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Article(id=1207271181695140658, tenantId=1146029695717560320, journalId=1205116964453384197, issueId=1207271180105499439, articleNumber=null, orderNo=null, doi=10.20040/j.cnki.1000-7709.2025.20241868, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1727971200000, receivedDateStr=2024-10-04, revisedDate=1731859200000, revisedDateStr=2024-11-18, acceptedDate=null, acceptedDateStr=null, onlineDate=1765765479730, onlineDateStr=2025-12-15, pubDate=1758729600000, pubDateStr=2025-09-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1765765479730, onlineIssueDateStr=2025-12-15, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1765765479730, creator=13701087609, updateTime=1765765479730, updator=13701087609, issue=Issue{id=1207271180105499439, tenantId=1146029695717560320, journalId=1205116964453384197, year='2025', volume='43', issue='9', pageStart='1', pageEnd='220', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1765765479351, creator=13701087609, updateTime=1765765681303, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1207272027254247478, tenantId=1146029695717560320, journalId=1205116964453384197, issueId=1207271180105499439, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1207272027254247479, tenantId=1146029695717560320, journalId=1205116964453384197, issueId=1207271180105499439, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=92, endPage=96, ext={EN=ArticleExt(id=1207271181997130550, articleId=1207271181695140658, tenantId=1146029695717560320, journalId=1205116964453384197, language=EN, title=Prediction of Thrust and Torque of TBM Based on Information Fusion and Stacked Convolutional Neural Networks, columnId=null, journalTitle=Water Resources and Power, columnName=null, runingTitle=null, highlight=null, articleAbstract=

It is the key issues of reasonably and accurately predicting the thrust and torque of tunnel boring machines (TBM) to realize the intelligent control of TBMs. This paper proposes a two-stage prediction method of knowledge-data-driven spatio-temporal stacked convolutional network (KD-NTS-GAT). Firstly, based on expert knowledge and the NTS-NOTEARS method, a new information fusion technique is proposed. The discrete expert experience and the continuous NTS-NOTEARS indicators is mapped and smoothly fused through clustering. The causal relationships among the key operating parameters of the TBM is quantitatively extracted to improve the authenticity of the causal relationships significantly. Then, causality is further combined as a prior knowledge with stacked convolutional network deep learning model for predicting thrust and torque of TBM. Taking the bid Ⅳ of Xinjiang Water Conveyance Tunnel Project as an example, a comparative analysis of the KD-NTS-GAT method and the pure data-driven method shows that the KD-NTS-GAT has better prediction capability on thrust and torque. The conclusions can provide a reference for the intelligent control of TBM construction.

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合理准确预测隧道掘进机的推力和扭矩是实现TBM智能化控制的关键问题之一。对此，提出一种两阶段知识数据双驱动时空堆叠卷积网络（KD-NTS-GAT）预测方法。首先基于专家知识表达与NTS-NOTEARS方法提出一种新的信息融合技术，通过聚类方法将离散的专家经验与NTS-NOTEARS连续指标进行映射并平滑融合，量化提取TBM关键运行参数之间的因果关系，显著提高了因果关系的真实性。然后，将因果关系作为先验知识进一步与堆叠卷积网络深度学习模型结合，用于预测TBM推力和扭矩。结合新疆输水隧洞工程Ⅳ标段，将KD-NTS-GAT方法与纯数据驱动结果进行对比分析，结果表明两阶段知识数据双驱动时空堆叠卷积网络具有更好的推力与扭矩预测能力。研究结论可为TBM施工智能化控制提供参考。

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杨耀红（1969-），男，教授、博导，研究方向为工程管理、资源环境管理，E-mail：

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杨耀红（1969-），男，教授、博导，研究方向为工程管理、资源环境管理，E-mail：

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杨耀红（1969-），男，教授、博导，研究方向为工程管理、资源环境管理，E-mail：

