFs的复合熵，采用K-means聚类算法将其分为高频和低频信号，并对高频信号进行线性叠加，得到重构的高频信号。
3) 使用VMD算法对高频信号进行二次分解，通过计算分解数据与原始数据之间的Pearson相关系数确定分解层数K，将VMD分解所得数据与CEEMDAN初步分解所得的低频信号和残差进行合并，得到最终的重构数据。
4) 初始化种群参数，确定蝴蝶位置、种群数量和动态转换概率。设定LightGBM的弱学习器数量、学习率和每棵树最大深度的取值范围分别为[100, 1 000]、[0.01, 0.3]和[1, 4]，选择nMAPE作为适应度函数。
5) 计算每只蝴蝶的适应度，选出最优适应度的当前位置并生成随机数。若随机数大于动态转换概率，蝴蝶向密度最大个体聚集，反之则随机移动。
6) 计算更新后所在位置的适应度，并记录蝴蝶所在位置。判断是否为最优解，若满足最优解，则算法结束，输出最优参数组合；若不满足，则返回步骤5)。
7) 根据最优参数组合建立LightGBM预测模型并进行预测分析。
3 案例分析
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选取新疆某混凝土面板堆石坝为研究对象。该水库坝高约110 m，坝顶高程1 654 m，坝顶长352 m，坝底最大宽度约400 m，年均径流量34.16亿m3，调节库容7 240万m3，总库容1.25亿m3。研究区主要水工建筑物包括混凝土面板堆石坝、深孔溢洪道、面孔溢洪道和厂房。
为验证本文预测模型的准确性，选取用于测量混凝土面板钢筋应力的钢筋计R09、R29和用于监测面板垂直缝接缝变形的单向测缝计J7-1、J17-1为实验对象。实验数据监测时段为2015-05-01—2020-12-08，监测频率为1次/d。将2015-05-01—2019-12-25数据作为训练集进行数据重构，2019-12-26—2020-12-08数据作为测试集，用于预测并验证模型精度，图 2~6为大坝库水位和所选测点的历史测值。
3.1 重构效果评价
为验证本文重构方法的有效性及优势，选取VMD、小波阈值(wavelet thresholding，WT)和高斯滤波(Gaussian filtering，GF)去噪方法作为对比，对R09测点数据进行分解重构。首先进行CEEMDAN分解，得到7个本征模态分量(IMFs)，然后依据式(3)计算每个IMF的排列熵和样本熵。为了融合2种熵指标的各自优势，同时保持二者在信号复杂度表征上的平衡，权重系数a、b均取0.5，以确保排列熵对信号动态结构的敏感性与样本熵对噪声影响的鲁棒性，避免单一熵指标对结果产生偏差，提高对复杂信号的描述能力。由式(5)得到复合熵，对复合熵采用K-means聚类算法以划分高、低频信号，得到各个本征模态分量的熵值，结果如表 1所示。
通过K-means聚类算法对复合熵进行聚类，其中IMF1、IMF2、IMF3、IMF4为高频信号，IMF5、IMF6、IMF7为低频信号。将高频信号线性叠加后进行VMD分解，VMD分解层数设定在[1, 10]范围内。通过循环计算重构高频信号与原始高频信号之间的Pearson相关系数，为保留重构信号的真实性和有效性，当Pearson相关系数大于设定值0.95时，确定并输出分解层数K=3。CEEMDAN分解和高频信号重构如图 7所示，可以看出，CEEMDAN分解所得的高频信号具有较高的杂乱度，包含大量不利于预测的噪声信息，需对其作进一步处理。使用VMD对CEEMDAN分解后的高频信号进行二次处理，信号平滑性显著提升，尖锐的噪声被有效抑制，整体波动趋于平稳。更重要的是，重构后的高频信号与原始信号之间的Pearson相关系数较高，表明重构信号在保持原始数据主要趋势的同时，能够成功去除噪声干扰，确保数据的有效性，从而提高大坝变形预测精度。
将重构后的高频信号、CEEMDAN分解后的低频信号和残差信号进行叠加，得到最终的重构数据，并与VMD、WT和GF得到的结果进行对比，结果如图 8、9所示。可以看出，VMD算法虽然具有较强的信号分解能力，能够有效分离不同频段的信号，但其主要缺点是分解层数难以准确确定。过多的分解层数可能导致信号过度分解，从而引入额外的噪声和不必要的细节；分解层数过少则可能无法充分捕捉信号中的多层次特征，导致信息丢失。
相比之下，小波去噪算法在去除噪声的同时能够较好地保留信号的整体形态，但其效果对参数选择非常敏感。阈值的设定和小波基函数的选择对于去噪效果起着至关重要的作用，不同参数可能导致去噪效果存在较大差异，尤其是在处理复杂信号时，参数选择不当可能导致去噪不彻底或信号过度平滑，进而影响数据的可靠性。
高斯去噪算法的平滑效果显著，能有效降低噪声，使数据表现更平稳。但这种平稳性会导致过度去噪的问题，在降低噪声的过程中可能会使信号的某些关键特征被抹去，从而引起数据失真。高斯去噪虽然操作简单且计算效率高，但其固定的卷积核使得该方法在处理具有复杂波动的信号时存在局限性，不易捕捉到信号中的微小变化。
