Research Article | | Peer-Reviewed

Research on Structural Safety Assessment of High-Speed Railway Tunnels Based on Partial Least Squares Regression

Received: 30 June 2026     Accepted: 24 July 2026     Published: 13 August 2026
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Abstract

Aiming at the problems of multicollinearity among multi-source monitoring indicators, insufficient modeling accuracy with small samples and strong subjectivity of traditional evaluation methods during the long-term operation of high-speed railway tunnels, a quantitative evaluation method for structural safety of high-speed railway tunnels based on partial least squares (PLS) regression is proposed. Six core monitoring indicators, including settlement displacement and horizontal displacement of tunnel lining and track, crack width and water seepage, are selected to establish the evaluation system, and the structural degradation index DI is defined to characterize the degradation degree of tunnel lining. Combining PLS with the variable importance in projection (VIP) criterion, a four-step modeling framework consisting of standardization, principal component extraction, coefficient solution and degradation index prediction is constructed. Component decomposition is adopted to reduce redundant correlation between indicators and improve the generalization ability of the model under small sample conditions. A high-speed railway tunnel in Southwest China is taken as a case for verification. The results show that the PLS model can effectively integrate multi-source monitoring data, quantify the degradation level of tunnel lining, accurately identify sections with severe diseases, and dynamically reflect the long-term evolution trend of structures. It provides quantitative technical support for structural health assessment, disease early warning and monitoring system optimization of mountain high-speed railway tunnels during operation.

Published in Science Research (Volume 14, Issue 4)
DOI 10.11648/j.sr.20261404.23
Page(s) 232-237
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

High-speed Railway Tunnel, Safety Assessment, Partial Least Squares Regression, Degradation Index, Variable Importance in Projection