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A causal-temporal graphic convolutional network (CT-GCN) approach for TBM load prediction in tunnel excavation[J]. Expert systems with applications, 2024, 238: 121977., articleTitle=A causal-temporal graphic convolutional network (CT-GCN) approach for TBM load prediction in tunnel excavation, refAbstract=null), Reference(id=1207271198799512232, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, doi=null, pmid=null, pmcid=null, year=2022, volume=112, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[11], rfOrder=10, authorNames=HOU S K, LIU Y R, journalName=Engineering applications of artificial intelligence, refType=null, unstructuredReference=HOU S K, LIU Y R. Early warning of tunnel collapse based on Adam-optimised long short-term memory network and TBM operation parameters[J]. Engineering applications of artificial intelligence, 2022, 112: 104842., articleTitle=Early warning of tunnel collapse based on Adam-optimised long short-term memory network and TBM operation parameters, refAbstract=null), Reference(id=1207271198963090096, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, doi=null, pmid=null, pmcid=null, year=2023, volume=24, issue=9, pageStart=801, pageEnd=816, url=null, language=null, rfNumber=[12], rfOrder=11, authorNames=WANG L T, ZHU F Z, LI J, journalName=Journal of Zhejiang university-SCIENCE A, refType=null, unstructuredReference=WANG L T, ZHU F Z, LI J, et al. A data-driven approach for modeling and predicting the thrust force of a tunnel boring machine[J]. 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TBM specifications

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技术参数取值技术参数取值
刀盘开挖直径/mm6 530刀盘额定扭矩/（kN·m）4 510
最大推进速度/（mm·min-1）160刀盘脱困扭矩/（kN·m）10 045
额定总推力/kN20 040刀盘转速/rpm0~9.8
最大总推力/kN17 070装机功率/kW2 800
), ArticleFig(id=1207271194731037152, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=CN, label=表1, caption=

TBM主要技术参数

, figureFileSmall=null, figureFileBig=null, tableContent=
技术参数取值技术参数取值
刀盘开挖直径/mm6 530刀盘额定扭矩/（kN·m）4 510
最大推进速度/（mm·min-1）160刀盘脱困扭矩/（kN·m）10 045
额定总推力/kN20 040刀盘转速/rpm0~9.8
最大总推力/kN17 070装机功率/kW2 800
), ArticleFig(id=1207271194827506150, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=EN, label=Tab. 2, caption=

Main operating parameters of TBM

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特征变量单位平均值最小值25%50%75%最大值
X1mm/min41.292.8130.5240.9051.5497.80
X2mm/r16.462.0012.816.2320.6446.71
X3kN149 123.00121 209.70141 919.50152 552.20154 070.00165 325.50
X4kW201.4410.38123.21182.99195.17719.65
X5rpm1.580.511.201.701.922.52
X6kN152.8922.09132.01153.05171.79260.53
X7A38.5518.0137.4438.5139.5250.32
Y1kN9 062.92804.067 685.279 214.9510 624.8516 455.26
Y2kN·m1 209.00131.09856.861 193.011 507.403 734.77
), ArticleFig(id=1207271195016249843, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=CN, label=表2, caption=

TBM主要运行参数

, figureFileSmall=null, figureFileBig=null, tableContent=
特征变量单位平均值最小值25%50%75%最大值
X1mm/min41.292.8130.5240.9051.5497.80
X2mm/r16.462.0012.816.2320.6446.71
X3kN149 123.00121 209.70141 919.50152 552.20154 070.00165 325.50
X4kW201.4410.38123.21182.99195.17719.65
X5rpm1.580.511.201.701.922.52
X6kN152.8922.09132.01153.05171.79260.53
X7A38.5518.0137.4438.5139.5250.32
Y1kN9 062.92804.067 685.279 214.9510 624.8516 455.26
Y2kN·m1 209.00131.09856.861 193.011 507.403 734.77
), ArticleFig(id=1207271195146273277, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=EN, label=Tab. 3, caption=

