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Article(id=1281933759008194956, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1281909275651969257, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2025.08.293, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1755964800000, receivedDateStr=2025-08-24, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1783566425324, onlineDateStr=2026-07-09, pubDate=1781452800000, pubDateStr=2026-06-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1783566425324, onlineIssueDateStr=2026-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1783566425324, creator=13701087609, updateTime=1783566425324, updator=13701087609, issue=Issue{id=1281909275651969257, tenantId=1146029695717560320, journalId=1281212831689347082, year='2026', volume='46', issue='6', pageStart='662', pageEnd='789', issueExtLink='null', onlineDate='null', pubDate='1781452800000', pubDateStr='2026-06-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1783560588038, creator='13701087609', updateTime=1783566454347, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1281933881221812905, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1281909275651969257, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1281933881221812906, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1281909275651969257, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=748, endPage=757, ext={EN=ArticleExt(id=1281933760845300109, articleId=1281933759008194956, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Landslide Displacement Prediction Model Based on Optimized Time Series Decomposition and Feature Selection, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Aiming at the problem that it is difficult for the temporal decomposition model to accurately distinguish the effects of induced factors on different displacement components, and the prediction accuracy is insufficient under the uncertainty of meteorological data, a landslide displacement prediction network model based on optimized time series decomposition and feature selection is proposed. Firstly, the variational modal decomposition (GA-VMD) method optimized by singular spectral analysis (SSA) and genetic algorithm is combined with induced factors to decompose the landslide displacement. Subsequently, an improved Nishihara model with fusion inducible factors is constructed to predict the trend term displacement, and the combined network of convolutional neural network and gated recurrent unit (CNN-SE-GRU) combined with compression and excitation network was used to model the period term displacement, and the random term displacement is reconstructed through frequency domain analysis. Finally, the probability interval of the displacement prediction results is constructed by combining kernel density estimation (KDE) and Monte Carlo simulation. Taking the Heifangtai landslide in Gansu province as an example, the RMSE and MAPE of the prediction model are 1.52 mm and 0.38%, respectively, and the prediction accuracy of the model is significantly improved compared with the traditional prediction model, providing more reliable technical support for landslide early warning.

, authors=Dongmin WANG1, Lihua ZHAO1, *, Wei QU1, Zimu HANG1, Li WANG1, authorsList=Dongmin WANG, Lihua ZHAO, Wei QU, Zimu HANG, Li WANG, authorCompany=null, correspAuthors=Lihua ZHAO, authorNote=null, 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=1281933777081450920, articleId=1281933759008194956, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=基于优化时序分解和特征选择的滑坡位移预测模型, columnId=1281933709121138897, journalTitle=大地测量与地球动力学, columnName=地球动力学, runingTitle=null, highlight=null, articleAbstract=

针对时序分解模型难以准确区分诱发因子对不同位移分量的作用, 以及在气象数据存在不确定性下预测精度不足的问题, 提出一种基于优化时序分解与特征选择的滑坡位移预测网络模型。首先, 利用奇异谱分析(SSA)与遗传算法优化的变分模态分解(GA-VMD)方法对滑坡位移在诱发因子驱动下进行分解; 随后, 构建融合诱发因子的改进西原模型预测趋势项位移, 采用结合卷积神经网络与压缩和激励网络的门控循环单元(CNN-SE-GRU)组合网络建模预测周期项位移, 通过频域分析重构随机项位移; 最后, 结合核密度估计(KDE)和蒙特卡洛(Monte Carlo)模拟方法, 构建位移预测结果的概率区间。以甘肃省黑方台滑坡为例, 预测模型的RMSE和MAPE分别为1.52 mm和0.38%, 预测精度较传统的预测模型显著提升, 为滑坡预警提供了更可靠的技术支撑。

, authors=王东民1, 赵丽华1, *, 瞿伟1, 杭资牧1, 王利1, authorsList=王东民, 赵丽华, 瞿伟, 杭资牧, 王利, authorCompany=null, correspAuthors=赵丽华, authorNote=

王东民, 硕士生, 主要从事滑坡监测数据处理研究, E-mail:

, correspAuthorsNote=
赵丽华, 博士, 副教授, 主要从事大地测量数据以及地质灾害高精度数据处理研究, E-mail:
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tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1281933759008194956, language=CN, label=图13, caption=XP04滑坡监测点数据展示, figureFileSmall=yrq4WIqnHtzlrsXK9U27yg==, figureFileBig=Ou604Y6cOoKLc34ZdNVFfw==, tableContent=null), ArticleFig(id=1281933821897589227, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1281933759008194956, language=EN, label=Tab. 1, caption=

