A runoff prediction method based on hyperparameter optimisation of a kernel extreme learning machine with multi-step decomposition

To improve the accuracy of runoff forecasting, a combined forecasting model is established by using the kernel extreme learning machine (KELM) algorithm optimised by the butterfly optimisation algorithm (BOA), combined with the variational modal decomposition method (VMD) and the complementary ensemble empirical modal decomposition method (CEEMD), for the measured daily runoff sequences at Jiehetan and Huayuankou stations and Gaochun and Lijin stations. The results show that the combined model VMD-CEEMD-BOA-KELM predicts the best. The average absolute errors are 30.02, 23.72, 25.75, 29.37, and the root mean square errors are 20.53 m(3)/s, 18.79 m(3)/s, 18.66 m(3)/s, and 21.87 m(3)/s, the decision coefficients are all above 90 percent, respectively, and the Nash efficiency coefficients are all more than 90%, from the above it can be seen that the method has better results in runoff time series prediction.