Performance evaluation of y1 and y2 under different time lags τ

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指标d平均绝对误差均方根误差R2
推力/kN0563.44989.870.832
 1516.49857.250.871
 2410.06732.110.912
 3446.73775.320.899
扭矩/（kN·m）0123.25167.020.786
 193.37118.130.923
 278.43108.240.955
 382.16112.040.938
), ArticleFig(id=1207271195225965061, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=CN, label=表3, caption=

y1、y2在不同时滞τ下的性能评价

, figureFileSmall=null, figureFileBig=null, tableContent=
指标d平均绝对误差均方根误差R2
推力/kN0563.44989.870.832
 1516.49857.250.871
 2410.06732.110.912
 3446.73775.320.899
扭矩/（kN·m）0123.25167.020.786
 193.37118.130.923
 278.43108.240.955
 382.16112.040.938
), ArticleFig(id=1207271195360182799, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=EN, label=Tab. 4, caption=

Correspondence between expert experience and data-driven

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专家经验13579
数据驱动（0.01~0.17）（0.17~0.26）（0.26~0.55）（0.55~0.69）（0.69~0.90）
), ArticleFig(id=1207271195532149273, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=CN, label=表4, caption=

专家经验离散指标与数据驱动聚类团体对应关系

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专家经验13579
数据驱动（0.01~0.17）（0.17~0.26）（0.26~0.55）（0.55~0.69）（0.69~0.90）
), ArticleFig(id=1207271195649589797, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=EN, label=Tab. 5, caption=

Evaluation values of model prediction performance before and after information fusion

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矩阵指标推力/kN扭矩/（kN·m）
NTS-GATGCN-BiLSTMNTS-GATGCN-BiLSTM
融合平均绝对误差410.06657.3578.4397.85
矩阵均方根误差732.11912.61108.24138.24
 R20.9120.8650.9550.926
数据驱平均绝对误差688.65751.26107.19109.43
动矩阵均方根误差989.871 014.30149.39164.50
 R20.8640.8330.9110.896
), ArticleFig(id=1207271196878520880, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=CN, label=表5, caption=

信息融合前后模型预测性能评价值

, figureFileSmall=null, figureFileBig=null, tableContent=
矩阵指标推力/kN扭矩/（kN·m）
NTS-GATGCN-BiLSTMNTS-GATGCN-BiLSTM
融合平均绝对误差410.06657.3578.4397.85
矩阵均方根误差732.11912.61108.24138.24
 R20.9120.8650.9550.926
数据驱平均绝对误差688.65751.26107.19109.43
动矩阵均方根误差989.871 014.30149.39164.50
 R20.8640.8330.9110.896
), ArticleFig(id=1207271196970795578, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=EN, label=Tab. 6, caption=

Prediction performance evaluation of KD-NTS-GAT，GCN-BiLSTM，and BiLSTM

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指标模型平均绝对误差均方根误差R2
推力/kNNTS-GAT410.06732.110.912
 GCN-BiLSTM766.911038.180.825
 BiLSTM798.211128.620.799
扭矩/（kN·m）NTS-GAT78.43108.240.955
GCN-BiLSTM123.25179.110.879
BiLSTM156.86197.630.851
), ArticleFig(id=1207271197063070271, tenantId=1146029695717560320, journalId=1205116964453384197, articleId=1207271181695140658, language=CN, label=表6, caption=

KD-NTS-GAT、GCN-BiLSTM、BiLSTM预测性能评估

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指标模型平均绝对误差均方根误差R2
推力/kNNTS-GAT410.06732.110.912
 GCN-BiLSTM766.911038.180.825
 BiLSTM798.211128.620.799
扭矩/（kN·m）NTS-GAT78.43108.240.955
GCN-BiLSTM123.25179.110.879
BiLSTM156.86197.630.851
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基于信息融合与堆叠卷积网络的TBM推力和扭矩预测
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杨耀红 1, 2 , 张哲 1 , 陈建国 3 , 李群胜 3 , 刘宇翔 1
水电能源科学 | 水工结构、水工材料与水利工程施工 2025,43(9): 92-96
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水电能源科学 | 水工结构、水工材料与水利工程施工 2025, 43(9): 92-96
基于信息融合与堆叠卷积网络的TBM推力和扭矩预测
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杨耀红1, 2 , 张哲1, 陈建国3, 李群胜3, 刘宇翔1
作者信息
  • 1.华北水利水电大学水利学院，河南 郑州 450046
  • 2.河南省水圈与流域水安全重点实验室，河南 郑州 450046
  • 3.河南省水利第一工程局集团有限公司，河南 郑州 450000

