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 KONG
1, Yong DING
1, *, Denghua LI
2, 3, authorsList=Hao KONG, Yong DING, Denghua LI, authorCompany=null, correspAuthors=Yong DING, authorNote=
, 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=
, correspAuthorsNote=
, copyrightStatement=
版权所有,未经授权,不得转载。, copyrightOwner=大地测量与地球动力学编辑部, extLink=null, articleAbsUrl=null, sourceXml=kjTHXgGBP1fmfp8PToR2cw==, magXml=XDht40XCPwAe8z0V5OM2qg==, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=LmXJ9qs2LHKF4HWWnoyR3A==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=UJ6A5tY/iIEAD+yuSGxyRQ==, mapNumber=null, fund=null)}, authors=[Author(id=1322506488136970409, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=KonghaoCE@njust.edu.cn, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1322506488262799531, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, authorId=1322506488136970409, language=EN, stringName=Hao KONG, firstName=Hao, middleName=null, lastName=KONG, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=
1, address=1 School of Safety Science and Engineering, Nanjing University of Science and Technology, 200 Xiaolingwei Street, Nanjing 210094, China, bio={"content":"
KONG Hao, postgraduate, majors in structural health monitoring, E-mail: KonghaoCE@njust.edu.cn
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KONG Hao, postgraduate, majors in structural health monitoring, E-mail: KonghaoCE@njust.edu.cn
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1, address=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, bio={"content":"
孔颢, 硕士生, 主要研究方向为结构健康监测, E-mail: KonghaoCE@njust.edu.cn
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孔颢, 硕士生, 主要研究方向为结构健康监测, E-mail: KonghaoCE@njust.edu.cn
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2, 3, address=2 Nanjing Hydraulic Research Institute, 34 Hujuguan, Nanjing 210029, China
3 Key Laboratory of Reservoir and Dam Safety, MWR, 34 Hujuguan, Nanjing 210029, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1322506489919549623, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, authorId=1322506489747583155, language=CN, stringName=李登华, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=
2, 3, address=2 南京水利科学研究院, 南京市虎踞关34号, 210029
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CEEMDAN-VMD-BOA-LightGBM flowchart, figureFileSmall=v0YBH79MFaxd69U4/DeEyw==, figureFileBig=LmXJ9qs2LHKF4HWWnoyR3A==, tableContent=null), ArticleFig(id=1322506493170135238, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图1, caption=
CEEMDAN-VMD-BOA-LightGBM流程, figureFileSmall=v0YBH79MFaxd69U4/DeEyw==, figureFileBig=LmXJ9qs2LHKF4HWWnoyR3A==, tableContent=null), ArticleFig(id=1322506493379850439, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 2, caption=
Historical water level of reservoir, figureFileSmall=tqwhww1LpnCI8HQP7jXD9Q==, figureFileBig=HJv7WspfacxM3leThLX1jQ==, tableContent=null), ArticleFig(id=1322506493467930824, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图2, caption=
水库历史水位, figureFileSmall=tqwhww1LpnCI8HQP7jXD9Q==, figureFileBig=HJv7WspfacxM3leThLX1jQ==, tableContent=null), ArticleFig(id=1322506493543428297, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 3, caption=
Historical data of measurement point R09, figureFileSmall=Gv0CA/NjdIA+058/B4xhLA==, figureFileBig=T9JUFoyN4MJvx6SUQyW+Sw==, tableContent=null), ArticleFig(id=1322506493648285898, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图3, caption=
R09测点历史数据, figureFileSmall=Gv0CA/NjdIA+058/B4xhLA==, figureFileBig=T9JUFoyN4MJvx6SUQyW+Sw==, tableContent=null), ArticleFig(id=1322506493723783371, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 4, caption=
Historical data of measurement point R29, figureFileSmall=kr7gBmr+0xix8Vd8WIlUqw==, figureFileBig=3ANVE4O3VLBsFTOKitSmbQ==, tableContent=null), ArticleFig(id=1322506493950275788, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图4, caption=
R29测点历史数据, figureFileSmall=kr7gBmr+0xix8Vd8WIlUqw==, figureFileBig=3ANVE4O3VLBsFTOKitSmbQ==, tableContent=null), ArticleFig(id=1322506494025773261, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 5, caption=
