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基于Koopman特征核的工业时频因果时延推理网络

翁若昊 郝矿荣 陈磊 丁贺 刘肖燕

翁若昊, 郝矿荣, 陈磊, 丁贺, 刘肖燕. 基于Koopman特征核的工业时频因果时延推理网络. 自动化学报, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c240810
引用本文: 翁若昊, 郝矿荣, 陈磊, 丁贺, 刘肖燕. 基于Koopman特征核的工业时频因果时延推理网络. 自动化学报, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c240810
Weng Ruo-Hao, Hao Kuang-Rong, Chen Lei, Ding He, Liu Xiao-Yan. Koopman feature kernel-based time-frequency causal and delay inference network for industrial systems. Acta Automatica Sinica, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c240810
Citation: Weng Ruo-Hao, Hao Kuang-Rong, Chen Lei, Ding He, Liu Xiao-Yan. Koopman feature kernel-based time-frequency causal and delay inference network for industrial systems. Acta Automatica Sinica, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c240810

基于Koopman特征核的工业时频因果时延推理网络

doi: 10.16383/j.aas.c240810 cstr: 32138.14.j.aas.c240810
基金项目: 中央高校基本科研业务费专项资金(2232021A-10),上海市扬帆计划 (22YF1401300)资助
详细信息
    作者简介:

    翁若昊:东华大学信息科学与技术学院硕士研究生. 主要研究方向为因果推理, 工业过程时序建模和机器学习. E-mail: 2232138@mail.dhu.edu.cn

    郝矿荣:博士, 东华大学信息科学与技术学院教授.1995年获得法国巴黎国家路桥学校数学与计算机科学博士学位. 主要研究方向包括神经网络, 图像处理, 智能控制, 流程工业的数字化与智能化. 本文通信作者. E-mail: krhao@dhu.edu.cn

    陈磊:博士, 东华大学信息科学与技术学院副教授. 主要研究方向为过程控制, 系统辨识, 工业大数据分析. E-mail: leichen@dhu.edu.cn

    丁贺:东华大学信息科学与技术学院博士研究生. 2020年获中国上海东华大学自动化专业工学学士学位.主要研究方向为不变表征学习与工业过程的时序预测. E-mail: 2211866@mail.dhu.edu.cn

    刘肖燕:博士, 东华大学高级实验师, 主要研究方向为智能仿真与优化. E-mail: liuxy@dhu.edu.cn

Koopman Feature Kernel-based Time-frequency Causal and Delay Inference Network for Industrial Systems

Funds: Supported by Fundamental Research Funds for the Central Universities (2232021A-10) and Shanghai Sailing Program (22YF1401300)
More Information
    Author Bio:

    WENG Ruo-Hao Master student at the College of Information Science and Technology, Donghua University. His research interest covers causal inference, time-series modeling in industrial processes, and machine learning

    HAO Kuang-Rong ph.D., Full Professor at the College of Information Sciences and Technology, Donghua University, Shanghai, China. She obtained her Ph.D. degree in Mathematics and Computer Science from Ecole Nationale des Ponts et Chaussées, Paris, France in 1995. Her research interest covers neural networks, image processing, intelligent control, and digitalization and intelligence of process industry. Corresponding author of this paper

    CHEN Lei Ph.D., Associate Professor at the College of Information Science and Technology, Donghua University. Her research interest covers process control, system identification, industrial big data analysis

    DING He Ph.D. candidate at the College of Information Science and Technology, Donghua University. Received a B.Eng. degree in Automation from Donghua University, Shanghai, China, in 2020. His research interest covers invariant representation learning and time-series prediction for industrial processes

    LIU Xiao-Yan Ph.D., Senior Experimentalist at Donghua University. Her research interest covers intelligent simulation and optimization

  • 摘要: 因果推理在复杂工业系统中对产能分析和产出优化具有重要意义. 然而, 现有方法难以有效处理这种高度非线性和时延的复杂因果关系. 为此提出了一种基于Koopman特征核的时频因果与时延推理网络(Koopman feature kernel-based time-frequency causal and delay inference network, KTFCDN), 用于复杂工业过程的因果分析与时延识别. 该方法结合Koopman特征变换与再生核理论设计了核回归层, 在保留时间信息的基础上, 将数据映射到高维再生核希尔伯特空间以提取时不变的非线性关系. 同时, 通过证明非线性格兰杰因果关系在时频域上的一致性, 进而在时域上融入频域特征以提取时间维度的全局信息并捕获变量间的时延关系. 此外, 针对长时延问题, 设计了基于状态空间模型的时延发现网络. 实验结果表明, 该方法在三个公共数据集上表现优异, 并在聚酯纤维酯化过程的实际应用中进一步验证了其有效性.
  • 图  1  第$ i$个KTFCDN结构

    Fig.  1  The $ i$-th KTFCDN structure

    图  2  不同的$ \gamma $值对应的各数据集因果发现F1分数

    Fig.  2  F1 scores of causal discovery for different datasets corresponding to different values of $ \gamma $

    图  3  因果邻接矩阵. 第一列提供了真实因果的可视化, 其他的提供了由因果发现方法 发现的因果图. 错误的因果关系用红色的方框标注.

