An ensemble model for monthly runoff prediction using least squares support vector machine based on variational modal decomposition with dung beetle optimization algorithm and error correction strategy

In order to enhance the runoff prediction accuracy, an ensemble prediction model based on least squares support vector machine (LSSVM) is proposed by including variational mode decomposition (VMD), dung beetle optimization algorithm (DBO), and error correction (EC) strategy. First, the monthly runoff time series is decomposed using DBO-optimized VMD (DVMD), yielding a series of intrinsic mode functions (IMF) series and a residual (Res). Then, the LSSVM based on DBO optimization predicts each sub-series column and residual. The final forecast results are achieved after the preliminary forecast results have been stacked and corrected by the DBO-LSSVM prediction error. To verify the reliability of the proposed model, it is applied to the monthly runoff prediction of the Xiajiang hydrological station in the Ganjiang River Basin, the Hongshanhe hydrological station in the Heihe River Basin, and the Jiayugaun hydrological station in the Heihe River Basin. The proposed model is evaluated using four evaluation indicators: RMSE, MAPE, NSEC, and R, and is compared with SVM, LSSVM, PSO-LSSVM, DBO-LSSVM, EEMD-LSSVM, CEEMDAN-LSSVM, DVMD-LSSVM, EEMD-DBO-LSSVM, CEEMDAN-DBO-LSSVM, and DVMD-DBO-LSSVM. Results show that the DVMD-DBO-LSSVM-EC model has the highest accuracy. During the test period, the NSEC of Xiajiang hydrological station is 0.9829, R is 0.9921, the NSEC of Hongshanhe hydrological station is 0.9981, R is 0.9991, and the NSEC of Jiayugaun hydrological station is 0.9772, R is 0.9897. The prediction effect of the model on the extreme value of the three stations after adding the error correction strategy has increased by 45.14%, 62.22%, and 29.49%, respectively, compared with the previous, which is closer to the actual value. The developed combination model offers a new approach to forecasting monthly runoff and extreme values.