Random term component internal period function curve of HF09 monitoring point

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分量类别 周期函数位移曲线
I1 I2 I3
随机项 0.277 8cos(80t+0.688 5π) 0.359 3cos(96t-0.634 2π) 0.285 6cos(104t-0.399 1π)
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HF09监测点随机项分量内部周期函数曲线

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分量类别 周期函数位移曲线
I1 I2 I3
随机项 0.277 8cos(80t+0.688 5π) 0.359 3cos(96t-0.634 2π) 0.285 6cos(104t-0.399 1π)
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Comparison of the performance of different prediction schemes

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实验方案 分解方法 主要预测模型 RMSE/mm MAE/mm MAPE/%
方案1 VMD多项式拟合-GRU 10.54 9.73 2.99
多项式拟合-BiTCN-BiGRU 16.53 13.66 4.17
未改进的西原模型-Hybrid-GRU 13.98 12.76 3.91
未改进的西原模型-CNN-SE-GRU 11.02 10.20 3.13
方案2 文中分解方法多项式拟合-GRU 4.32 3.59 1.13
多项式拟合-BiTCN-BiGRU 5.59 5.43 1.68
未改进的西原模型-Hybrid-GRU 4.28 4.28 1.25
未改进的西原模型-CNN-SE-GRU 3.32 3.10 0.96
本文方案 文中分解方法 文中组合预测模型 1.52 1.20 0.38
), ArticleFig(id=1281933824460308974, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1281933759008194956, language=CN, label=表2, caption=

不同预测方案性能对比

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实验方案 分解方法 主要预测模型 RMSE/mm MAE/mm MAPE/%
方案1 VMD多项式拟合-GRU 10.54 9.73 2.99
多项式拟合-BiTCN-BiGRU 16.53 13.66 4.17
未改进的西原模型-Hybrid-GRU 13.98 12.76 3.91
未改进的西原模型-CNN-SE-GRU 11.02 10.20 3.13
方案2 文中分解方法多项式拟合-GRU 4.32 3.59 1.13
多项式拟合-BiTCN-BiGRU 5.59 5.43 1.68
未改进的西原模型-Hybrid-GRU 4.28 4.28 1.25
未改进的西原模型-CNN-SE-GRU 3.32 3.10 0.96
本文方案 文中分解方法 文中组合预测模型 1.52 1.20 0.38
), ArticleFig(id=1281933824644858351, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1281933759008194956, language=EN, label=Tab. 3, caption=

Comparison of predictive performance of different forecasting models for the Xinpu landslide

, figureFileSmall=null, figureFileBig=null, tableContent=
实验方案 分解方法 主要预测模型 RMSE/mm MAE/mm MAPE/%
方案1 VMD多项式拟合-GRU 14.95 12.79 1.68
多项式拟合-BiTCN-BiGRU 16.56 13.63 1.80
未改进的西原模型-Hybrid-GRU 10.62 8.62 1.14
未改进的西原模型-CNN-SE-GRU 9.88 8.16 1.08
方案2 文中分解方法多项式拟合-GRU 5.13 4.18 0.45
多项式拟合-BiTCN-BiGRU 4.74 3.75 0.40
未改进的西原模型-Hybrid-GRU 4.19 3.83 0.41
未改进的西原模型-CNN-SE-GRU 3.07 2.63 0.28
本文方案 文中分解方法 文中组合预测模型 1.43 1.06 0.11
), ArticleFig(id=1281933825689240048, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1281933759008194956, language=CN, label=表3, caption=

不同预测方案在新铺滑坡的预测性能对比

, figureFileSmall=null, figureFileBig=null, tableContent=
实验方案 分解方法 主要预测模型 RMSE/mm MAE/mm MAPE/%
方案1 VMD多项式拟合-GRU 14.95 12.79 1.68
多项式拟合-BiTCN-BiGRU 16.56 13.63 1.80
未改进的西原模型-Hybrid-GRU 10.62 8.62 1.14
未改进的西原模型-CNN-SE-GRU 9.88 8.16 1.08
方案2 文中分解方法多项式拟合-GRU 5.13 4.18 0.45
多项式拟合-BiTCN-BiGRU 4.74 3.75 0.40
未改进的西原模型-Hybrid-GRU 4.19 3.83 0.41
未改进的西原模型-CNN-SE-GRU 3.07 2.63 0.28
本文方案 文中分解方法 文中组合预测模型 1.43 1.06 0.11
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基于优化时序分解和特征选择的滑坡位移预测模型
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王东民 1 , 赵丽华 1, * , 瞿伟 1 , 杭资牧 1 , 王利 1
大地测量与地球动力学 | 地球动力学 2026,46(6): 748-757
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大地测量与地球动力学 |地球动力学 2026 , 46 (6) : 748 -757
基于优化时序分解和特征选择的滑坡位移预测模型
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王东民1 , 赵丽华1, * , 瞿伟1, 杭资牧1, 王利1
作者信息
  • 1 长安大学地质工程与测绘学院, 西安市, 710054
通讯作者:
赵丽华, 博士, 副教授, 主要从事大地测量数据以及地质灾害高精度数据处理研究, E-mail:
作者简介:

