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基于鲁棒加权模糊聚类的污水处理过程监测方法

张瑞垚 周平

张瑞垚, 周平. 基于鲁棒加权模糊聚类的污水处理过程监测方法. 自动化学报, 2022, 48(9): 2198−2211 doi: 10.16383/j.aas.c200392
引用本文: 张瑞垚, 周平. 基于鲁棒加权模糊聚类的污水处理过程监测方法. 自动化学报, 2022, 48(9): 2198−2211 doi: 10.16383/j.aas.c200392
Zhang Rui-Yao, Zhou Ping. Robust weighted fuzzy clustering for sewage treatment process monitoring. Acta Automatica Sinica, 2022, 48(9): 2198−2211 doi: 10.16383/j.aas.c200392
Citation: Zhang Rui-Yao, Zhou Ping. Robust weighted fuzzy clustering for sewage treatment process monitoring. Acta Automatica Sinica, 2022, 48(9): 2198−2211 doi: 10.16383/j.aas.c200392

基于鲁棒加权模糊聚类的污水处理过程监测方法

doi: 10.16383/j.aas.c200392
基金项目: 国家自然科学基金(61890934, 61790572, 61991400), 辽宁省“兴辽英才计划”(XLYC1907132)和中央高校基本科研业务费(N180802003)资助
详细信息
    作者简介:

    张瑞垚:东北大学硕士研究生. 2018年获东北大学学士学位. 主要研究方向为数据驱动质量监测. E-mail: zryao_neu@163.com

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

Robust Weighted Fuzzy Clustering for Sewage Treatment Process Monitoring

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:

    ZHANG Rui-Yao Master student at Northeastern University. He received his bachelor degree from Northeastern University in 2018. His main research interest is data-driven quality monitoring

    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: 针对非线性强、先验故障知识少、异常工况识别难的污水处理过程监测问题, 提出一种基于鲁棒加权模糊c均值(Robust weighted fuzzy c-means, RoW-FCM)聚类与核偏最小二乘(Kernel partial least squares, KPLS)的过程监测方法. 首先, 针对污水处理过程的高维非线性耦合特性, 采用核偏最小二乘对高维输入变量进行降维; 其次, 针对传统基于最近邻分配的模糊c均值算法对离群点敏感以及存在聚类不平衡簇的问题, 提出充分考虑样本间相互关系的基于鲁棒加权模糊c均值聚类算法. 通过引入可能性划分矩阵作为权值参数实现不同样本数据的区分加权, 提高了离群点数据聚类的鲁棒性, 同时引入聚类大小控制参数解决不平衡簇的问题. 进一步将基于鲁棒加权模糊c均值算法对核偏最小二乘降维后的得分矩阵进行聚类, 利用聚类得到的隶属度矩阵实现异常工况的检测; 最后, 建立隶属度矩阵与过程变量的回归模型, 并利用得到的变量贡献矩阵描述变量对各个簇的解释程度, 实现异常工况的识别. 数值仿真以及污水处理过程数据实验表明该方法具有更好的鲁棒性能, 在异常工况检测和识别上具有较好的效果.
  • 图  1  污水处理工艺流程示意图

