Enhancing long-term river water quality prediction: Construction and validation of an improved hybrid model

To prevent eutrophication of river caused by excessive inputs of nutrients, accurately predicting these nutrient concentrations is of utmost importance. However, long-term accurate predictions of nutrients concentrations remain a challenge. In this study, an improved hybrid algorithm combining adaptive variational mode decomposition and multi-functional recurrent fuzzy neural network (AVMD-MFRFNN) was proposed. Firstly, whale optimization algorithm (WOA) was developed to identify the optimal number of modes for variational mode decomposition (VMD). Then VMD was employed to decompose input data into intrinsic mode fractions (IMFs), benefiting for reducing the noise effect and non-stationarity of data. Then, MFRFNN with the capability of characterizing complex data was developed to train and test the IMFs. The proposed AVMD-MFRFNN achieved impressive results with the root mean square errors (RMSEs) of 0.036 mg/L, 0.758 mg/L and 1.435 mg/L for predicting total phosphorus (TP), chemical oxygen demand (CODMn) and total nitrogen (TN) after 168 hours. These results signify a decrease of 5.3%, 14.1% and 30.1% compared to the second-best compared method. Moreover, this study demonstrates the potential that integrating the proposed AVMD with other methods can enhance the modeling performance of time series. Furthermore, sensitivity analysis results further validate the effectiveness of WOA in optimizing VMD parameter. Finally, the applicability of AVMD-MFRFNN was confirmed by the data from another river section. These results provide new insights and technical support into the management and preservation of river water environment.