王东民, 硕士生, 主要从事滑坡监测数据处理研究, E-mail:

Landslide Displacement Prediction Model Based on Optimized Time Series Decomposition and Feature Selection
Dongmin WANG1 , Lihua ZHAO1, * , Wei QU1, Zimu HANG1, Li WANG1
Affiliations
  • 1 School of Geological Engineering and Geomatics, Chang'an University, Xi'an 710054, China
出版时间: 2026-06-15 doi: 10.14075/j.jgg.2025.08.293
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摘要
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针对时序分解模型难以准确区分诱发因子对不同位移分量的作用, 以及在气象数据存在不确定性下预测精度不足的问题, 提出一种基于优化时序分解与特征选择的滑坡位移预测网络模型。首先, 利用奇异谱分析(SSA)与遗传算法优化的变分模态分解(GA-VMD)方法对滑坡位移在诱发因子驱动下进行分解; 随后, 构建融合诱发因子的改进西原模型预测趋势项位移, 采用结合卷积神经网络与压缩和激励网络的门控循环单元(CNN-SE-GRU)组合网络建模预测周期项位移, 通过频域分析重构随机项位移; 最后, 结合核密度估计(KDE)和蒙特卡洛(Monte Carlo)模拟方法, 构建位移预测结果的概率区间。以甘肃省黑方台滑坡为例, 预测模型的RMSE和MAPE分别为1.52 mm和0.38%, 预测精度较传统的预测模型显著提升, 为滑坡预警提供了更可靠的技术支撑。

滑坡位移预测  /  时序分解  /  特征选择  /  神经网络  /  误差传播建模

Aiming at the problem that it is difficult for the temporal decomposition model to accurately distinguish the effects of induced factors on different displacement components, and the prediction accuracy is insufficient under the uncertainty of meteorological data, a landslide displacement prediction network model based on optimized time series decomposition and feature selection is proposed. Firstly, the variational modal decomposition (GA-VMD) method optimized by singular spectral analysis (SSA) and genetic algorithm is combined with induced factors to decompose the landslide displacement. Subsequently, an improved Nishihara model with fusion inducible factors is constructed to predict the trend term displacement, and the combined network of convolutional neural network and gated recurrent unit (CNN-SE-GRU) combined with compression and excitation network was used to model the period term displacement, and the random term displacement is reconstructed through frequency domain analysis. Finally, the probability interval of the displacement prediction results is constructed by combining kernel density estimation (KDE) and Monte Carlo simulation. Taking the Heifangtai landslide in Gansu province as an example, the RMSE and MAPE of the prediction model are 1.52 mm and 0.38%, respectively, and the prediction accuracy of the model is significantly improved compared with the traditional prediction model, providing more reliable technical support for landslide early warning.