    • 杨耀红（1969-），男，教授、博导，研究方向为工程管理、资源环境管理，E-mail：

Prediction of Thrust and Torque of TBM Based on Information Fusion and Stacked Convolutional Neural Networks
Yao-hong YANG1, 2 , Zhe ZHANG1, Jian-guo CHEN3, Qun-sheng LI3, Yu-xiang LIU1
Affiliations
  • 1.School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
  • 2.Henan Provincial Key Laboratory of Hydrosphere and Watershed Water Security, Zhengzhou 450046, China
  • 3.Henan Water Conservancy First Engineering Bureau Group Co., Ltd., Zhengzhou 450000, China
出版时间: 2025-09-25 doi: 10.20040/j.cnki.1000-7709.2025.20241868
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摘要
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合理准确预测隧道掘进机的推力和扭矩是实现TBM智能化控制的关键问题之一。对此，提出一种两阶段知识数据双驱动时空堆叠卷积网络（KD-NTS-GAT）预测方法。首先基于专家知识表达与NTS-NOTEARS方法提出一种新的信息融合技术，通过聚类方法将离散的专家经验与NTS-NOTEARS连续指标进行映射并平滑融合，量化提取TBM关键运行参数之间的因果关系，显著提高了因果关系的真实性。然后，将因果关系作为先验知识进一步与堆叠卷积网络深度学习模型结合，用于预测TBM推力和扭矩。结合新疆输水隧洞工程Ⅳ标段，将KD-NTS-GAT方法与纯数据驱动结果进行对比分析，结果表明两阶段知识数据双驱动时空堆叠卷积网络具有更好的推力与扭矩预测能力。研究结论可为TBM施工智能化控制提供参考。

TBM  /  信息融合  /  NTS-NOTEARS  /  堆叠卷积网络

It is the key issues of reasonably and accurately predicting the thrust and torque of tunnel boring machines (TBM) to realize the intelligent control of TBMs. This paper proposes a two-stage prediction method of knowledge-data-driven spatio-temporal stacked convolutional network (KD-NTS-GAT). Firstly, based on expert knowledge and the NTS-NOTEARS method, a new information fusion technique is proposed. The discrete expert experience and the continuous NTS-NOTEARS indicators is mapped and smoothly fused through clustering. The causal relationships among the key operating parameters of the TBM is quantitatively extracted to improve the authenticity of the causal relationships significantly. Then, causality is further combined as a prior knowledge with stacked convolutional network deep learning model for predicting thrust and torque of TBM. Taking the bid Ⅳ of Xinjiang Water Conveyance Tunnel Project as an example, a comparative analysis of the KD-NTS-GAT method and the pure data-driven method shows that the KD-NTS-GAT has better prediction capability on thrust and torque. The conclusions can provide a reference for the intelligent control of TBM construction.

