Fuzzy Neural Network-Based Iterative Multi-Step Prediction with Time Delay for WWTP

Multi-step prediction is developed to exploit the current values of variables to estimate the future behavior of WWTP over multiple timesteps. However, since the existence of time delay can influence the data distribution and the relationship between variables in WWTP, the performance of the multi-step prediction model will be degraded. To address this issue, a fuzzy neural network-based iterative multi-step prediction (FNN-IMSP) with time delay for WWTP is proposed in this paper. First, a dynamic time delay mechanism is designed to determine the appropriate time delay at each time point among process variables in WWTP. Then, the proposed mechanism can reveal the dynamical correlation between variables to assist in the multi-step prediction. Second, an iterative multi-step strategy, leveraging both previous and current values, is introduced in the FNN-based prediction method. Then, the proposed prediction model can estimate further future variation tendency. Third, an adaptive second-order algorithm is employed to update the parameters of FNN-IMSP. Then, the adaptive ability and prediction accuracy of FNN-IMSP can be improved. Finally, FNN-IMSP is validated on a real WWTP. The experimental results indicate that the prediction model can achieve outstanding prediction performance.