landslide displacement prediction  /  time series decomposition  /  feature selection  /  neural network  /  error propagation modeling
王东民, 赵丽华, 瞿伟, 杭资牧, 王利. 基于优化时序分解和特征选择的滑坡位移预测模型. 大地测量与地球动力学, 2026 , 46 (6) : 748 -757 . DOI: 10.14075/j.jgg.2025.08.293
Dongmin WANG, Lihua ZHAO, Wei QU, Zimu HANG, Li WANG. Landslide Displacement Prediction Model Based on Optimized Time Series Decomposition and Feature Selection[J]. Journal of Geodesy and Geodynamics, 2026 , 46 (6) : 748 -757 . DOI: 10.14075/j.jgg.2025.08.293
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我国滑坡灾害发育广泛，每年由滑坡导致的社会安全问题和经济损失均位于世界首位。我国政府历来高度重视自然灾害防治工作，习近平总书记在2018年中央财经委员会第三次会议上明确提出“要建立高效科学的自然灾害防治体系，提高全社会自然灾害防治能力”[1]。对滑坡灾害进行及时准确的预测预报已成为保障重大工程建设、防灾减灾和社会经济可持续发展的迫切战略需求。
近年来，随着高分辨率监测技术的普及，多源数据融合分析成为趋势[2-4]，时序分解与机器学习方法被广泛用于滑坡位移预测[5-7]。当前滑坡预测主要包括2种方法：基于物理机制的蠕变模型[8-9]，能够反映滑坡长期演化特征，但过于依赖地质参数，导致适用范围有限；基于数据驱动的深度学习模型[10-11]，具备较强的非线性建模能力，但难以解释滑坡的复杂作用机制。尽管已有研究取得了一定进展，但现有预测模型普遍存在3个问题：1)分解方法未充分考虑诱发因子对各分量的差异性影响，导致位移分量物理意义不明确；2)趋势项拟合常采用简单线性方法，忽略地质演化的非线性特征；3)忽视了实际预测时诱发因子数据不确定性对模型的影响，缺乏对不确定性的合理建模。
基于上述问题，本文选取甘肃黑方台区域为实验区域，提出一种基于优化时序分解与特征选择的滑坡位移预测模型。首先，利用奇异谱分析(singular spectrum analysis，SSA)提取出滑坡位移和诱发因子的趋势项分量，再利用特征工程方法选取与非趋势分量相关的诱发因子，采用遗传算法(genetic algorithm，GA)优化的变分模态分解(variational mode decomposition，VMD)方法对滑坡位移进行基于诱发因子驱动的分解，有效分解出受诱发因子影响的周期项分量，提高位移分解的准确性；随后，考虑诱发因子对各分量的影响，构建融合诱发因子的西原模型以预测位移的趋势项分量，结合卷积神经网络(convolutional neural network，CNN)与压缩和激励网络(squeeze-and-excitation networks，SE)的门控循环单元(gated recurrent unit，GRU)模型以预测周期项分量，通过频域分析重构为周期函数进行随机项分量建模；最后，考虑实际预测时诱发因子的误差分布，本文结合核密度估计(kernel density estimation，KDE)和蒙特卡洛(Monte Carlo)模拟误差传播过程，构建预测概率区间。在上述预测模型中，优化的时序分解和特征选择模型不仅明确了诱发因子对位移分量的差异化影响，还实现了高精度、可解释的滑坡位移预测。
1 研究方法
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1.1 技术路线
基于优化时序分解和特征选择的滑坡预测技术路线为：1)根据时间序列理论和相关性分析，确定诱发因子对不同分量的影响，将位移分解为趋势项位移、周期项位移和随机项位移3个部分；2)构建融合诱发因子的西原模型和CNN-SE-GRU组合模型，分别预测趋势项和周期项分量，随机项通过频域分析重构为周期函数进行建模；3)针对气象预测误差，利用核密度估计与蒙特卡洛方法进行误差传播建模，构建位移预测的概率区间；4)整合各分量预测结果与预测区间，完成滑坡位移的时序预测(图 1)。
1.2 滑坡位移分解
现有滑坡位移时序分解模型主要为加性模型，可表示为：
$F_t=T_t+C_t+R_t$