    Fig.  1  Schematic diagram of sewage treatment process

    图  2  本文监测算法建模策略

    Fig.  2  The monitoring algorithm modeling strategy in this paper

    图  3  仿真实验数据及聚类效果图

    Fig.  3  Simulation experiment data and clustering effect diagrams

    图  4  测试数据集

    Fig.  4  Test data sets

    图  5  不平衡簇实验聚类效果图

    Fig.  5  Experimental clustering effect of unbalanced clusters

    图  6  离群点实验聚类效果图

    Fig.  6  Experimental clustering effect of outlier points

    图  7  FCM隶属度矩阵

    Fig.  7  FCM membership matrix

    图  8  PCM可能性矩阵

    Fig.  8  PCM possibility matrix

    图  9  PFCM隶属度矩阵

    Fig.  9  PFCM membership matrix

    图  10  RoW-FCM隶属度矩阵

    Fig.  10  RoW-FCM membership matrix

    图  11  异常工况识别结果

    Fig.  11  Recognition results of abnormal conditions

    表  1  FCM、PCM、PFCM、RoW-FCM 聚类参数

    Table  1  FCM, PCM, PFCM, RoW-FCM clustering parameters

    编号FCMPCMPFCMRoW-FCM
    ${ {{\boldsymbol{U}}} }_1^{\rm T}$${ {{\boldsymbol{U}}} }_2^{\rm T}$${ {{\boldsymbol{W}}} }_1^{\rm T}$${ {{\boldsymbol{W}}} }_2^{\rm T}$${ {{\boldsymbol{U}}} }_1^{\rm T}$${ {\boldsymbol{U}} }_2^{\rm T}$${ {{\boldsymbol{W}}} }_1^{\rm T}$${ {{\boldsymbol{W}}} }_2^{\rm T}$${ {{\boldsymbol{U}}} }_1^{\rm T}$${ {{\boldsymbol{U}}} }_2^{\rm T}$${ {{\boldsymbol{W}}} }_1^{\rm T}$${ {{\boldsymbol{W}}} }_2^{\rm T}$
    10.9730.0270.7990.7980.0210.9790.0260.5470.9910.0090.8330.999
    20.9910.0090.8590.8580.0100.9890.0320.7550.9890.0110.8390.999
    30.9950.0050.8610.8600.0020.9980.0320.9401.000.0001.0001.000
    40.9670.0330.8480.8480.0260.9750.0320.5550.9890.0110.8340.999
    50.9880.0120.9160.9160.0130.9870.0420.7700.9860.0140.8400.998
    60.0120.9880.9160.9170.9870.0130.7700.0420.0120.9880.9990.861
    70.0090.9910.8590.8600.9890.0110.7550.0320.0110.9890.9990.835
    80.0050.9950.8610.8620.9980.0020.9400.0320.0000.9991.0000.998
    90.0330.9670.8480.8490.9750.0260.5550.0320.0110.9890.9990.835
    100.0270.9730.7990.8000.9790.0210.5470.0260.0100.9900.9990.811
    110.5000.5000.9970.9970.5000.5000.1250.1250.0690.9310.9850.274
    120.5000.5000.6320.6320.5000.5000.0260.0260.9970.0040.0600.999
    聚类中心v1 = (−3.616, 0.383) v1 = (0.001, 0.369)v1 = (−3.736, 0.240)v1 = (−3.989, 0.010)
    v2 = (3.616, 0.384)v2 = (0.007, 0.369)v2 = (3.736, 0.240)v2 = (3.910, 0.000)
    偏移距离r1 = 0.543r1 = 4.016r1 = 0.357r1 = 0.010
    r2 = 0.543r2 = 4.010r2 = 0.357r2 = 0.090
    下载: 导出CSV

    表  2  影响污水处理过程出水水质的主要过程变量

    Table  2  The main process variables that affect the effluent quality of the sewage treatment process

    编号符号变量物理含义编号符号变量物理含义
    1Qin进水流量15SS,3反应池 3易生物降解有机底物量
    2SNH,in进水氨浓度16SALK,3反应池 3 池碱度
    3XBH,1反应池 1活性异养菌生物量17XBH,4反应池 4 活性异养菌生物量
    4SNO,1反应池 1 硝氮浓度18XBA,4反应池 4 活性自养菌生物量
    5SS,1反应池 1 易生物降解有机底物量19SO,4反应池 4 溶解氧浓度
    6SALK,1反应池 1 池碱度20SNH,4反应池 4 氨氮浓度
    7XBH,2反应池 2 活性异养菌生物量21SS,4反应池 4 易生物降解有机底物量
    8SNO,2反应池 2 硝氮浓度22SALK,4反应池 4 池碱度
    9SS,2反应池 2 易生物降解有机底物量23XBH,5反应池 5 活性异养菌生物量
    10SALK,2反应池 2 池碱度24XBA,5反应池 5 活性自养菌生物量
    11XBH,3反应池 3 活性异养菌生物量25SO,5反应池 5 溶解氧浓度
    12XBA,3反应池 3 活性自养菌生物量26SNH,5反应池 5 氨氮浓度
    13SO,3反应池 3 溶解氧浓度27SS,5反应池 5 易生物降解有机底物量
    14SNH,3反应池 3 氨氮浓度28SALK,5反应池 5 池碱度
    下载: 导出CSV

    表  3  不同算法的聚类准确度与迭代次数

    Table  3  Clustering accuracies and numbers of iterations of different algorithms

    工况类型聚类正确率 (%)聚类收敛迭代次数
    (收敛精度$10^{-5}, \;$30次仿真)
    FCMPCMPFCMRoW-FCMFCMPCMPFCMRoW-FCM
    正常工况92.380.893.997.5
    异常工况 175.06.376.396.045.11429.123.6
    异常工况 280.33.577.597.0
    下载: 导出CSV

    表  4  异常工况识别结果表

    Table  4  Abnormal condition recognition result table

    编号正常工况异常工况 1异常工况 2编号正常工况异常工况 1异常工况 2
    10.1330.3390.528150.2540.4650.281
    20.1500.3210.530160.2970.2550.448
    30.4540.4810.065170.4500.4640.086
    40.4530.3950.152180.3540.4240.223
    50.0930.5770.331190.2380.2600.503
    60.3050.2470.448200.1240.3520.524
    70.4560.4770.067210.2360.4820.283
    80.0100.3070.683220.2810.2450.475
    90.2410.4730.286230.4460.4580.096
    100.3610.2900.349240.3520.4180.230
    110.4530.4710.076250.0520.3100.639
    120.3530.4290.218260.1180.3140.568
    130.2550.1670.578270.2290.4820.289
    140.2080.4250.367280.2910.2590.450
    下载: 导出CSV
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  • 收稿日期:  2020-06-09
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