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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.Abstract: Aiming at the problems of strong nonlinearity, little prior knowledge of faults, and difficulty in identifying abnormal working-conditions in the sewage treatment process, this paper proposes a novel process monitoring method based on robust weighted fuzzy c-means (RoW-FCM) clustering and kernel partial least squares (KPLS). First, the KPLS algorithm is presented to reduce the dimensionality of the high-dimensional input variables for the sewage treatment process with complicated nonlinear coupling characteristics. Second, the fact that in view of the traditional fuzzy c-means algorithm based on nearest neighbor assignment is sensitive to outliers and there are unbalanced clusters in clustering, an RoW-FCM clustering algorithm is proposed, which fully considers the relationship between samples. For this RoW-FCM, by introducing the possibility partition matrix as the weight parameter to distinguish and weight different samples, the robustness of outlier data clustering is improved, and the problem of unbalanced cluster is solved by introducing the cluster size control parameter. By clustering the score matrix after dimension reduction with KPLS, the membership matrix can be obtained, which will be used for detecting the abnormal working-conditions. On this basis, the regression model between the membership matrix and the process variables is established, and the resulted variable contribution matrix, which describes the explanatory degree of each cluster, will be used to identify the abnormal working-conditions. At last, both numerical simulation and data experiments of sewage treatment process show that the proposed method has better robust performance and better effect in detecting and identifying the abnormal working-conditions.
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表 1 FCM、PCM、PFCM、RoW-FCM 聚类参数
Table 1 FCM, PCM, PFCM, RoW-FCM clustering parameters
编号 FCM PCM PFCM RoW-FCM ${ {{\boldsymbol{U}}} }_1^{\rm T}$ ${ {{\boldsymbol{U}}} }_2^{\rm T}$ ${ {{\boldsymbol{W}}} }_1^{\rm T}$ ${ {{\boldsymbol{W}}} }_2^{\rm T}$ ${ {{\boldsymbol{U}}} }_1^{\rm T}$ ${ {\boldsymbol{U}} }_2^{\rm T}$ ${ {{\boldsymbol{W}}} }_1^{\rm T}$ ${ {{\boldsymbol{W}}} }_2^{\rm T}$ ${ {{\boldsymbol{U}}} }_1^{\rm T}$ ${ {{\boldsymbol{U}}} }_2^{\rm T}$ ${ {{\boldsymbol{W}}} }_1^{\rm T}$ ${ {{\boldsymbol{W}}} }_2^{\rm T}$ 1 0.973 0.027 0.799 0.798 0.021 0.979 0.026 0.547 0.991 0.009 0.833 0.999 2 0.991 0.009 0.859 0.858 0.010 0.989 0.032 0.755 0.989 0.011 0.839 0.999 3 0.995 0.005 0.861 0.860 0.002 0.998 0.032 0.940 1.00 0.000 1.000 1.000 4 0.967 0.033 0.848 0.848 0.026 0.975 0.032 0.555 0.989 0.011 0.834 0.999 5 0.988 0.012 0.916 0.916 0.013 0.987 0.042 0.770 0.986 0.014 0.840 0.998 6 0.012 0.988 0.916 0.917 0.987 0.013 0.770 0.042 0.012 0.988 0.999 0.861 7 0.009 0.991 0.859 0.860 0.989 0.011 0.755 0.032 0.011 0.989 0.999 0.835 8 0.005 0.995 0.861 0.862 0.998 0.002 0.940 0.032 0.000 0.999 1.000 0.998 9 0.033 0.967 0.848 0.849 0.975 0.026 0.555 0.032 0.011 0.989 0.999 0.835 10 0.027 0.973 0.799 0.800 0.979 0.021 0.547 0.026 0.010 0.990 0.999 0.811 11 0.500 0.500 0.997 0.997 0.500 0.500 0.125 0.125 0.069 0.931 0.985 0.274 12 0.500 0.500 0.632 0.632 0.500 0.500 0.026 0.026 0.997 0.004 0.060 0.999 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 = 0.543 r1 = 4.016 r1 = 0.357 r1 = 0.010 r2 = 0.543 r2 = 4.010 r2 = 0.357 r2 = 0.090 
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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 1 Qin 进水流量 15 SS,3 反应池 3易生物降解有机底物量 2 SNH,in 进水氨浓度 16 SALK,3 反应池 3 池碱度 3 XBH,1 反应池 1活性异养菌生物量 17 XBH,4 反应池 4 活性异养菌生物量 4 SNO,1 反应池 1 硝氮浓度 18 XBA,4 反应池 4 活性自养菌生物量 5 SS,1 反应池 1 易生物降解有机底物量 19 SO,4 反应池 4 溶解氧浓度 6 SALK,1 反应池 1 池碱度 20 SNH,4 反应池 4 氨氮浓度 7 XBH,2 反应池 2 活性异养菌生物量 21 SS,4 反应池 4 易生物降解有机底物量 8 SNO,2 反应池 2 硝氮浓度 22 SALK,4 反应池 4 池碱度 9 SS,2 反应池 2 易生物降解有机底物量 23 XBH,5 反应池 5 活性异养菌生物量 10 SALK,2 反应池 2 池碱度 24 XBA,5 反应池 5 活性自养菌生物量 11 XBH,3 反应池 3 活性异养菌生物量 25 SO,5 反应池 5 溶解氧浓度 12 XBA,3 反应池 3 活性自养菌生物量 26 SNH,5 反应池 5 氨氮浓度 13 SO,3 反应池 3 溶解氧浓度 27 SS,5 反应池 5 易生物降解有机底物量 14 SNH,3 反应池 3 氨氮浓度 28 SALK,5 反应池 5 池碱度
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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)FCM PCM PFCM RoW-FCM FCM PCM PFCM RoW-FCM 正常工况 92.3 80.8 93.9 97.5 — — — — 异常工况 1 75.0 6.3 76.3 96.0 45.1 14 29.1 23.6 异常工况 2 80.3 3.5 77.5 97.0 — — — —
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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 1 0.133 0.339 0.528 15 0.254 0.465 0.281 2 0.150 0.321 0.530 16 0.297 0.255 0.448 3 0.454 0.481 0.065 17 0.450 0.464 0.086 4 0.453 0.395 0.152 18 0.354 0.424 0.223 5 0.093 0.577 0.331 19 0.238 0.260 0.503 6 0.305 0.247 0.448 20 0.124 0.352 0.524 7 0.456 0.477 0.067 21 0.236 0.482 0.283 8 0.010 0.307 0.683 22 0.281 0.245 0.475 9 0.241 0.473 0.286 23 0.446 0.458 0.096 10 0.361 0.290 0.349 24 0.352 0.418 0.230 11 0.453 0.471 0.076 25 0.052 0.310 0.639 12 0.353 0.429 0.218 26 0.118 0.314 0.568 13 0.255 0.167 0.578 27 0.229 0.482 0.289 14 0.208 0.425 0.367 28 0.291 0.259 0.450
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