本文提出的重构算法通过保留低频信号和残差信号，仅对高频信号进行分解重构，这种策略能够有效提高数据的平稳性，同时保留大坝变形数据的真实性和可靠性，避免出现过度分解、参数敏感性和过度去噪的问题。
为全面评价本文数据重构方法的效果，引入平滑度r、均方根误差(RMSE)和归一化互相关系数(normalized cross correlation，NCC)作为评价指标。平滑度r越小，信号越平稳；RMSE越小，信号重构效果越好；NCC越接近1，信号特征保留越多。
$r=\frac{\sum\limits_{i=1}^{n-1}\left|x_i-x_{i+1}\right|}{n}$
$\text { RMSE }=\sqrt{\frac{\sum\limits_{i=1}^n\left(y_i-x_i\right)^2}{n}}$
$\mathrm{NCC}=\frac{\sum\limits_{i=1}^n y_i x_i}{\sqrt{\left(\sum\limits_{i=1}^n y_i^2\right)\left(\sum\limits_{i=1}^n x_i^2\right)}}$
在大坝变形监测中，保留信号的物理意义至关重要。本文方法通过有效分离和重构信号，不仅能保留信号的主要特征，还可保持其物理意义的完整性。
计算以上4种方法的评价指标，结果见表 2。以R09测点为例进行分析，可以发现：1)在平滑度指标上，本文方法为0.102，虽然略高于其他方法，但这表明本文方法在降噪的同时保留了更多的信号细节和大坝变形的有用信息，而不是简单地将信号进行过度平滑，从而损失关键信息。2)在RMSE指标上，本文方法为0.138 mm，远低于其他方法，表明在消除噪声的同时，本文方法能够更好地保留信号原始特征，与原始信号的差异最小，从而确保大坝变形数据的准确性和可靠性。3)在NCC这一关键指标上，本文方法为0.999 77，高于其他方法，表明本文方法能够最有效地保留信号原始特征，使得重构后的信号与原始信号之间的相关性更强，从而提供更为真实可信的信号重构效果。
综合来说，本文方法具有更强的多尺度分析能力，能够有效分离出信号中的不同频率成分，使得在处理大坝变形监测数据时，能够更好地捕捉到不同时间尺度上的变化特征。与传统的小波阈值和高斯滤波去噪方法相比，本文方法不仅能够在细节层面上进行处理，还能在整体趋势层面上提供准确的分析结果。
3.2 预测模型精度评价
为验证本文预测模型的精度，选取XGBoost和LightGBM算法作为基础预测模型进行对比。为有效量化预测模型的精度，选取平均绝对百分比误差(MAPE)、均方误差(MSE)、平均绝对误差(MAE)和可决系数(R2)作为评价指标。考虑到当预测值为0时无法计算MAPE，故采用实测最大值的绝对值作为辅助决策，将实测值和预测值进行归一化，实测值与预测值残差的绝对值归一化后的平均值即为预测结果的归一化平均百分比误差(nMAPE)，计算公式如下：
$A^{\prime}(t)=A(t) /|A(t)|_{\max }$
$F^{\prime}(t)=F(t) /|F(t)|_{\max }$
$\mathrm{nMAPE}=\frac{1}{T} \sum\limits_{t=1}^T\left|A^{\prime}(t)-F^{\prime}(t)\right|$
式中，A(t)为实测值；F(t)为预测值；A′(t)为归一化实测值；F′(t)为归一化预测值。
为验证本文寻优算法的优越性，引入粒子群优化算法(PSO)和鲸鱼优化算法(WOA)作为对比，寻优算法初始参数均设置为number=30、迭代次数num_iterations=100。由图 10可知，在相同初始参数条件下，BOA展现出优异的全局搜索能力。尽管其迭代次数较多，但BOA最终获得最优的适应度值，表明其在寻优过程中能够更有效地找到最优参数组合。相比之下，尽管PSO和WOA的迭代次数相对较少，但二者的最终适应度值均未能达到BOA的水准。
通过迭代寻优可确定最优参数，n_estimators=765，learning_rate=0.023，max_depth=3，将最优参数组合作为预测模型的输入对训练集进行建模，使用模型对测试集进行预测。
由图 11、12和表 3可知，本文方法结合了BOA与LightGBM的优势，使预测模型能够充分挖掘数据中的复杂非线性关系，提高预测精度。