式中，Ft表示累积位移；Tt表示滑坡体受自身条件改变引起的趋势项位移分量；Ct表示受到外界诱发因子干扰引起的周期项位移分量；Rt表示微小的随机形变。
然而，在滑坡系统中，一些外界诱发因子(如温度、湿度等)不仅会引发滑坡位移产生周期性变化，还会长期作用于滑坡体改变其自身地质条件，从而对趋势项位移产生累积影响。因此，本文提出一种基于诱发因子驱动启发的优化滑坡位移分解方法，分解流程如下：
1) 趋势项分量提取。奇异谱分析(SSA)是通过将一维时间序列嵌入高维相空间并进行奇异值分解得到趋势项、周期项和噪声项的方法[12-13]。文中SSA用于提取滑坡位移和诱发因子序列的趋势性变化成分，实现对趋势项、非趋势项分量的有效分离。对提取到的各分量作相关性分析，通过特征工程方法选定与各位移分量显著相关的诱发因子。
相较于普遍使用的时序分解方法，基于诱发因子驱动启发的分解策略提取趋势项为基于诱发因子驱动分解出周期项及后续预测提供基础。
2) 周期项与随机项的分量分解。滑坡位移的非趋势项分量包括受到诱发因子波动影响的周期项分量和微小的随机项分量2个部分。变分模态分解(VMD)可以将非趋势项分解为若干具有特定频率范围的本征模态函数(IMF)[14]，本文将VMD分解的IMF重构为周期项和随机项分量。
为深入分析诱发因子对周期项的驱动机制，本文采用遗传算法(GA)确定VMD的分量数和惩罚因子，将诱发因子的非趋势分量与滑坡位移子序列的相关系数矩阵构建为适应度函数，实现以适应度驱动的全局参数优选，从而分解出与诱发因子显著相关的滑坡位移分量。最终，将与诱发因子非趋势性分量显著相关的低频模态部分重构为周期项分量，而高频模态则归类为不受诱发因子影响的随机项。
通过基于诱发因子驱动启发的分解策略对滑坡位移进行时序分解，能够保证各位移分量在预测时与诱发因子维持高度相关，提高预测精度和增强模型的物理意义。
1.3 滑坡位移预测
1.3.1 趋势项分量预测
滑坡体的趋势项位移主要表现为源于非线性地质组成的蠕变特征。孙晓明等[15]提出西原损伤蠕变模型，可较为全面地描述岩体的非线性蠕变问题。由于地质参数获取困难，因此在使用西原模型预测趋势项时采用拟合未知参数的方法。此外，西原损伤蠕变模型在进行趋势项预测时，无法表达诱发因子对滑坡体位移的长期调控作用。基于此，本文引入诱发因子的趋势项分量对位移趋势项分量进行拟合，提出一种融合诱发因子变量的西原模型，其拟合表达式如下：
$T_t=\boldsymbol{Q} \boldsymbol{E}+p_1\left(1-\exp p_2 t\right)+p_3 t^3+p_4 t^2+p_5 t+p_6$
其中，Tt为待拟合的趋势项分量； Q 为诱发因子对应参数矩阵； E 为线性处理后的诱发因子趋势项分量；t为天数；p1~p6均为待求解参数。
1.3.2 周期项分量预测
周期项位移主要受诱发因子非趋势性波动驱动，呈现出非线性与时序耦合特征。因此，在对其进行建模与预测时，需要能够同时捕捉非线性特征与时间依赖性的模型结构。
卷积神经网络(CNN)适用于多变量时间序列预测的深层次特征提取[16]，而注意力机制中的压缩和激励网络(SE)能够提高CNN对关键信息的感知能力[17]。另外，为了有效捕捉序列数据中的时间依赖性，本文引入门控循环单元(GRU)进行预测。综上，本文构建CNN-SE-GRU的组合预测模型预测周期项分量。
1.3.3 随机项分量预测
根据傅里叶变换的定义，函数满足一定条件时可以表示成三角函数或它们积分的线性组合。本文将随机项分量视为三角函数组合，通过频域分析提取幅值与相位信息，以实现对随机项的函数重构：
$D_t=\sum\limits_{i=1}^m I_{\mathrm{i}}$
其中，Dt表示随机项位移；m表示三角函数分量的个数；Ii表示频域分析中得到的三角函数。
1.4 滑坡预测区间
滑坡位移预测中，通常以实测气象数据作为变量输入，而在实际应用中，未来时间段的实测气象数据并不可得，只能依赖气象预测值。由于气象预测数据与实测数据存在系统性误差和不确定性，直接将其作为模型输入将导致滑坡位移预测结果出现偏差。
为解决气象预测误差导致预测偏差的问题，本文将气象预测误差视为随机变量，其对于滑坡位移预测结果的影响可建模为概率传播过程。基于此，本文提出一种基于核密度估计与蒙特卡洛模拟结合的位移概率区间预测方法，用于刻画气象预测误差引发的滑坡位移预测结果的不确定性范围。
1.4.1 预测数据误差估计
为构建气象预测误差的概率分布模型，本文通过核密度估计估算历史气象预测误差的概率分布。KDE是一种将核平滑应用于概率密度估计的非参数估计方法，其通过以核为权重来估计随机变量的概率密度函数[18]。为了得到更准确的预测概率区间，本文选用规则化最小方差估计设定带宽大小控制概率密度函数的平滑程度，并选用高斯核作为核函数控制样本点的影响形状。
1.4.2 预测概率区间确定