TBM  /  information fusion  /  NTS-NOTEARS  /  stacked convolutional network
杨耀红, 张哲, 陈建国, 李群胜, 刘宇翔. 基于信息融合与堆叠卷积网络的TBM推力和扭矩预测. 水电能源科学, 2025 , 43 (9) : 92 -96 . DOI: 10.20040/j.cnki.1000-7709.2025.20241868
Yao-hong YANG, Zhe ZHANG, Jian-guo CHEN, Qun-sheng LI, Yu-xiang LIU. Prediction of Thrust and Torque of TBM Based on Information Fusion and Stacked Convolutional Neural Networks[J]. Water Resources and Power, 2025 , 43 (9) : 92 -96 . DOI: 10.20040/j.cnki.1000-7709.2025.20241868
正文
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1 引言
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隧道掘进机（TBM）作为一种现代化的隧道施工设备，在公路铁路工程、西部陆海新通道、国家水网、抽水蓄能电站、地下矿山等重大工程中得到了广泛应用。掘进机的推力和刀盘扭矩是两项至关重要的参数，过大的推力可能会导致永久隧道衬砌出现裂缝和损坏，甚至影响整体结构的完整性。高扭矩通常表现为刀盘磨损严重，可能导致卡机风险[1]。近年来，TBM参数预测方法也得到了迅速发展，大量机器学习、神经网络等人工智能方法得以应用[2]。采用数据驱动方法获得不同参数的重要性分数[3]、考虑时间维度[4]、提取数据隐性特征和时间相关特征[5]等方法以提高预测准确性。但它们仍主要依赖于数据模式，缺少理论模型支撑，在揭示输入和输出变量之间的非线性关系时，很难解释其内在逻辑[6]。基于因果关系的模型更具解释性和鲁棒性，因为它们能够摒弃机器学习中的虚假关联关系，真实反映变量之间的相互影响[7]。同时在工程施工过程中，专家基于现场管理的感知、对设备操控的体验及对复杂问题的处理，形成了丰富的工程经验，这些经验知识是理解变量关系和指导TBM施工的宝贵财富。因此研究数据驱动与专家经验结合的人工智能方法，是解决掘进机推力和刀盘扭矩等参数精准预测的途径之一。为合理精准预测TBM施工推力和扭矩，本文提出了一种基于知识、数据双驱动两阶段KD-NTS-GAT方法，第一阶段为KD-NTS，结合专家经验和数据驱动技术，发掘TBM关键参数之间的因果关系；第二阶段为NTS-GAT，利用这些因果关系矩阵作为先验知识，结合数据驱动进行预测；该方法融合了知识驱动和数据驱动，旨在量化TBM关键参数之间的因果关系，以帮助模型更好地学习和推理。
2 研究方法
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2.1 NTS-NOTEARS因果发现算法
NTS-NOTEARS是一种基于分数的时间序列数据结构学习方法，结构学习转化为数值优化问题，能够快速识别特征与目标变量之间的全局最优因果关系图[8]。该网络捕获变量之间的非线性、滞后（切片间）和瞬时（切片内）关系。此方法使用给出的时间序列数据{Xt：t=1，2，…，T}，一维CNN学习局部不变特征并将它们在数据序列中聚合来学习高阶序列特征。两个变量之间边缘的估计依赖强度是它们的核权重的L2范数：
式中，为权重强度。
最后，将权重阈值应用于每个时间步k，以修剪具有弱依赖性强度的边缘并定义每个变量的父集。NTS-NOTEARS方法克服NOTEARS不能处理数据间非线性关系、先验知识（如禁止或必需边缘）作为附加的优化约束及时间序列中滞后性缺陷[9]。
2.2 图注意力网络
注意力机制的图卷积神经网络（GAT）可以学习参数之间的拓扑结构关系，能够捕获节点间的复杂关系。GAT的目标是计算两个节点之间的权重eij。Whi代表使用一个模型自己学习共享的权重向量W来对原始特征向量做维度转换，i、j均转化之后拼接，再用一个全连接作为相似计算函数，激活函数为LeakyRelu，此时全连接后产出一个值：
所有的全连接值再做softmax归一化得到最终i、j节点的权重值αij：