从R09测点结果来看，本文方法相较于传统方法具有明显优势。在nMAPE指标方面，本文方法比XGBoost、未经BOA优化的LightGBM、VMD、GF和WT模型分别降低22.5%、18.2%、16.2%、20.7%和21.2%。nMAPE的显著降低表明本文方法在预测精度上有明显提升，尤其是在处理大坝变形这种复杂非线性数据时，能够更好地捕捉和还原信号的真实变化趋势。在MSE指标方面，本文方法相较于对比模型分别降低26.7%、16.8%、24.1%、25.4%和28.1%。MSE的显著降低进一步表明本文方法在重构信号时的有效性，能够在降低噪声的同时保留原始信号的关键特征，使预测误差大幅减小。在MAE指标方面，本文方法相较于对比模型分别降低22.5%、18.2%、16.2%、20.7%和21.3%。MAE的显著降低表明本文方法不仅在整体误差上具有优势，还在每个预测点的误差幅度上表现出色，意味着模型对极值和异常点的预测更加精确。相比之下，其他方法在处理异常数据时存在较大的误差波动，特别是在高噪声背景下更为明显。尽管各模型的R2相近，但本文方法仍具有最高的拟合精度，表明其能够平衡复杂非线性信号，提供更稳定准确的预测结果。
4 结语
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1) 本文提出一种结合复合熵与聚类算法的二次模态分解数据重构方法，通过精准区分并重构大坝监测数据中的高频和低频信号，显著提升数据平稳性和有效性，进而提高预测模型的精度。实验结果表明，本文方法相较于传统方法(如VMD、GF和WT)具有较强的适用性和鲁棒性，特别是在复杂环境下具备广泛应用潜力。
2) 本文通过BOA算法优化LightGBM模型，显著提升了大坝安全监测模型的预测精度。模型优化过程能有效减少人为参数设置的不确定性，提高模型的可操作性和计算效率。
3) 本文方法仍存在一定的局限性，如提出的复合熵与聚类算法的计算复杂度较高，在大规模多测点场景下可能面临一定的计算资源压力。后续研究可结合高效的优化算法或分布式计算技术，以进一步提升方法的实用性。
基金
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  • 国家重点研发计划(2024YFC3210703)
  • 国家自然科学基金(U2240221)
  • 国家自然科学基金(51979174)
  • 中央级公益性科研院所基本科研业务费专项(Y724011)
文献
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2025年第45卷第11期
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引用本文
BibTeX
文章信息
doi: 10.14075/j.jgg.2024.12.548
  • 接收时间：2024-12-02
  • 首发时间：2026-10-29
  • 出版时间：2025-11-15
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文章信息
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出版历史
  • 收稿日期：2024-12-02
基金
National Key Research and Development Program of China(2024YFC3210703)
国家重点研发计划(2024YFC3210703)
National Natural Science Foundation of China(U2240221)
国家自然科学基金(U2240221)
National Natural Science Foundation of China(51979174)
国家自然科学基金(51979174)
Special Fund for Basic Scientific Research of Central Public Research Institutes(Y724011)
中央级公益性科研院所基本科研业务费专项(Y724011)
作者信息
    1 南京理工大学安全科学与工程学院, 南京市孝陵卫街200号, 210094
    2 南京水利科学研究院, 南京市虎踞关34号, 210029
    3 水利部水库大坝安全重点实验室, 南京市虎踞关34号, 210029

通讯作者:

丁勇, 博士, 副教授, 主要研究方向为结构健康监测, E-mail:

DING Yong, PhD, associate professor, majors in structural health monitoring, E-mail:

参考文献
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https://castjournals.cast.org.cn/joweb/ddcl/CN/10.14075/j.jgg.2024.12.548
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