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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.Abstract: In the process of wastewater treatment, effluent quality indices are the most important indicators to measure the performance of wastewater treatment, which need to be monitored strictly. However, the existing sensor technology is difficult to measure them in real time and accurately. Therefore, a novel sparse robust modeling method based on random vector functional-link networks (RVFLNs) and Schweppe-type generalized M-estimation (GM-estimation) is proposed for on-line robust estimation of effluent quality indices. First of all, aiming at the multicollinearity of conventional RVFLNs hidden layer matrix, which leads to the failure of the least squares estimation, sparse partial least squares (SPLS) algorithm is used to replace the least squares estimation of output weights of RVFLNs, and a SPLS-RVFLNs algorithm is proposed. This algorithm can not only solve the multicollinearity problem of traditional RVFLNs effectively, but also select modeling variables to improve the interpretability and prediction accuracy of the model. At the same time, considering that the SPLS-RVFLNs algorithm is affected by outliers in both directions of hidden layer matrix and output layer matrix, Schweppe-type GM-estimation is further used to improve the robustness, thus a GM-SPLS-RVFLNs algorithm is proposed, which can improve the sparse robustness of the model significantly. Finally, the GM-SPLS-RVFLNs algorithm is used to predict effluent quality indices of wastewater treatment process. The experimental results show that the proposed method not merely solves the problems of multicollinearity and poor robustness of conventional RVFLNs, but has good prediction accuracy and generalization performance as well.
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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 BOD COD TSS 10 0.0372 0.2321 0.1733 15 0.0290 0.1781 0.1569 20 0.0290 0.1574 0.1350 25 0.0258 0.1496 0.1211 30 0.0247 0.1440 0.1150 35 0.0223 0.1345 0.1043 40 0.0225 0.1343 0.1032 50 0.0224 0.1337 0.1054 100 0.0221 0.1340 0.1022 200 0.0227 0.1325 0.1015 
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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 RMSE MAPE R square BOD COD TSS BOD COD TSS BOD COD TSS RVFLNs 0.1689 1.2691 0.8442 0.0532 0.0215 0.0581 0.7550 0.7068 0.7817 Robust RVFLNs 0.0931 0.6572 0.4539 0.0242 0.0100 0.0242 0.9303 0.9285 0.9413 PRM RVFLNs 0.0893 0.5389 0.4015 0.0216 0.0078 0.0200 0.9330 0.9501 0.9522 GM-SPLS-RVFLNs 0.0301 0.1765 0.1259 0.0056 0.0016 0.0045 0.9959 0.9976 0.9974
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