# Multi-Scale Temporal Convolutional Networks for Effluent COD Prediction in Industrial Wastewater
## 1 Introduction  
As the scale of industrial development expands, environmental problems caused by production activities have become increasingly prominent. Industrial wastewater from sectors such as metallurgy, dyeing, and pulp and papermaking contains excessive amounts of heavy metals and refractory organics, which severely pollute soil and water resources, destroy ecosystems, and lead to negative impacts on human health [1, 2]. Additionally, the harmful substances in industrial wastewater can volatilize with the rising temperature, resulting in air pollution. Thus, industrial wastewater has become one of the significant global environmental challenges. Effective treatment and enhanced regulatory mechanisms are crucial for environmental protection and the sustainable development of industries [3]. It is essential to regulate specific wastewater discharge standards based on industrial categories and pollutant types to control water pollution and maintain ecological balance. Because of the large amount of wastewater discharge, the complex composition of pollutants, and poor biodegradability [4], pre-treatment is required before carrying out the biochemical treatment again for the converted small molecular substances [5]. By combining hardware sensors with data-driven soft measurement methods, wastewater treatment plants (WWTPs) can monitor complex processes in real-time and realize the indirect estimation of key indicators that are difficult to measure in practice [6, 7]. Furthermore, this enables early warning of abnormal conditions, leading to more efficient and reliable process control. Chemical oxygen demand (COD) is the amount of consumed oxygen when the dissolved and suspended matter are exposed to a specific oxidizing agent, which is considered a critical index for evaluating the organic pollution level in wastewater [8]. However, monitoring the COD concentrations online using hardware sensors involves high costs, and some substances in the water body can react irreversibly with the sensor elements, which has negative impacts on their accuracy and lifespan [9]. Thus, data-driven soft sensor methods for modeling COD concentrations in wastewater are widely applied in practical industrial operations. Since machine learning methods can systematically learn relationships between variables from historical data, there have been a number of studies and applications of them in recent years [10]. [PERSON] and co-workers [11] provided a new insight in real-time COD prediction using several novel models combining hybridizing kernel-based extreme learning machines (ELM) with intelligent optimization algorithms. To make reliable predictions with time series data, [PERSON] et al. [12] utilized autoregressive integrated moving average (ARIMA) as a fundamental structure and incorporated the outlier robust ELM technique to model the nonlinear and linear variables separately, thereby improving the accuracy of predicted effluent COD. Although ARIMA can explain the relationship between current and historical values using autoregression, differencing, and moving average calculations, its reliability significantly decreases when the input is an irregularly sampled time series with multiple data patterns. The appearance of deep learning methods provides an effective direction to these problems. Deep learning models based on the recurrent neural network (RNN), which has a chain structure, have been applied in smart WWTPs in recent years because of their ability to learn historical trends in the temporal dimension [13; 14]. Examples include the long short-term memory network (LSTM), which introduces gating mechanisms into the RNN units [15; 16; 17], and gated recurrent units (GRU), which improves gating structure in LSTM to reduce the number of parameters in training [18; 19; 20]. These models generate future trends by historical dependencies in time series, and all of them achieved accurate estimations of effluent COD, heavy metal, and sludge volume index with the inputs observed in both single and entire wastewater treatment processes.