H. Liu et al. : Effluent Quality Prediction of Papermaking WWTPs Using SEL
FIGURE 5. BSM1 layout.
TABLE 3. Process variables in BSM1.
The Kernel function is of key importance in SVR. Among all of the kernel functions, RBF is the most commonly used one. Its main advantage is that even if prior knowledge of the data is absent, the prediction effect is still robust. There- fore, RBF was adopted in this work. The kernel parameter γ directly affects the complexity of data distribution in the higher dimensional space, and hence needs to be confirmed first. If γ is too small, it will perform like linear kernel func- tion. On the contrary, it will perform like polynomial kernel function. Another important parameter of SVR is the regu- larization parameter C also known as penalty factor, which is used to achieve a compromise between empirical risk and confidence level. If C value is too high, the SVR tends to result in over-fitting phenomenon. On the contrary, smaller C value is often accompanied with under-fitting problems. The grid searching method [31] was adopted to search for a suitable combination of C and γ in this work. The key to constructing a well-performed ANN lies in finding a suitable network structure and activation function. Considering the data size is not large, the three-layer network structure was chosen in this work. The number of hidden layer nodes, the activation function of hidden layer, and output layer were selected according to the actual prediction performance. The specific parameters of the base-learning algorithms are shown in Table 4.
C. ENSEMBLE LEARNING MODELS COMPARISON To compare SEL with other types of ensemble learning methods in terms of prediction accuracy, random forest (RF) model based on bagging algorithm and adaptive boost- ing (AdaBoost) model based on boosting algorithm were con- structed by using the same wastewater data. The base-learners of RF and AdaBoost are both decision trees. Considering that prediction of wastewater effluent indices is essentially a regression task, the CART (classification and regression tree) is selected as the decision tree which is not pruned during the modeling process. The main difference between RF and AdaBoost is that the former integrates decision trees in a parallel manner, while the latter integrates decision trees in a serial manner. In terms of RF, the main tuning parameters include the number of decision trees n tree and random vari- ables used at each split m try . In terms of AdaBoost, the main tuning parameters include the number of iterations n T and learning rate of base-learners ν . All of above-mentioned tun- ing parameters were obtained by grid searching method. D. RESULTS AND DISCUSSION To directly observe the prediction performance of SEL, we provide prediction figures for real wastewater data and simulation wastewater data. As shown in Figures 6 and 7, the data points of the two cases are both well modeled
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