1.引言
随着高速铁路网络向山区延伸,隧道占比持续攀升。长期运营中受围岩蠕变、地下水渗流和列车动荷载耦合作用,衬砌结构逐渐产生裂缝、渗漏水、变形等病害,严重威胁行车安全。结构健康监测系统已逐步部署,但多源监测数据间存在显著的共线性,传统经验阈值法和层次分析法主观性强,难以客观融合多指标信息。偏最小二乘(PLS)回归集成了主成分分析、典型相关分析和多元回归的优势,能在变量多重共线和小样本条件下建立稳健模型。本文以西南地区某高铁隧道为对象,构建6项核心监测指标的PLS结构退化指数预测模型,并通过实例验证其有效性。
2.偏最小二乘原理与隧道结构安全评价理论
2.1.偏最小二乘回归基本原理
偏最小二乘回归(Partial Least Squares Regression,PLS)是一种多因变量对多自变量的统计建模方法,由Wold等人在20世纪80年代提出。其核心思想是在自变量空间和因变量空间中分别提取相互正交的主成分,使提取的成分既能最大程度的携带自变量的变异信息,也能最好的对因变量进行解释。与普通最小二乘回归相比,PLS无需对自变量进行正交变换即可处理变量之间的多重共线性问题,能有效解决样本量小于自变量维数的问题。具体定义如下:
定义标准化后的自变量矩阵为X(n×p),因变量矩阵为Y(n×q),PLS按式(1)与(2)对X和Y分别进行双线性分解:
X=TPT+E(1)
Y=UQT+F(2)
式中:T、U分别为X和Y的得分矩阵(n×k,k为主成分数);
P(p×k)和Q(q×k)分别为X和Y的载荷矩阵;
E和F为残差矩阵。
PLS采用迭代算法逐次提取主成分。在第h步中,权值向量wh的求解准则为最大化得分向量thuh的协方差:
wh=Xh-1TuhXh-1Tuh(3)
式中:Xh-1为经h-1次残差更新后的自变量矩阵;
uh为第h步中因变量的得分向量;
||·||表示欧氏范数。
提取得分向量后,建立X得分与Y得分之间的线性内部关系:
uh=bhth(4)
式中:bh=thTuhthTth为第h个内部回归系数。
主成分数k的选取直接影响模型的预测精度与泛化能力,采用交叉有效性指标作为判定准则,其数学表达式如下:
Qh2=1-PRESShSSh-1(5)
式中:PRESSh为加入第h个成分后留一交叉验证的预测残差平方和;
SSh-1为含h-1个成分时的拟合残差平方和。
Qh2<0.0975时,表明第h个成分对模型预测能力的边际贡献不足,停止继续提取。
2.2.隧道结构安全评价理论
隧道结构安全评价是一个从数据采集到状态定级的多环节系统工程。张凯南系统研究了运营隧道健康监测预警指标与安全等级的对应关系,提出了多指标融合评估的基本框架。梅晓腾进一步从时空多源信息关联的角度,建立了铁路隧道状态评估中的数据融合方法。许芳在此基础上提出了涵盖数据采集、指标量化、模型分析和状态定级四个阶段的运营隧道服役性能评估流程,强调评价模型应能够综合利用多源检测数据,兼顾评定结果的准确性和可操作性。
高铁隧道在运营期主要面临衬砌裂损和渗漏水两类典型病害。杨松通过统计分析指出,衬砌裂缝和渗漏水是导致隧道结构性能退化的主要因素,且两者往往相伴发生。叶鹏飞研究了富水地层条件下隧道衬砌结构的力学特性变化规律,发现围岩水压力的长期作用会加速衬砌刚度衰减和裂缝扩展。
裂缝是隧道衬砌结构损伤的最直观表征。徐万宇系统研究了裂缝宽度、深度和密度三维特征与二衬剩余承载力的定量关系,建立了裂缝特征参数到承载能力退化程度的映射模型,为基于裂缝监测数据评估结构安全状态提供了理论依据。
为综合反映隧道结构多维度退化程度,定义结构退化指数(Degradation Index,DI)如式(6)所示,取0~100连续值,DI值越大,表明结构退化越严重,安全风险越高。
DI=αix̃iαi=1(6)
式中:x̃i为第i个监测指标经归一化处理后的数值,αi为对应的权重系数;
3.基于偏最小二乘的隧道结构安全评价模型
3.1.监测指标体系构建
监测指标的选取遵循科学性、代表性和可获取性原则,以现行铁路隧道监测规范为主要依据。《邻近铁路营业线施工安全监测技术规程》(TB 10314-2021)规定了铁路隧道施工及运营期变形监测的项目和技术要求;《城市轨道交通工程测量规范》(GB 50308-2008)则对盾构和矿山法隧道的监测频率及预警阈值提出了指导性要求;《铁路工程测量规范》(TB10101-2018)明确了隧道内沉降观测和水平位移观测的精度指标。
