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污水处理过程出水水质稀疏鲁棒建模

闻超垚 周平

闻超垚, 周平. 污水处理过程出水水质稀疏鲁棒建模. 自动化学报, 2022, 48(6): 1469−1481 doi: 10.16383/j.aas.c200707
引用本文: 闻超垚, 周平. 污水处理过程出水水质稀疏鲁棒建模. 自动化学报, 2022, 48(6): 1469−1481 doi: 10.16383/j.aas.c200707
Wen Chao-Yao, Zhou Ping. Sparse robust modeling of effluent quality indices in wastewater treatment process. Acta Automatica Sinica, 2022, 48(6): 1469−1481 doi: 10.16383/j.aas.c200707
Citation: Wen Chao-Yao, Zhou Ping. Sparse robust modeling of effluent quality indices in wastewater treatment process. Acta Automatica Sinica, 2022, 48(6): 1469−1481 doi: 10.16383/j.aas.c200707

污水处理过程出水水质稀疏鲁棒建模

doi: 10.16383/j.aas.c200707
基金项目: 国家自然科学基金(61890934, 61790572, 61991400), 辽宁省“兴辽英才计划”项目(XLYC1907132), 中央高校基本科研业务费项目(N180802003)资助
详细信息
    作者简介:

    闻超垚:东北大学硕士研究生. 于2018年获得武汉理工大学学士学位. 主要研究方向为数据驱动建模与优化. E-mail: mr_qilintong@163.com

    周平:东北大学教授. 分别于2003年, 2006年, 2013年获得东北大学学士学位、硕士学位和博士学位. 主要研究方向为工业过程运行反馈控制, 数据驱动建模与控制等. 本文通信作者. E-mail: zhouping@mail.neu.edu.cn

Sparse Robust Modeling of Effluent Quality Indices in Wastewater Treatment Process

Funds: Supported by National Natural Science Foundation of China (61890934, 61790572, 61991400), Liaoning Revitalization Talents Program (XLYC1907132), and Fundamental Research Funds for the Central Universities (N180802003)
More Information
    Author Bio:

    WEN Chao-Yao Master student at Northeastern University. He received his bachelor degree from Wuhan University of Technology in 2018. His research interest covers data-driven modeling and optimization

    ZHOU Ping Professor at Northeastern University. He received his bachelor, master and Ph.D. degrees from Northeastern University in 2003, 2006 and 2013 respectively. His research interest covers operation feedback control of industrial process, data-driven modeling and control. Corresponding author of this paper

  • 摘要: 污水处理过程中, 出水水质参数是衡量污水处理性能的最重要指标, 需要进行严格监测, 但现有传感技术难以对其进行实时准确地在线测量. 因此, 提出一种新型的基于随机权神经网络(Random vector functional-link networks, RVFLNs)与Schweppe型广义M估计(Generalized M-estimation, GM-estimation)的稀疏鲁棒建模方法, 用于水质指标的在线鲁棒预测. 首先, 针对常规RVFLNs隐含层矩阵存在多重共线性而导致最小二乘估计失效的问题, 利用稀疏偏最小二乘(Sparse partial least squares, SPLS)代替RVFLNs输出权值求解的最小二乘估计, 从而提出SPLS-RVFLNs. 该算法不仅可有效解决传统RVFLNs的多重共线性问题, 还可以进行建模变量选择, 提高模型的可解释性和最终的预测精度. 同时, 考虑到SPLS-RVFLNs在求解输出权值时会同时受到隐含层矩阵和输出层矩阵两个方向离群点的影响, 进一步采用Schweppe型广义M估计对SPLS-RVFLNs进行鲁棒改进, 从而提出GM-SPLS-RVFLNs, 可显著提高模型的稀疏鲁棒性能. 最后, 将提出的GM-SPLS-RVFLNs用于污水处理过程出水水质指标预测建模, 数据实验结果表明所提方法不仅解决了常规RVFLNs多重共线性和鲁棒性差的问题, 而且具有很好的预测精度和泛化性能.
  • 图  1  污水处理过程工艺流程图

    Fig.  1  Wastewater treatment process flow diagram

    图  2  建模误差与潜变量和隐含层节点数的关系图

    Fig.  2  The relationship between the RMSE and the number of latent variables and hidden layer nodes

    图  3  输入样本无离群点输出样本不同比例离群点时的出水水质指标估计RMSE箱形图

    Fig.  3  The box diagram of the estimation RMSE of effluent quality indices for input sample without outliers and output sample with outliers of different rates

    图  4  输入样本含5%离群点输出样本不同比例离群点时的出水水质指标估计RMSE箱形图

    Fig.  4  The box diagram of the estimation RMSE of effluent quality indices for input sample with 5% outliers and output sample with outliers of different rates

    图  5  输入样本含15%离群点输出样本不同比例离群点时的出水水质指标估计RMSE箱形图

    Fig.  5  The box diagram of the estimation RMSE of effluent quality indices for input sample with 15% outliers and output sample with outliers of different rates

    图  6  输入样本含25%离群点输出样本不同比例离群点时的出水水质指标估计RMSE箱形图

    Fig.  6  The box diagram of the estimation RMSE of effluent quality indices for input sample with 25% outliers and output sample with outliers of different rates

    图  7  输入样本含35%离群点输出样本不同比例离群点时的出水水质指标估计RMSE箱形图

    Fig.  7  The box diagram of the estimation RMSE of effluent quality indices for input sample with 35% outliers and output sample with outliers of different rates

    图  8  输入输出样本均含25%离群点时, 不同方法出水水质指标建模效果

    Fig.  8  Modeling results of effluent quality indices with different methods for input and output samples with 25% outliers

    图  9  输入输出样本均含25%离群点时, 不同方法水质指标散点图

    Fig.  9  The scatter plot of effluent quality indices with different methods for input and output samples with 25% outliers

    图  10  输入输出样本均含25%离群点时, 不同方法水质指标估计误差PDF曲线

    Fig.  10  The PDF curve of effluent quality indices estimation error with different methods for input and output samples with 25% outliers

    图  11  输入输出含不同比例离群点时, 不同建模方法的输出权值中所含“0”的数量曲线

    Fig.  11  The curve of the number of output weights with ‘0’ value with different methods for input and output samples with outliers of different rates

    表  1  10个潜变量时, 建模误差与隐含层节点个数之间的关系表

    Table  1  The relationship between the RMSE and the number of hidden layer nodes when 10 latent variables

    隐含层节点个数RMSE
    BODCODTSS
    100.03720.23210.1733
    150.02900.17810.1569
    200.02900.15740.1350
    250.02580.14960.1211
    300.02470.14400.1150
    350.02230.13450.1043
    400.02250.13430.1032
    500.02240.13370.1054
    1000.02210.13400.1022
    2000.02270.13250.1015
    下载: 导出CSV

    表  2  输入输出样本均含25%离群点时, 不同水质指标建模方法性能指标对比

    Table  2  The comparison of performance indexes of effluent quality indices with different methods for input and output samples with 25% outliers

    模型RMSEMAPER square
    BODCODTSSBODCODTSSBODCODTSS
    RVFLNs0.16891.26910.84420.05320.02150.05810.75500.70680.7817
    Robust RVFLNs0.09310.65720.45390.02420.01000.02420.93030.92850.9413
    PRM RVFLNs0.08930.53890.40150.02160.00780.02000.93300.95010.9522
    GM-SPLS-RVFLNs0.03010.17650.12590.00560.00160.00450.99590.99760.9974
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-08-31
  • 修回日期:  2020-10-27
  • 网络出版日期:  2021-04-27
  • 刊出日期:  2022-06-02

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