考虑到气象数据的变化主要影响周期项位移的预测结果，且机器学习模型作为“黑箱”模型难以显式表征输入误差对输出结果的函数映射关系。蒙特卡洛方法作为一种统计模拟方法，是指使用随机数来解决很多计算问题的方法[19]。基于此，本文利用蒙特卡洛方法模拟输入误差在模型中的传播过程，进而构建预测输出的概率区间。
预测区间获取的具体流程为：在测试集阶段，对气象预测输入变量施加基于KDE构建的误差扰动；从误差分布中随机采样多组扰动值，叠加至气象预测输入，构建扰动样本集；对扰动样本集逐一预测，得到对应的多组滑坡位移预测结果；统计所有预测结果的分布，依据指定置信水平确定滑坡位移预测结果的上下置信边界，形成预测概率区间。该方法能够有效刻画诱发因子不确定性对预测结果的影响，为滑坡预警中的风险容忍度判断与阈值设定提供数据支撑。
2 研究区域概况
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2.1 测区概况
黑方台黄土台塬位于甘肃省永靖县盐锅峡镇，纬度范围为36°04′10″~36°07′20″N，经度范围为103°16′40″~103°20′50″E[20]。该台塬最高海拔1 759.5 m，最低海拔1 560.4 m，相对高差达199.1 m，形成了塬边20°~70°的坡度变化[21]。据统计，黑方台台塬每亩年均灌溉量约559.04 m3，每年灌溉集中在3月和11月，该时间段蒸发量小于100 mm且降水量小于10 mm。
从黑方台地层剖面图(图 2)可以看出，该区域的地质结构自上至下依次为马兰黄土组成的风积黄土层、黄河冲积形成的阶地冲积层和砂泥岩组成的黄河阶地基座[22]。
2.2 数据来源
此次实验的研究数据包括诱发因子温度T(℃)、湿度H(%)、累积降水量CR(mm)、日均灌溉强度(mm/d)，以及GNSS监测的滑坡累积位移(mm)数据。其中，气象数据来源于中国气象数据网, 根据统计资料，可将灌溉过程视为不受蒸发和降雨补给的水分下渗过程，平均灌溉强度为14 mm/d；滑坡位移数据来源于长安大学在甘肃省黑方台党川滑坡体上布设的北斗/GNSS高精度监测站(图 3)，其中党川段滑坡的中部变形较大，故选取HF09监测点所在范围开展实验。
3 滑坡位移预测应用与分析
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3.1 滑坡位移分解与相关性分析
利用SSA对滑坡位移数据和全部诱发因子进行趋势项分量提取，窗口长度L设置为100，接近样本数据N的一半以保证趋势与周期结构的有效分离，嵌入维数K设置为N-L+1自动确定，模态分组依据奇异值贡献率阈值(本文设置为95%)与W-correlation图结构共同决定，确保趋势、周期及噪声分量划分合理、稳定。
图 4所示即为得到的滑坡位移和诱发因子的趋势项分量。为量化诱发因子与不同位移分量间的相关性，进一步计算皮尔逊相关系数，构建热力图(图 5)。其中，Tt、Ht和Ct分别表示温度、湿度和累积降水量趋势项分量，Tf、Hf和CRf分别表示温度、湿度和累积降水量非趋势项分量，IR表示灌溉强度。
据图 5可以看出，位移趋势项分量与温度、累积降水量和湿度的趋势项分量相关性较强，证明在滑坡系统中外界诱发因子对位移趋势项具有一定影响；位移非趋势项分量与温度、降水的非趋势项部分有较强的相关性，而与湿度非趋势项部分的相关性较弱。因此，在特征选择阶段应优先考虑与各分量高度相关的诱发因子分量。
随后，利用GA-VMD对非趋势项位移作分解处理，将K的搜索范围设定为[3, 6]，α的搜索范围设定为[1 000，2 500]。遗传算法的种群规模设置为200，最大迭代次数为200，精英比例为10%，交叉概率为0.8，用以兼顾全局优化能力与计算效率。适应度函数由原始信号与重构信号的均方误差及各模态与诱发因子相关系数矩阵构成。图 6所示即为利用GA-VMD分解模型对非趋势项位移数据进行分解得到的不同频率时序分量，将低频分量IMF2、IMF3叠加作为周期项分量，高频分量IMF1则作为随机项分量。
3.2 滑坡位移预测
3.2.1 趋势项位移分量预测
据图 5所示的热力图可以看出，实验点滑坡位移趋势项分量主要受到温度、降水与湿度的长期影响。温度变化主要通过冻融与蒸发机制影响滑坡体结构稳定性，累积降水量通过改变孔隙水压力影响滑坡变形速率，湿度则通过调节表层土壤水分交换过程影响滑坡形变过程。根据式(2)的改进西原模型，利用指数和对数函数将诱发因子变量线性化后的拟合式如下：
$\begin{gathered}T_t=q_1 \cdot \exp \left(-\operatorname{temp}_t\right)+q_2 \cdot \ln \left(\text { cum_prec }_t\right)+ \\q_3 \cdot \operatorname{humi}_t+p_1\left(1-\exp p_2 t\right)+p_3 t^3+ \\p_4 t^2+p_5 t+p_6\end{gathered}$