综合上述规范,本文选取6项核心监测指标作为PLS回归模型的输入变量:隧道壁沉降(X1)、隧道壁水平位移(X2)、轨道沉降(X3)、轨道水平位移(X4)、裂缝宽度(X5)、渗水量(X6)。各指标的单位分别为mm、mm、mm、mm、mm、L/(m2·d)。其中,X1和X2由全站仪自动化监测系统获取,测量精度±0.6mm;X3和X4同样由全站仪测量,以轨枕上布设的监测棱镜为观测目标;X5由振弦式裂缝计自动采集,量程0~25mm,精度±0.01mm;X6采用人工周期性量测方式,每季度检测一次衬砌接缝渗水量。所有指标经统一时间窗口(季度均值)聚合后纳入模型输入。
3.2.PLS回归建模流程
PLS回归模建立共包含四个阶段,具体如下所示:
阶段一:数据标准化,对6维输入矩阵X(n×6)和退化指数向量Y(n×1)分别进行Z-score标准化处理,消除各指标量纲差异对建模的影响。归一化后各变量均值为0、标准差为1,确保后续主成分提取不受原始量级差异干扰。
阶段二:主成分提取,按照公式(1)~(5)描述的双线性分解和交叉有效性准则,迭代提取k个相互正交的主成分。每次提取后,对X和Y矩阵进行残差缩减,从当前矩阵中减去已提取成分的部分,再基于残差矩阵进行下一轮提取,保证各主成分之间严格正交。k的取值由交叉有效性指标Qh2判定,保留Qh2≥0.0975的所有部分。
阶段三:回归系数求解,利用提取的k个主成分建立PLS回归方程:
Ŷ=XBPLS(7)
BPLS=W(PTW)-1CT(8)
式中:BPLS为PLS回归系数矩阵,由权重矩阵W、X载荷矩阵P和Y权重矩阵C共同确定。
阶段四:退化指数预测,将待评断面的监测数据矩阵结合式(6),计算该断面的结构退化指数预测值。
3.3.变量重要性分析
为量化各监测指标对结构退化指数预测的相对贡献程度,引入变量重要性投影(Variable Importance in Projection,VIP)指标,其数学表达式如下所示,当某变量的VIP值超过均值时,表明其贡献高于平均贡献水平;VIP值越大表示该指标对模型预测的贡献越大
VIPj=ph=1kRd(Y;th)whj2h=1kRd(Y;th)(9)
式中:p为输入变量个数;
k为保留的主成分数;
Rd(Y;th)为第h个主成分th对因变量Y的方差解释量;
whj为权重矩阵W中第j个变量在第h主成分上的权重系数。
3.4.模型评价准则
本文采用决定系数(R2)、均方根误差(Root Mean Square Error,RMSE)和平均绝对误差(Mean Absolute Error,MAE)三项指标对模型功能进行综合评价,数学表达式如式所示:
R2=1-i=1n(yi-ŷi)2i=1n(yi-y̅i)2(10)
RMSE=1ni=1n(yi-ŷi)2(11)
MAE=1ni=1nyi-ŷi(12)
式中:yi为第i个断面真实退化指数DI;
ŷi为PLS 模型输出的预测退化指数;
y̅i为全部样本真实DI的平均值;
n为样本数。
R2越接近1表示模型拟合优度越高,RMSE和MAE越小表示预测偏差越小。
4.实例分析
4.1.工程概况
选取西南地区某高速铁路隧道作为实例分析对象,该隧道为双线单洞结构,隧道穿越低中山剥蚀地貌区,最大埋深约180m,围岩以Ⅲ~Ⅳ级为主,节理裂隙发育,地下水类型为基岩裂隙水,局部富水段日涌水量可达200m³/d,存在渗漏风险。
该隧道监测区段里程为K12+350~K12+550,全长200m,沿隧道纵向间隔20m布设10个监测断面(编号S1~S10),每个断面在拱顶、拱腰、轨枕等关键位置设置监测点。监测项目包括:隧道壁与轨道的沉降位移监测、水平位移监测(采用徕卡TS60全站仪(测角精度0.5″,测距精度0.6mm+1ppm)),监测频率为1次/天;衬砌关键裂缝宽度变化监测(采用振弦式裂缝计(量程0~25mm,分辨率0.01mm)),监测频率为1次/小时;衬砌接缝及施工缝进行人工渗水检测,检测频率1次/每季度。
4.2.监测数据
以2025年第三季度为结构安全评估时段,对10个断面的监测数据进行季度均值聚合,得到建模数据集,监测数据计算所得退化指数DI如表1所示:
表1 典型断面监测数据与退化指数。