Historical data of measurement point J7-1, figureFileSmall=ScumzVaIqVeWk6UUq2YvNQ==, figureFileBig=QhNc3AdNv5Kxo5Z5G+u+9g==, tableContent=null), ArticleFig(id=1322506494097076430, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图5, caption=
J7-1测点历史数据, figureFileSmall=ScumzVaIqVeWk6UUq2YvNQ==, figureFileBig=QhNc3AdNv5Kxo5Z5G+u+9g==, tableContent=null), ArticleFig(id=1322506494168379599, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 6, caption=
Historical data of measurement point J17-1, figureFileSmall=eZne7BQ8XZ88hz38GCfBBQ==, figureFileBig=WOuCu6q4H7eTcJ9gre9xnA==, tableContent=null), ArticleFig(id=1322506494273237200, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图6, caption=
J17-1测点历史数据, figureFileSmall=eZne7BQ8XZ88hz38GCfBBQ==, figureFileBig=WOuCu6q4H7eTcJ9gre9xnA==, tableContent=null), ArticleFig(id=1322506494382289105, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 7, caption=
CEEMDAN decomposition and high frequency signal reconstruction, figureFileSmall=PboEggLwlqmPxe6zVsdigg==, figureFileBig=1vi+sVYL05rhPPkQSVY5GQ==, tableContent=null), ArticleFig(id=1322506494457786578, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图7, caption=
CEEMDAN分解和高频信号重构, figureFileSmall=PboEggLwlqmPxe6zVsdigg==, figureFileBig=1vi+sVYL05rhPPkQSVY5GQ==, tableContent=null), ArticleFig(id=1322506494520701139, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 8, caption=
Noise reduction comparison of measurement point R09, figureFileSmall=Uz7m+2HdIlEDLedxi3wAEQ==, figureFileBig=za9ZdcaEx02FzXq0SxyxQA==, tableContent=null), ArticleFig(id=1322506494596198612, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图8, caption=
R09测点降噪对比, figureFileSmall=Uz7m+2HdIlEDLedxi3wAEQ==, figureFileBig=za9ZdcaEx02FzXq0SxyxQA==, tableContent=null), ArticleFig(id=1322506494667501781, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 9, caption=
Noise reduction comparison of measurement point R29, figureFileSmall=Yd3toTMfizRReDnlkKM9XA==, figureFileBig=NJ0ZBTztgIAtk2JEcoG2Fw==, tableContent=null), ArticleFig(id=1322506494747193558, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图9, caption=
R29测点降噪对比, figureFileSmall=Yd3toTMfizRReDnlkKM9XA==, figureFileBig=NJ0ZBTztgIAtk2JEcoG2Fw==, tableContent=null), ArticleFig(id=1322506494818496727, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 10, caption=
Iteration curves of optimization algorithm, figureFileSmall=Qo1VvPYdna/+XBs6oO7TCQ==, figureFileBig=xjv+8eNKoez0dpFaxRv/Uw==, tableContent=null), ArticleFig(id=1322506494893994200, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图10, caption=
优化算法迭代曲线, figureFileSmall=Qo1VvPYdna/+XBs6oO7TCQ==, figureFileBig=xjv+8eNKoez0dpFaxRv/Uw==, tableContent=null), ArticleFig(id=1322506494973685977, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 11, caption=
Comparison of prediction models of measurement point R09, figureFileSmall=okibxejmFgQrRvt53sqmYQ==, figureFileBig=banwis5cF454C5d/7vepZA==, tableContent=null), ArticleFig(id=1322506495065960666, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图11, caption=
R09测点预测模型对比, figureFileSmall=okibxejmFgQrRvt53sqmYQ==, figureFileBig=banwis5cF454C5d/7vepZA==, tableContent=null), ArticleFig(id=1322506495128875227, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Fig. 12, caption=
Comparison of prediction models of measurement point R29, figureFileSmall=T9mytWHQhCsHL4tiq6cJ3g==, figureFileBig=j9/iYVRrcHufYvwl0G2RbQ==, tableContent=null), ArticleFig(id=1322506495216955612, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=CN, label=图12, caption=
R29测点预测模型对比, figureFileSmall=T9mytWHQhCsHL4tiq6cJ3g==, figureFileBig=j9/iYVRrcHufYvwl0G2RbQ==, tableContent=null), ArticleFig(id=1322506495326007517, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322506476480999551, language=EN, label=Tab. 1, caption=
Entropy values of intrinsic mode functions
, figureFileSmall=null, figureFileBig=null, tableContent=
| 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
, figureFileSmall=null, figureFileBig=null, tableContent=
| 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
, figureFileSmall=null, figureFileBig=null, tableContent=
| 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 |
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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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