式中，tempt为温度的趋势性分量；cum_prect为累积降水量的趋势性分量；humit为湿度的趋势性分量；q1、q2、q3均为诱发因子对应参数。
基于最小二乘拟合对滑坡位移的趋势项分量进行拟合，最终得到拟合曲线如下：
$\begin{gathered}T_t=-1.0523 \cdot \exp \left(\mathrm{temp}_t\right)+25.8764 \cdot \\\ln \left(\mathrm{cum}_{-} \mathrm{prec}_t\right)+0.0036 \cdot \mathrm{humi}_t- \\0.0143(1-\exp (-0.0273 t))-0.0004 t^3+ \\0.0032 t^2+0.0711 t+0.0089\end{gathered}$
图 7展示了HF09监测点的位移趋势项分量拟合曲线，可以看出，该模型整体拟合度较高，能够有效反映滑坡体的趋势性变化。
3.2.2 周期项分量预测
据图 5所示，周期项位移主要受到温度、累积降水量的非趋势项分量和灌溉强度影响，采用CNN-SE-GRU组合预测模型将上述数据作为模型输入项对周期项分量进行预测。
结合实际数据特性和多组实验优化确定了相应超参数：卷积核大小设为3，卷积通道数设为32，SE注意力卷积核大小设为3，以增强通道特征的交互能力；GRU隐含单元数设为32，用于表征时间依赖特征；训练初始学习率为0.001，并引入L2正则化以提升模型泛化能力。预测结果如图 8所示，模型预测曲线与实际观测值保持较好一致，说明该组合模型在多变量预测时效果较好。
3.2.3 随机项分量预测
利用频率分析方法提取随机项中的频率和相位，根据式(3)将其重构为三角函数组合，具体频率成分见表 1。重构得到的三角函数组合如式(6)所示，图 9所示为随机项的拟合结果。
$\begin{gathered}D_t=0.2778 \cos (80 t+0.6885 \pi)+ \\0.3593 \cos (96 t-0.6342 \pi)+ \\0.2856 \cos (104 t-0.3991 \pi)\end{gathered}$
3.3 滑坡位移区间预测
在获取历史气象预报数据与对应的实测气象数据后，首先计算温度与降雨等气象要素的预测误差序列。基于这些误差样本，采用核密度估计方法构建气象预测误差的概率分布模型。本研究使用高斯核构建概率模型，并通过规则化最小方差准则确定带宽，通过核函数平滑地估计误差的概率密度函数，以保证误差分布估计的稳定性与代表性。气象预测误差的核密度估计结果如图 10所示。
在得到气象预测误差的概率模型后，为了模拟误差在位移预测模型中的传播机制，本文基于蒙特卡洛方法构建了扰动样本集。在预测阶段，从KDE建立的误差分布中随机采样大量误差扰动，并逐一叠加至未来气象预测序列，生成一系列可能的未来气象数据。
随后，将上述扰动后的气象数据依次输入滑坡位移预测模型，获得大量位移预测样本。通过统计所有位移模拟样本的分布，可计算不同置信水平下的预测区间。本文以95%置信水平为例构建位移预测区间，最终得到HF09监测点的滑坡位移概率区间如图 11所示。该方法可有效补偿气象预测不确定性带来的输出偏差，提供更具鲁棒性的预测区间，为实际滑坡预警提供辅助判断依据。
3.4 预测结果分析
根据上述预测结果，将位移趋势项分量、周期项分量、随机项分量和预测概率范围结果叠加后，图 12所示即为HF09监测点的整体预测结果。以均方根误差RMSE与平均绝对百分比误差MAPE作为精度指标，得到预测模型的RMSE和MAPE分别为1.52 mm和0.38%，模型预测效果良好。
为对比文中预测模型的预测效果，设计消融试验方案如下：1)方案1, 利用VMD直接分解滑坡位移，将全部诱发因子数据作为预测模型的输入项，分别采用多项式拟合和GRU、BiTCN-BiGRU (bidirectional temporal convolutional network-bidirectional gated recurrent unit)的组合模型以及未改进的西原模型拟合和Hybrid-GRU(hybrid attention-gated recurrent unit)、CNN-SE-GRU的组合模型进行位移预测；2)方案2, 在方案1的基础上，采用本文提出的位移分解方法并利用组合模型进行预测。
