H. Liu et al. : Effluent Quality Prediction of Papermaking WWTPs Using SEL
generalization capability. From the viewpoint of diversity, SEL has a better prospect [24]. If the well-trained base-learning algorithms with higher prediction accuracy are prerequisites to SEL, the meta- learning algorithm determines the quality of SEL to a degree. Multi-response linear regression (MLR) has been confirmed as the most suitable meta-learning algorithm in SEL. Dif- ferent from the voting or average methods in Bagging and Boosting, SEL uses MLR to further generalize the output values of the base-learning algorithms. Previous research has shown that the main superiority of MLR depends on its powerful function for reducing variance and bias of different base-learning algorithms [25]. In recent years, SEL has been successfully applied to the industrial field as a real-time prediction method. Divina developed an approach for short-term electricity consumption forecasting based on SEL. Compared with other conven- tional methods, the proposed method realized an efficient and promising way for solving the forecasting accuracy prob- lem [26]. Khairalla proposed a modified SEL method to predict the average growth rate of total oil demand, which was superior to other benchmark methods in the aspects of error rate and directional accuracy [27]. Sun successfully applied SEL to the river ice forecasting field and obtained a better prediction result with higher accuracy [28]. In this work, a novel SEL algorithm is proposed to predict the wastewater effluent indices. This article is organized in the following manner. In Section 2, the training and testing processes are illustrated in more details, then the modeling principles of base-learning algorithms and meta-learning algorithm are briefly introduced. In Section 3, data processing and parame- ter optimization are illustrated first, and then other ensemble learning methods are introduced for comparison. To evaluate the prediction performance of SEL, both real wastewater data and simulation wastewater data are used for modeling. Finally, the conclusions are given in Section 4. II. METHODS SEL can improve estimation ability by combining the advan- tages of several different algorithms. In this work, SEL can be divided into two parts. The first part contains base-learning algorithms and the second part is the meta-learning algorithm. The base-learning algorithms should be efficient, diversiform and simple. As a prerequisite for building an ensemble model, strong learning ability of base-learning algorithm is helpful to improve the predicted performance of SEL. In terms of training principle, the diversity between each base learner should be as large as possible, which enables SEL to inter- pret data characteristics from multiple perspectives. More- over, lower computational complexity will be beneficial to further improvement and optimization. Based on the above criteria, PLS, SVR, and ANN are chosen as the candidate base-learning algorithm. Compared with the simple average and voting strategy, MLR has access to a further general- ization result, which is also the most commonly used meta- learning algorithm at present.
method such as PLS usually shows bad modeling perfor- mance when nonlinear characteristic exists in the WWTP data [9]. Embedding kernel functions into PLS has been considered as an effective way for improving the prediction performance, in which the original data is transformed into a high-dimensional feature space by nonlinear mapping [10]. Compared with PLS, ANN has better nonlinear fitting per- formance and adaptive learning ability, which allows ANN to be successfully applied in WWTPs [11], [12]. However, there always exist low efficiency and local minimum problems in the ANN modeling process. To improve its modeling perfor- mance, the original ANN model needs to combine with other optimization methods such as fuzzy subtractive clustering and optimize fuzzy rule [13]. Although SVR has proven to work well under limited data sets, the computational cost is relatively large for large-scale data sets [14]. Aiming at curbing this limitation of the conventional SVR, the LSSVR algorithm has been proposed and it can provide a more effec- tive solution by transforming the optimization problem into a set of linear equations problem [15]. Reducing the computing complexity, the improved LSSVR model can be successfully applied for predicting the wastewater effluent indices [16]. However, conventional models inevitably have some lim- itations. Without further optimization, none of the original models has the capability to interpret the complex charac- teristics of wastewater treatment processes. Moreover, there always exists a contradiction between model complexity and its generalization ability for limited samples. It is difficult and usually impossible for an over-optimized model to reach high prediction performance for all the data sets. Fortunately, it has been confirmed that ensemble learning methods could improve prediction accuracy without making the model too complicated [17]. Rather than transforming a single model and hoping the modified model to display its full poten- tial, ensemble learning methods combine different types of models’ advantages to achieve a better prediction perfor- mance. By considering various viewpoints of training data and multiple training principles, ensemble learning methods can be of great benefit for excavating the potential informa- tion between WWTP variables so the model’s generaliza- tion ability is greatly increased. Ensemble learning methods have been an important direction of process modeling in future. All of the conventional models are also called base-learners in ensemble learning methods which improve prediction ability by diversifying its base-learners [18]. At present, ensemble learning methods are generally divided into three types: Bagging, Boosting and stacking ensemble learning (SEL) [19]–[21]. For Bagging and Boosting, the emphasis is mainly placed on the data resampling technique [22], [23]. Thus, the diversity between all of the base-learners is focused on the multiformity of the training samples. Unlike Bagging and Boosting, SEL pays more attention to the diversity of training principles. More specifically, SEL integrates several distinct base-learning algorithms through a meta-learning algorithm, which aims to improve the prediction accuracy and
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