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  • ISSN 1006-3080
  • CN 31-1691/TQ

一种改进的非线性多变量格兰杰因果检验在污水处理过程参数关系分析中的研究

唐山 杨丹 彭鑫 钟伟民 万峰

唐山, 杨丹, 彭鑫, 钟伟民, 万峰. 一种改进的非线性多变量格兰杰因果检验在污水处理过程参数关系分析中的研究[J]. 华东理工大学学报(自然科学版). doi: 10.14135/j.cnki.1006-3080.20211118002
引用本文: 唐山, 杨丹, 彭鑫, 钟伟民, 万峰. 一种改进的非线性多变量格兰杰因果检验在污水处理过程参数关系分析中的研究[J]. 华东理工大学学报(自然科学版). doi: 10.14135/j.cnki.1006-3080.20211118002
TANG Shan, YANG Dan, PENG Xin, ZHONG Weimin, WAN Feng. Research on An Improved Nonlinear Multivariable Granger Causality Test in the Analysis of the Relationship between Parameters of Wastewater Treatment Process[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20211118002
Citation: TANG Shan, YANG Dan, PENG Xin, ZHONG Weimin, WAN Feng. Research on An Improved Nonlinear Multivariable Granger Causality Test in the Analysis of the Relationship between Parameters of Wastewater Treatment Process[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20211118002

一种改进的非线性多变量格兰杰因果检验在污水处理过程参数关系分析中的研究

doi: 10.14135/j.cnki.1006-3080.20211118002
基金项目: 国家自然科学基金重大项目(61890930-3);国家杰出青年科学基金(61925305);中央高校基本科研业务费
详细信息
    作者简介:

    唐山:作者简介:唐 山(1997-),男,湖南人,硕士生,研究方向:工业过程建模、控制与优化,E-mail: y30190746@mail.ecust.edu.cn

    通讯作者:

    彭 鑫,E-mail: xinpeng@ecust.edu.cn

    钟伟民,E-mail: wmzhong@ecust.edu.cn

  • 中图分类号: TP274.2

Research on An Improved Nonlinear Multivariable Granger Causality Test in the Analysis of the Relationship between Parameters of Wastewater Treatment Process

  • 摘要: 传统线性多变量格兰杰因果检验通过引入条件变量来判断两个变量之间是否存在因果关系,但对条件变量的选择往往具有主观性而缺乏合理的规则,针对这个问题,本文提出一种可筛选条件变量的非线性多变量格兰杰因果检验方法。该方法使用支持向量回归构建检验方程适应非线性条件,通过分析两两变量间关系构建初步结构后选择条件变量,基于所选条件变量再进行非线性多变量格兰杰因果检验;引入两种拓扑结构避免对不产生伪因果问题的真实关系重复检验;在数字仿真和污水处理基准仿真平台上的实验结果表明本文方法能适应非线性条件,在通过筛选条件变量减少无关变量的干扰以及引入拓扑结构后,该方法有更准确的检验结果,在计算强度上也有更好的表现。

     