从表 2各方案预测结果可以看出，以RMSE和MAPE为预测性能评价指标，对于HF09监测点，文中提出的预测模型较其他模型预测精度显著提升。方案1利用VMD直接分解滑坡位移，将全部外界影响特征作为预测模型的输入项，这类模型主要忽略了不同影响特征间存在一定的信息冗余以及不能表达各因子对滑坡位移的耦合作用，即使依靠注意力机制提取特征，也无法保证预测精度。方案2采用本文提出的时序分解策略，对比方案1考虑了诱发因子对不同分量的差异化影响，使得整体预测模型预测精度较方案1有所提升，但没有考虑诱发因子对趋势项拟合的影响以及随机项分量的利用，预测精度较差。
本文采用的综合预测模型有效分离了各诱发因子影响的滑坡位移部分，通过相关性理论明确了诱发因子对各位移分量的差异性作用。在确定预测模型时，引入改进西原模型作为组合预测模型之一，增强了模型的可解释性与泛化能力；还通过特征工程以及注意力机制与机器学习模型组合构建预测模型，并将不受外界影响的位移分量单独建模预测，而非现有预测模型中整体叠加建模进行预测，增强了整体的预测精度。最后，考虑实际应用时气象数据来源自身的不确定性，本文利用概率区间作为对预测结果的补充，增强了预测结果在预警决策场景中的可靠性。
3.5 模型在不同滑坡场景下的适用性分析
为检验本文提出的滑坡预测方法在不同地质条件下的通用性，本文进一步选取三峡库区的新铺滑坡对模型的预测效果进行验证。新铺滑坡与黑方台滑坡具有显著不同的变形控制机制，其形变主要受到库水位和降雨因素的影响，呈现近似“阶跃”的时序位移特征。本文选取长安大学在新铺滑坡所布设XP04监测点位移以及诱发因子的监测数据，具体如图 13所示。
为了体现该模型在新铺滑坡的预测性能，预测流程与模型训练与上文保持一致，计算不同模型的预测精度指标作为对比，具体数据如表 3所示。
由表 3可知，本文方法在新铺滑坡中的预测精度均优于对比模型，且仍能保持较高的预测稳定性与适应性，表明该方法在不同类型、不同变形机制和不同地质环境的滑坡场景中具有较好的通用性和推广价值。
4 结语
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本文针对滑坡位移预测中存在的多因素耦合机理复杂、传统模型物理解释性弱及气象不确定性传播难以建模等问题，提出一种基于优化时序分解与特征选择的滑坡位移预测模型，该模型在分解精度、建模能力与结果稳健性方面均取得较好效果。主要结论如下：1)基于诱发因子对滑坡位移的差异化影响进行位移分解，明确诱发因子对位移分量的影响。2)考虑诱发因子影响对各分量分别建模预测，引入融合诱发因子的西原模型预测趋势项位移，能够反映滑坡体受诱发因子长期作用下的蠕变演化过程；建立CNN-SE-GRU模型预测周期项位移，能够有效捕捉诱发因子对周期项的耦合作用以及时间依赖性；通过频域分析建模随机项，充分挖掘周期性信息并保证数据利用率，提升整体预测效果。3)通过引入核密度估计与蒙特卡洛方法，实现气象预测误差对位移结果的传播建模，构建基于扰动机制的预测置信区间，为滑坡预警系统提供了可量化的风险评估依据。4)在实证研究中，本文模型在RMSE与MAPE指标上分别达到1.52 mm与0.38%，显著优于其他常用模型，验证了本文方法在精度和稳定性方面的优势。
为将位移预测区间结果应用于滑坡监测与预警，可考虑以未来位移速率(即置信区间的标准差)超过各级阈值的概率来量化不同预警等级的风险。基于概率区间的预警机制能够充分考虑预测不确定性，将预测区间与速率阈值统一到“未来状态发生概率”的框架之下，实现从连续概率输出到离散预警等级的映射，更契合滑坡预警系统的实际需求。
基金
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  • 国家重点研发计划(2024YFC3012603)
  • 国家自然科学基金(42174006)
  • 陕西省杰出青年科学基金(2022JC-18)
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2026年第46卷第6期
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doi: 10.14075/j.jgg.2025.08.293
  • 接收时间：2025-08-24
  • 首发时间：2026-07-09
  • 出版时间：2026-06-15
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  • 收稿日期：2025-08-24
基金
国家重点研发计划(2024YFC3012603)
国家自然科学基金(42174006)
陕西省杰出青年科学基金(2022JC-18)
作者信息
    1 长安大学地质工程与测绘学院, 西安市, 710054

通讯作者:

赵丽华, 博士, 副教授, 主要从事大地测量数据以及地质灾害高精度数据处理研究, E-mail:
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