另使用多头注意力机制（multi-head attention）来稳定self-attention的学习过程，即对式（3）调用K组相互独立的注意力机制，然后将输出结果拼接起来：
式中，‖表示拼接操作；为第k个注意力机制计算的权重系数；Wk为对应的输入线性变换的权重矩阵。
2.3 BiLSTM网络
除了变量之间的因果关系外，TBM参数还存在时间依赖性[10]。LSTM可以记忆历史信息并将其应用于当前输出，从而实现网络中的状态反馈[11]。LSTM有一个特定的内存块，由输入门、输出门、遗忘门和单元状态组成，公式为：
式中，ft为时间t的输入门状态；ht-1、xt分别为上一刻细胞隐藏状态、当前输入；Wi、bi分别为输入门的权重和偏置；Wc、bc分别为细胞状态的权矩阵和偏项；为临时细胞状态；tanh为双曲切线激活函数；Ct、Ct-1均为细胞状态；it为记忆门；7为Hadamard；ot为输出门；Wo、bo分别为输出门的矩阵和偏置。
BiLSTM算法作为LSTM的变异算法，在LSTM的基础上向前向序列层增加了一个后向序列层，从输入变量中提取更全面的信息，可以充分利用前一个时间序列的信息来预测下一个时间点的目标。BiLSTM网络结构见图1。
2.4 信息融合与堆叠卷积网络KD-NTS-GA模型
基于NTS-NOTEARS方法将专家经验和数据驱动相融合，检测并量化TBM关键操作参数之间的因果关系。然后，将GAT与BiLSTM相结合形成堆叠网络，从空间与时间两个维度进行数据处理，所发现的因果关系可以用作先验知识，进一步训练深度学习模型，实现推力与扭矩的精准预测。所提出的深度框架具有2层GAT网络和3层BiLSTM网络[12]。每个GAT层均有28个神经元，激活函数是ReLU。每个BiLSTM层有200个单元，选择Adam作为优化器，学习率设置为0.001。MSE为损失函数的度量。预测模型实施流程见图2。
3 案例分析
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3.1 工程背景
新疆隧洞工程，标段（桩号23+600~40+823）隧洞由南向北依次穿过北天山南麓中—高山区及分水岭、北麓中—高山区及第三系断陷盆地区等，地面高程1 570~3 469 m。隧洞埋深>500 m的洞段长度约占88.7%，埋深>1 000 m的洞段长度约占50.0%，埋深>2 000 m的洞段长度约占6.7%，最大埋深为2 242 m。采用一台开敞式TBM进行开挖，TBM的主要技术参数见表1。洞径为6.53 m，隧洞坡度为2‰，主要以Ⅱ（28.3%）、Ⅲ（38.5）类围岩为主和少量Ⅳ（15.4）、Ⅴ（17.8%）围岩。
3.2 参数选取
全断面掘进机的载荷参数是整个顶升系统、支护系统和后配套系统共同作用的结果。因此，掘进机的推力和扭矩不可避免地受到地质条件、掘进机支护体系统的稳定性及后配套清渣速度等多方面综合影响。基于现有研究成果和专家经验[12-13]，选择的输入参数包括推进速度（X1）、贯入度（X2）、撑靴撑紧力（X3）、刀盘功率（X4）、刀盘转速（X5）、推进泵压力（X6）、皮带传送机电流（X7），以及推力（Y1）、扭矩（Y2）。这些参数不但能够反映开挖过程中围岩等级情况，多个时间段的输入还能捕捉刀盘的磨损，设备运行状态变化。参数数据包括从时间状态t-1到t-2的Xi、Yi的序列值，以及时间状态t下X1、X2、X3、X5、X7序列值。采用min-max标准化处理原始数据，采用四分位距（IQR）方法剔除异常点。剔除后有4 210组数据，每个参数数值分布情况见表2。
3.3 信息融合结果分析
为确定最佳最大时滞τ，t到t-3的时间状态被选为候选值，以证明最适合因果发现模型训练的时间状态。表3中列出了y1、y2的每个时间状态的模型评估结果。由表3可知，τ=2为最合适的选择，该模型具有比τ=0、τ=1的结果更好的性能。
获取数据驱动的因果关系后，通过对选取三位TBM操作相关的专家进行问卷调查与咨询，获取专家对不同参数之间的因果关系强度赋值，将赋值相对大小分为弱、较弱、一般、较强、强五种离散指标，分别用1、3、5、7、9表示，对参数之间因果关系强度进行评价。采用德尔菲法，通过专家讨论将意见逐渐收敛。图3（a）为专家讨论后一致参数之间的因果关系和因果关系的强度。专家评价体系下与机器学习体系下因果强度映射关系见表4。图3（b）为专家经验作为先验知识以及在时滞系数等于2的情况下专家经验与数据驱动相融合的因果关系图。
将融合后的因果关系转化为邻接矩阵，见图4。
3.4 预测结果分析
