ES-MSCNN: An Echo State Multi-Scale Convolutional Neural Network for Multi-Step Prediction of Wastewater Quality Variables

Given the limitations of hardware sensors together with strong nonlinearities and nexus between variables in wastewater treatment processes (WWTPs), the measurement of key quality variables is usually inaccurate or even impossible. Moreover, due to the short data sampling period, the single-output single-step prediction model cannot meet the actual demand. Therefore, this paper proposes a new soft sensor, termed as the Echo State Multi-Scale Convolutional Neural Network (ES-MSCNN), designed for accurate multivariate multi-step prediction. ES-MSCNN first generates an echo state representation (ESR) containing temporal information through an echo state network (ESN). Subsequently, a convolutional neural network (CNN) is employed to avoid the shallowness of ESN and further extract high-dimensional feature information from the data. Besides, a multi-scale learning strategy is used in the convolutional module to capture multi-timescale features and improve the multivariate prediction accuracy. Validation on the benchmark simulation model 2 platform and comparison with several models indicate that the proposed ES-MSCNN has higher accuracy and stronger robustness in multi-step prediction tasks with multi-input and multi-output.