断面

里程

X1(mm)

X2(mm)

X3(mm)

X4(mm)

X5(mm)

X6(L/m2·d)

DI

S1

K12+350

2.31

1.15

1.82

0.93

0.12

0.08

24.6

S3

K12+390

4.87

2.36

3.15

1.78

0.35

0.21

38.9

S5

K12+430

8.92

4.51

6.23

3.42

0.68

0.45

62.3

S7

K12+470

12.46

6.87

8.95

5.21

1.05

0.72

85.7

S10

K12+530

3.15

1.68

2.41

1.24

0.18

0.11

28.3

表1可知,监测区段中部的S5~S7断面各指标值明显偏高,退化指数均在60以上,表明该区域结构退化较为严重。该区段恰好对应隧道最大埋深位置(K12+430附近,埋深约178m),围岩级别以Ⅳ级为主,节理密度高,地下水位高于拱顶约25m,长期高水压作用导致衬砌受力条件恶劣,与监测数据反映的退化规律相吻合。
4.3.结果分析
将10个断面按照7:3的比例随机划分为训练集(7个断面)和测试集(3个断面)。经交叉有效性分析,确定最佳主成分数k=3。模型性能评价结果如表2所示:
表2 PLS模型性能评价结果。

数据集

R2

RMSE

MAE

最佳主成分数

训练集

0.923

3.847

2.961

3

测试集

0.886

5.124

4.073

表2可知,PLS回归模型在训练集和测试集上的决定系数R2分别达到0.923和0.886,均方根误差RMSE分别为3.847和5.124,平均绝对误差MAE分别为2.961和4.073。模型在训练集和测试集上均表现出较高的预测精度和泛化能力,证明PLS回归能够有效处理6项监测指标间的多重共线性问题,建立起稳健的结构退化指数映射关系。
计算6项核心监测指标的变量重要性投影(VIP)值,具体如表3所示:
表3 变量重要性投影(VIP)排序结果。

排名

指标

VIP值

1

X5 裂缝宽度

1.245

2

X1 隧道壁沉降

1.138

3

X3 轨道沉降

0.967

4

X6 渗水量

0.892

5

X2 隧道壁水平位移

0.834

6

X4 轨道水平位移

0.776

表3可知,裂缝宽度(X5)和隧道壁沉降(X1)的VIP值均大于1,分别为1.245和1.138,是影响结构退化指数的最关键指标。这一结果与徐万宇关于裂缝特征与二衬承载能力退化关系的理论分析高度吻合,表明衬砌裂缝的开裂程度直接决定了结构承载力的衰减速率。隧道壁沉降作为围岩变形向衬砌传递的直接表征,同样对结构安全状态具有显著的指示作用。以上结果表明,裂缝宽度(X5)和隧道壁沉降(X1)两指标的监测传感器应作为重点维护对象,在巡检中优先保障其数据连续性和可靠性。轨道沉降(X3)和渗水量(X6)的VIP值虽低于1,分别排第3和第4位,但作为辅助指标仍能提供有效的补充信息。
5.结论
本文针对高铁运营隧道多源监测数据融合分析中的变量共线性与样本有限性难题,提出了基于偏最小二乘回归的高铁隧道结构安全评价模型,以西南地区某高铁隧道200m检测区段为实例进行了验证,主要结论如下。
(1)构建了涵盖隧道壁沉降、隧道壁水平位移、轨道沉降、轨道水平位移、裂缝宽度和渗水量共6项核心指标的结构安全评价指标体系,融合了全站仪自动化监测、裂缝计自动化监测和周期性渗水检测三类数据源,实现了多维度隧道结构状态的量化表征。
(2)建立了PLS回归模型,通过交叉有效性准则确定最佳主成分数k=3,成功实现6项共线性监测指标到结构退化指数的高精度映射,训练集R2=0.923,测试集R2=0.886,表明模型具有良好的拟合精度和泛化能力。
(3)VIP分析结果表明,裂缝宽度(VIP=1.245)和隧道壁沉降(VIP=1.138)是结构退化的最敏感指标,与隧道衬砌力学退化机理一致,验证了PLS模型的可解释性,也为监测系统传感器布设方案的优化提供了定量依据。
(4)实例分析表明,该模型能够有效识别检测区段内退化程度的空间分布规律,为运营隧道区段级安全评估提供了定量化决策支撑。
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    Zhengchuan, H. (2026). Research on Structural Safety Assessment of High-Speed Railway Tunnels Based on Partial Least Squares Regression. Science Research, 14(4), 232-237. https://doi.org/10.11648/j.sr.20261404.23

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    ACS Style

    Zhengchuan, H. Research on Structural Safety Assessment of High-Speed Railway Tunnels Based on Partial Least Squares Regression. Sci. Res. 2026, 14(4), 232-237. doi: 10.11648/j.sr.20261404.23