选取全部数据的80%进行模型训练，其余的20%数据进行训练模型的性能评估。为进行信息融合前后预测性能的对比分析，选取NTS-GAT、GCN-BiLSTM模型分别进行预测性能测试，预测性能评价值见表5。由表5可知，NTS-GAT与GCN-BiLSTM模型，在输入由专家经验融入的因果关系矩阵后显著提升算法性能。当GCN-BiLSTM邻接矩阵为融合专家经验的因果关系矩阵时，模型性能会逼近甚至高于纯数据驱动的NTS-GAT模型，这也展现出融合专家经验的知识数据双驱动因果关系矩阵会有更好的性能。同时可以看出，NTS-GAT模型在输入专家融合因果关系矩阵相对于输入纯数据驱动的因果关系矩阵上的提升普遍高于GCN-BiLSTM模型。
为进一步验证所提KD-NTS-GAT模型的整体性能，选取其他模型进行对比，结果见表6。传统的基于BiLSTM的模型，由于缺乏含有先验知识的邻接矩阵输入，也没有对参数间空间特征的捕捉，所以预测误差较大。另外，不含先验知识作为输入的GCN-BiLSTM堆叠模型的性能优于BiLSTM方法。表6中的相应结果同表5中输入数据驱动邻接矩阵作为先验知识的预测结果相比略微逊色。这可能是因为纯数据驱动所给出的先验知识不完全准确，并且由于GCN网络虽然也能够捕捉空间特征，但传统的GCN假设图中的所有边均具有同等重要性，没有GAT网络符合实际。所提出的NTS-GAT预测模型方法在输入KD-NTS信息融合模型发掘的因果关系后对预测有更好的改进。总之，与BiLSTM、GCN-BiLSTM方法相比，NTS-GAT分别实现了34.34%、28.24%的平均改进。结果进一步表明了KD-NTS-GAT在TBM载荷参数预测中的良好性能。
4 结论
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针对TBM推力和扭矩精准预测问题，提出一种两阶段知识数据双驱动时空堆叠卷积网络（KD-NTS-GAT）预测模型。基于NTS-NOTEARS的信息融合方法，一定程度上克服了纯数据驱动因果关系发现模型的“黑箱”问题，提高了因果关系发现的可靠性。GAT与BiLSTM相结合形成的堆叠网络，可以将数据空间结构学习和数据时间序列学习相结合，将表达可靠因果关系的邻接矩阵作为先验知识，融合到数据学习中，可以强化训练学习效果。通过纯数据驱动模型和知识数据双驱动模型的计算对比分析，进一步表明信息融合模型具有显著的预测优势。
基金
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  • 国家自然科学基金项目(51679089)
  • 河南省学科创新引智基地项目“智慧水利”(GXJD004)
  • 河南省水利厅科技攻关项目(GG202358)
文献
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2025年第43卷第9期
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文章信息
doi: 10.20040/j.cnki.1000-7709.2025.20241868
  • 接收时间：2024-10-04
  • 首发时间：2025-12-15
  • 出版时间：2025-09-25
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出版历史
  • 收稿日期：2024-10-04
  • 修回日期：2024-11-18
基金
国家自然科学基金项目(51679089)
河南省学科创新引智基地项目“智慧水利”(GXJD004)
河南省水利厅科技攻关项目(GG202358)
作者信息
    1.华北水利水电大学水利学院，河南 郑州 450046
    2.河南省水圈与流域水安全重点实验室，河南 郑州 450046
    3.河南省水利第一工程局集团有限公司，河南 郑州 450000
参考文献
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https://castjournals.cast.org.cn/joweb/sdnykx/CN/10.20040/j.cnki.1000-7709.2025.20241868
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小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
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