## 1 Introduction  
The awareness of environmental protection in the society has been gradually improving due to better education on sustainability, and wastewater treatment has become one of the important research topics in the field of environmental protection. Biochemical oxygen demand (BOD) is one of the major parameters of effluent quality indices of wastewater treatment processes. Real-time and accurate monitoring of BOD is the key factor to improve the automatic control of the performance of wastewater treatment processes. However, due to the strong nonlinear and time-varying characteristics of wastewater treatment processes as well as the capacity of current detection methods [1] and measurement accuracies of the sensors and instruments, it is difficult to achieve accurate real-time and on-line measurement of BOD data; this limits the application of closed-loop control in wastewater treatment processes [2]. Hence, there is a great need on how to measure BOD rapidly and accurately to control the wastewater treatment processes. Recently, the development of soft sensing technology provides a new way of measuring variables which are not measurable on-line in real-time. Especially, researchers have applied soft sensing technology to model the wastewater treatment processes and have achieved good results. [PERSON] et al. [3] considered the inflow (Q) as well as the chemical oxygen demand (COD), pH, the suspended solids (SS) and the total nitrogen (TN) of the influent as the auxiliary variables to model a feed-forward three-layer multiple inputs and single output (MISO) neural network, called adaptive growing and pruning (AGP) network. The parameters of the neural network were trained by back propagation (BP) algorithm. This soft sensor model was used to predict the BOD concentration of effluent in their simulation study. Simple learning algorithm has the greatest advantage as it can speed up the measurement, but unfortunately the prediction accuracy is not sufficient for it to be applied in real-time. [PERSON] et al. [4] proposed a soft sensor method for the measurement of BOD based on a self-organizing neural network with random weights (SNNRW). It used the output weight vector to calculate the sensitivity of the hidden layer nodes to the residual. Based on the sensitivity analysis, it could remove less sensitive nodes of the hidden layer by itself according to the level of the sensitivity. It can achieve higher prediction accuracy while performing much more complex calculations. [PERSON] [5] proposed an online soft BOD measurement method based on an echo sound network (ESN) algorithm. The weights of the ESN are trained and obtained by online learning method. The range of learning rate of ESN network is analyzed and determined by Lyapunov theory, which ensured the convergence of the algorithm. This algorithm improved the accuracy of prediction and the adaptability of the model, but with high computation load. The extreme learning machine (ELM) is a new feed-forward neural network learning algorithm which was originally proposed by Professor [PERSON] of Nanyang Technological University [6]. It has the advantages of simple training process, higher training speed and strong anti-interference ability [7]. The training time is greatly reduced compared to other networks, as ELM only needs to set the number of hidden layer nodes, and the randomly generated input weights and hidden layer thresholds are no longer adjusted in the training process. Through experiments, [PERSON] et al. [8] demonstrated that ELM has higher training speed and better generalization ability than BP neural network and support vector machine (SVM). Therefore, soft sensor technology based on ELM learning algorithm has been widely applied in industrial process measurement [9; 10]. Compared to BP neural network learning algorithm, ELM can avoid issues such as easy to get local optimum solution [11], poor performance indices and low learning rate.