Robust Neural Network Modeling With Small-Worldness for Effluent Total Phosphorus Prediction in Wastewater Treatment Process

As a key water quality parameter in the wastewater treatment process (WWTP), the accurate measurement of total phosphorus (TP) would effectively prevent the effluent water from eutrophication. Although soft measurement models can successfully predict effluent TP, the model prediction is unreliable because outliers will inevitably exist in actual WWTP due to a variety of disturbances. To solve this problem, a novel robust small-world feedforward neural network (RSWFNN) is proposed to improve the robustness of effluent TP prediction. First, the robust Spearman rank correlation analysis is used to determine auxiliary variables intrinsically correlated with the effluent TP. Second, inspired by the fault tolerance of the human brain from its small world property, the small-worldness is introduced to obtain a robust network architecture. Third, the robust learning algorithm using the loss function of regularized M-estimation is proposed to suppress the responses of outliers to improve the robustness of the model. Finally, the corresponding two hyperparameters are determined by an adaptive adjustment strategy, thus ensuring the effectiveness of suppressing outliers. Our experimental results have shown that RSWFNN has stronger robustness and better prediction performance to predict effluent TP than other modeling methods, and the superiority of robustness becomes more obvious with the increase of outlier proportion.