Soft-sensing of Wastewater Treatment Process via Deep Belief Network with Event-triggered Learning

Abstract

Due to the complex dynamic behavior of a Wastewater Treatment Process (WWTP), the existing soft-sensing models usually fail to efficiently and accurately predict its effluent water quality. Especially when a lot of practical data is provided and we do not know which data-pair is more valuable, WWTP modeling becomes a time-consuming process. The main reason is that the existing soft-sensing models update their parameters at each data-pair in one iteration, while some update operations are meaningless. To address this thorny problem, this paper proposes a Deep Belief Network with Event-triggered Learning (DBN-EL) to improve the efficiency and accuracy of soft-sensing model in WWTP. First, some events are defined according to different running condition during the process of training DBN-based soft-sensing model. The different running condition is dominated by the fluctuation of error-reduction rate. Second, an event-triggered learning strategy is designed to construct DBN-EL, whose parameters are updated only when a positive event is triggered. Thirdly, we present the convergence analysis of DBN-EL based on the optimization in a Markov process. Finally, the effectiveness of DBN-EL is demonstrated on soft-sensing of total phosphorus concentration in a practical WWTP system. In experiment, DBN-EL is compared with nine different models on soft-sensing of WWTP. The experimental results show that the efficiency of DBN-EL is 27.6%–64.9% higher than that of nine competitive models, which indicates that the proposed model is readily available for industrial deployment.

Introduction

Wastewater treatment is absolutely essential for municipal civilization. Nowadays, biological wastewater treatment is the most feasible one, which is widely applied to a municipal Wastewater Treatment Process (WWTP). Due to its complex nonlinear dynamics with large disturbances and uncertain time-delay, WWTP modeling is a challenging task [26], [9]. Under the strict environmental regulations, soft-sensing models for effluent quality of wastewater are so vital [6], [30], [19]. A fast and accurate soft-sensing model of effluent quality not only gives an explicit description of dynamics, but also provides an alert reference for the next action in advance if abnormal operation occurs. Therefore, how to obtain excellent modeling performance of effluent quality is indispensable for the optimal operation and control of WWTP.

In existing soft-sensing models of effluent quality in WWTP, artificial neural networks (ANNs) have been widely applied to model and predict effluent quality. In particular, Canete et al. develop an ANN-based soft sensor for the online prediction of effluent chemical oxygen demand [1], which has been proved to be effective. Li et al. propose a self-organizing cascade ANN based on random weights to approximate the effluent total phosphorous (TP) [11], which achieves desired performances in practical WWTP. In Han et al. [8], a self-organizing recurrent neural network is proposed to predict the dissolved oxygen in WWTP, where a spiking-based self-adjusting algorithm is developed to tune the structure and parameters. Qiao et al. propose an incremental radial basis function neural network to model and predict effluent TP in WWTP [20], where a modified second-order algorithm is utilized to train the neuronal activity. Additionally, some other improved ANNs are applied to model and predict effluent quality and achieve desired performances [4]. These ANN-based soft-sensing models have achieved success in applications of WWTP modeling. However, they face two main challenges:

• Poor Capability of Extracting Deep Features. The existing ANN-based soft-sensing models are of shallow learning structures, which cannot mine and extract effective features from practical-complex data in WWTP. For some practical applications, however, effective features from a dataset are helpful to enable an efficient learning process. Therefore, their absence not only leads to a high computational need, but also results in unsatisfactory modeling performance.

• Time-Consuming Learning Process. The existing ANN-based soft-sensing models update their weight parameters at each data-pair in one iteration. When much practical data is provided and we do not know which one is more valuable for a training process, the operation of updating weight parameters at each data-pair tend to be useless. In this case, a time-consuming learning process is inevitable.

To solve these two problems, many efforts have been made in recent years [13], [14], [15], [16], [17], [18], [34], [35], [36]. Deep belief network (DBN), as a deep learning model, has been widely studied and applied to extract deep features and model various industrial processes [27], [37], [38], [39]. DBN can encode raw complex data into feature-vectors with different levels by training several stacked restricted Boltzmann machines (RBMs). The performance of extracting effective features can be guaranteed by minimizing reconstruction error. With its hierarchical learning capability, DBN-based learning models can achieve outstanding performance by using more effective features of practical-complex data. Sun et al. propose a deep belief echo-state network (DBESN) for nonlinear system modeling [22], where DBN is considered as a features extractor to provide echo-state network with effective input. The experimental results of DBEN indicate that DBN is effective in extracting deep features. In Wang et al. [28], DBN is first used to extract effective features from raw data, then its output is considered as the input of a fuzzy neural network (FNN). The resulting SDB-FNN model achieves desired modeling accuracy. In recent years, event-triggered optimization is used to reduce the computational complexity of modeling and control of industrial processes. Because event-triggered optimization updates parameters only when certain events occur, it is more efficient than time-triggered methods, which is demonstrated by extensive experiments in Luo and Zhou [12]. Wang et al. present a dynamic event-triggered optimization for nonlinear stochastic systems, and its effectiveness is demonstrated by a class of numerical examples [32]. Ramesh et al. propose a feasible method that gives comprehensive analysis and theoretical proof for the effectiveness of event-triggered optimization [21]. However, there is no unified method that can effectively address the two problems.

How to effectively address both problems is what we concern in this work. Considering the effluent TP concentration modeling in WWTP as a specific application background, we propose an Event-Triggered DBN (DBN-EL) model to pursue faster and more accurate modeling performance than traditional neural network. In the proposed DBN-EL model, updating weight parameters is conducted only when a certain event is triggered. First, the triggering event is defined according to error-reduction rate and corresponding number of iterations. If the fluctuation of error-reduction rate goes beyond or falls within a predefined threshold, a corresponding event is triggered. Second, once some events are triggered, and means that the current data-pair is valuable, the weight parameters are updated at the current iteration. Compared with the existing methods, the main contributions of this work are:

• It proposes an event-triggered DBN learning model, DBN-EL, which can extract effective feature from practical-complex data of WWTP. More importantly, DBN-EL is trained on the extracted effective feature and updates its weight parameters only when a positive event is triggered. In this case, the real dynamics of TP concentration in WWTP system can be efficiently and accurately approximated.

• It proposes an effective method to improve the effectiveness of data by using event-triggered strategy. The event-triggered strategy is actually a selective response mechanism that does not respond to any outlier data.

• It presents the convergence and stability analysis of event-triggered learning algorithm based on the optimization in Markov process, which can improve interpretability and transferability of DBN-EL.

The rest of this work is organized as follows. We present problem formulations and preliminaries in Section 2, provide DBN-EL and its computational complexity analysis in Section 3, give convergence analysis in Section 4, give experimental results in Section 5, present the discussion in Section 6, and conclude this work in Section 7.