    Fig.  3  Causal adjacency matrices. The first column provides a visualization of the ground truth causal relationships, while the others present the causal graphs discovered by causal discovery methods. Incorrect causal relationships are highlighted with red boxes.

    图  4  聚酯纤维生产酯化阶段工艺方案

    Fig.  4  Process scheme of esterification stage

    图  5  比较不同预测步数预测指标收敛情况

    Fig.  5  Comparison of convergence of prediction metrics with different prediction steps

    表  1  因果发现比较实验

    Table  1  Causal discovery comparison experiment

    模型VARLorenz-96fMRI5fMRI6fMRI7fMRI9
    accF1accF1accF1accF1accF1accF1
    TCDF960.8235720.4528760.6250860.6667680.5000560.4211
    PCMCI960.9091810.6250600.6667820.7000800.8000560.6452
    eSRU900.7222830.7792720.6316880.6250680.5556680.6363
    NGC980.9523970.9630840.7500920.8000840.7500680.5000
    GVAR990.9756980.9756760.7692900.6875880.8235800.8059
    CRVAE910.8000960.9478800.7619940.8500800.7619720.6923
    KTFCDN1001.0000990.9873920.8889960.9000960.9524880.8235
    下载: 导出CSV

    表  2  时延发现比较实验

    Table  2  Time delay discovery comparison experiment

    模型 VAR-10 VAR-50 VAR-70 VAR-100 fMRI5 fMRI6 fMRI7 fMRI9
    TCDF 1.000 0.9861 0.9327 0.8894 0.8609 0.8805 0.8925 0.9063
    PCMCI 1.000 0.9856 0.9830 0.9466 0.8795 0.8962 0.9063 0.9160
    NGC 1.000 0.9855 0.9760 0.9020 0.8610 0.8689 0.8570 0.9310
    KTFCDN 1.000 1.000 1.000 1.000 0.8972 0.9439 0.9695 0.9975
    下载: 导出CSV

    表  3  KTFCDN消融研究结果

    Table  3  Ablation study results of KTFCDN

    模型VARLorenz-96fMRI5fMRI6fMRI7fMRI9
    accF1accF1accF1accF1accF1accF1
    cLSTM 98 0.95 97 0.96 84 0.75 92 0.80 84 0.75 68 0.50
    TFCDN 100 1.00 98 0.95 84 0.75 94 0.84 88 0.82 80 0.71
    KCDN 100 1.00 94 0.93 88 0.84 94 0.86 92 0.89 84 0.75
    KTFCDN 100 1.00 99 0.99 92 0.89 96 0.90 96 0.95 88 0.82
    下载: 导出CSV

    表  4  KTFCDN运行效率分析

    Table  4  Computational efficiency analysis of KTFCDN

    节点数量 时间窗
    口长度
    参数量(M) FLOPs(MMac) 每epoch训练
    时间(s)
    5 10 0.26 2.49 2.37
    5 50 0.83 14.85 7.09
    5 100 2.54 35.72 9.21
    10 10 0.59 5.82 12.26
    10 50 1.63 39.23 38.34
    10 100 4.77 103.23 93.73
    15 10 0.91 9.36 29.66
    15 50 2.34 67.26 114.68
    15 100 6.62 185.99 280.53
    下载: 导出CSV

    表  5  聚酯纤维酯化数据集预测实验结果

    Table  5  Prediction results on the polyester fiber esterification dataset

    模型 单步预测 三步预测 五步预测
    MAE RMSE MAE RMSE MAE RMSE
    Base 0.4557 1.2153 0.6016 1.6172 0.7118 1.8534
    TCDF 0.8770 2.4114 0.9875 2.6900 1.0401 2.7822
    PCMCI 0.4230 1.1564 0.5887 1.6691 0.6623 1.8487
    eSRU 0.4520 1.1873 0.6075 1.6512 0.6932 1.8914
    GVAR 0.4429 1.2987 0.6568 2.0803 0.7680 2.3720
    NGC 0.5360 1.2447 0.6580 1.6117 0.7503 1.8641
    KTFCN 0.4250 1.1681 0.5751 1.6408 0.6425 1.8496
    KTFCDN 0.4103 1.1403 0.5538 1.5691 0.6298 1.7433
    下载: 导出CSV
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