  • 图  1  (a)真实结构 (b)初步结构

    Figure  1.  (a) True structure (b) Preliminary structure

    图  2  不产生伪因果问题的结构

    Figure  2.  A structure without pseudo causality problems

    图  3  产生伪因果问题的典型拓扑结构

    Figure  3.  Typical topological structure that produces false causality problems

    图  4  NSC-MVGC流程图

    Figure  4.  Flowchart of NSC-MVGC

    图  5  非线性过程的真实因果结构图

    Figure  5.  Real causal structure of nonlinear process

    图  6  MVGC得到的因果结构

    Figure  6.  Causal structure of MVGC test

    图  7  VAR-GC生成的初步结构图

    Figure  7.  Preliminary structure generated by VAR-GC

    图  8  SC-MVGC得到的因果结构

    Figure  8.  Causal structure of SC-MVGC

    图  9  SVR-MVGC得到的因果结构

    Figure  9.  Causal structure of SVR-MVGC

    图  10  SVR-GC生成的初步结构图

    Figure  10.  Preliminary structure generated by SVR-GC

    图  11  NSC-MVGC得到的因果结构

    Figure  11.  Causal structure of NSC-MVGC

    图  12  SVR-MVGC检验X3为X2原因时RSS0与RSS1对样本预测差异的比较,虚线为两者的差值,大于0表示RSS1预测偏差更小

    Figure  12.  The comparison of the sample prediction difference of RSS1 and RSS0 testing X3 is the reason of X2 by SVR-MVGC. The dotted line is the difference between RSS0 and RSS1.greater than 0 means that the RSS1 forecast deviation is smaller greater than 0 means that the RSS1 prediction deviation is smaller

    图  13  非线性过程的真实因果结构图

    Figure  13.  Real causal structure of nonlinear process

    图  14  不同方法的检验结果

    Figure  14.  Test results of different methods

    图  15  SVR-GC生成的初步结构图

    Figure  15.  Preliminary structure generated by SVR-GC

    图  16  不同方法检验X3是否为X5原因时计算RSS0和RSS1的累计残差和以及计算出的P值(图14中的蓝色线)

    Figure  16.  The cumulative difference between RSS0 and RSS1 and P-value value calculated by different methods when testing whether X3 is the cause of X5 whether X3 (the blue line in Fig 14)

    图  18  SVR-GC得到的初步结构图

    Figure  18.  Preliminary relationship tested by SVR-GC test

    图  19  NSC-MVGC得到的检验结果

    Figure  19.  Causal structure of NSC-MVGC

    图  20  不同方法在检验过程中需训练的参数量

    Figure  20.  The amount of trained parameters in the testing process by different methods

    图  17  SVR-MVGC得到的因果结构

    Figure  17.  Test results of SVR-MVGC

    表  1  MVGC的检验结果

    Table  1.   Test result of MVGC

    Tested variablesStatistic FP-valueCausality test resultTested variablesStatistic FP-valueCausality test result
    X2→X11.5750.207NoX4→X301No
    X3→X1334.930YesX5→X31.6370.19No
    X4→X11311.60YesX1→X466.190Yes
    X5→X12165.740YesX2→X40.240.78No
    X1→X21.060.34NoX3→X4128.40Yes
    X3→X22210YesX5→X410290Yes
    X4→X2989.240YesX1→X50.0090.99No
    X5→X21608.90YesX2→X50.50.6No
    X1→X3116.90YesX3→X50.150.85No
    X2→X3189.080YesX4→X5154.3170Yes
    ① X2→X1 means that X2 is the cause of X1.
    下载: 导出CSV

    表  2  各方法的检验结果与真实结构的比较

    Table  2.   The test results of each method are compared with the real structure

    Tested variablesReal relationshipNSC-MVGCSC-MVGCSVR-MVGCMVGC
    X1→X311111
    X1→X410101
    X2→X311111
    X3→X100101
    X3→X200111
    X3→X400101
    X4→X111111
    X4→X211111
    X4→X511111
    X5→X111111
    X5→X211111
    X5→X411111
    准确率0.910.750.830.75
    ① 0 means the relationship does not exist, 1 means the relationship exists.
    下载: 导出CSV

    表  3  各方法在检验过程中选择的条件变量数

    Table  3.   The number of conditional variables selected by each method

    Tested variablesNSC-MVGCSC-MVGCSVR-MVGCMVGC
    X4→X11233
    X5→X11233
    X1→X22333
    X4→X22333
    X1→X31233
    …………………………
    X4→X52333
    下载: 导出CSV

    表  4  各方法在检验过程中的运行时间

    Table  4.   The runtime in the testing process by different methods

    CaseRun time(s)
    SVR-MVGCNSC-MVGC
    Case 10.60.9
    Case 20.631.02
    BSM1 simulation16.310.1
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-11-18
  • 网络出版日期:  2022-04-25

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