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    AMA Style

    Zhengchuan H. Research on Structural Safety Assessment of High-Speed Railway Tunnels Based on Partial Least Squares Regression. Sci Res. 2026;14(4):232-237. doi: 10.11648/j.sr.20261404.23

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  • @article{10.11648/j.sr.20261404.23,
      author = {Hao Zhengchuan},
      title = {Research on Structural Safety Assessment of High-Speed Railway Tunnels Based on Partial Least Squares Regression},
      journal = {Science Research},
      volume = {14},
      number = {4},
      pages = {232-237},
      doi = {10.11648/j.sr.20261404.23},
      url = {https://doi.org/10.11648/j.sr.20261404.23},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sr.20261404.23},
      abstract = {Aiming at the problems of multicollinearity among multi-source monitoring indicators, insufficient modeling accuracy with small samples and strong subjectivity of traditional evaluation methods during the long-term operation of high-speed railway tunnels, a quantitative evaluation method for structural safety of high-speed railway tunnels based on partial least squares (PLS) regression is proposed. Six core monitoring indicators, including settlement displacement and horizontal displacement of tunnel lining and track, crack width and water seepage, are selected to establish the evaluation system, and the structural degradation index DI is defined to characterize the degradation degree of tunnel lining. Combining PLS with the variable importance in projection (VIP) criterion, a four-step modeling framework consisting of standardization, principal component extraction, coefficient solution and degradation index prediction is constructed. Component decomposition is adopted to reduce redundant correlation between indicators and improve the generalization ability of the model under small sample conditions. A high-speed railway tunnel in Southwest China is taken as a case for verification. The results show that the PLS model can effectively integrate multi-source monitoring data, quantify the degradation level of tunnel lining, accurately identify sections with severe diseases, and dynamically reflect the long-term evolution trend of structures. It provides quantitative technical support for structural health assessment, disease early warning and monitoring system optimization of mountain high-speed railway tunnels during operation.},
     year = {2026}
    }
    

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  • TY  - JOUR
    T1  - Research on Structural Safety Assessment of High-Speed Railway Tunnels Based on Partial Least Squares Regression
    AU  - Hao Zhengchuan
    Y1  - 2026/08/13
    PY  - 2026
    N1  - https://doi.org/10.11648/j.sr.20261404.23
    DO  - 10.11648/j.sr.20261404.23
    T2  - Science Research
    JF  - Science Research
    JO  - Science Research
    SP  - 232
    EP  - 237
    PB  - Science Publishing Group
    SN  - 2329-0927
    UR  - https://doi.org/10.11648/j.sr.20261404.23
    AB  - Aiming at the problems of multicollinearity among multi-source monitoring indicators, insufficient modeling accuracy with small samples and strong subjectivity of traditional evaluation methods during the long-term operation of high-speed railway tunnels, a quantitative evaluation method for structural safety of high-speed railway tunnels based on partial least squares (PLS) regression is proposed. Six core monitoring indicators, including settlement displacement and horizontal displacement of tunnel lining and track, crack width and water seepage, are selected to establish the evaluation system, and the structural degradation index DI is defined to characterize the degradation degree of tunnel lining. Combining PLS with the variable importance in projection (VIP) criterion, a four-step modeling framework consisting of standardization, principal component extraction, coefficient solution and degradation index prediction is constructed. Component decomposition is adopted to reduce redundant correlation between indicators and improve the generalization ability of the model under small sample conditions. A high-speed railway tunnel in Southwest China is taken as a case for verification. The results show that the PLS model can effectively integrate multi-source monitoring data, quantify the degradation level of tunnel lining, accurately identify sections with severe diseases, and dynamically reflect the long-term evolution trend of structures. It provides quantitative technical support for structural health assessment, disease early warning and monitoring system optimization of mountain high-speed railway tunnels during operation.
    VL  - 14
    IS  - 4
    ER  - 

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Author Information
  • Chengdu High-speed Railway Maintenance Depot, China Railway Chengdu Bureau Group Co., Ltd., Chengdu, China