Novel forecasting models for immediate-short-term to long-term influent flow prediction by combining ANFIS and grey wolf optimization

Abstract Accurate influent flow forecasting plays a significant role in management, operation, scheduling and utilization of the sewage treatment plants. In design and operate such plants, it is essential to measure and forecast the influent flow rate in wastewater plants. In this paper, the Very immediate-short-term to long-term influent flow rate are modeled and forecasted by a new developed hybrid model of ANFIS and Grey Wolf Optimizer (GWO). The objective of this study is the integration of GWO with ANFIS in forecasting multi-ahead influent flow rate. The forecast horizon of the model is from 5 min up to 10 days bases on Gamma Test (GT) feature selection of input combinations. As the parameters of ANFIS have effect on the forecasting accuracy, these parameters are adjusted and optimized by using Grey Wolf Optimizer (GWO). Then the choice of appropriate input parameters at different prediction horizons from Very immediate-short-term (5-min ahead) to long-term (10 days ahead) was discussed for influent forecasting. The statistical indices of RMSE, NSE, MAE, RAE, R 2 , d, CI and graphical evaluations such as scatter-plots with confidence bounds, error distributions, Taylor diagrams, box-plots and empirical cumulative distribution function (ECDF) were implemented for assessing the performance of all models in prediction horizons. Furthermore as another novelty in the present paper, recursive forecasting models based on previous forecasted values is used to improve the accuracy and applicability of ANFIS-GWO in recursive predictions. Our Results showed that: (1) the hybrid of ANFIS-GWO significantly improved the prediction accuracy. (2) ANFIS-GWO performs more efficiently than the ANFIS in almost all of the prediction horizons (ANFIS-GWO1: 5 min ahead; ANFIS-GWO11: 1–2 days ahead; ANFIS-GWO8: one week ahead). (3) The performance of models in influent flow forecasting is significantly influenced by the prediction horizon. The computational results confirmed that the ANFIS-GWO performs well in all of prediction horizons. Equally the true values and the trends are precisely forecasted by the ANFIS-GWO. Results of this novel study demonstrate that reliable estimates of influent flow rate from 5-min up to 10 days in advance can be achieved using the developed direct and recursive hybrid GWO models.