To overcome the low accuracy, poor reliability, and delay in the current drought prediction models, we propose a new extreme learning machine (ELM) based on an improved variational mode decomposition (VMD). The model first redefines the output of the hidden layer of the ELM model with orthogonal triangular matrix decomposition (QR) to construct an orthogonal triangular ELM (QR-ELM), and then introduces an online sequence learning mechanism (OS) into the QR-ELM to construct an online sequence OR-ELM (OS-QR-ELM), which effectively improves the efficiency of the ELM model. The mutual information extension method was then used to extend both ends of the original signal to improve the VMD end effect. Finally, VMD and OS-QR-ELM were combined to construct a drought prediction method based on the VMD-OS-QR-ELM. The reliability and accuracy of the VMD-OS-QR-ELM model were improved by 86.19% and 93.20%, respectively, compared with those of the support vector regression model combined with empirical mode decomposition. Furthermore, the calculation efficiency of the OS-QR-ELM model was increased by 88.65% and 85.32% compared with that of the ELM and QR-ELM models, respectively.

To improve the accuracy, reliability and validity of flood prediction models, this study proposes a regularized broad learning (RBL) model based on an improved variational mode decomposition (VMD). Firstly, grey correlation analysis was used to improve the endpoint effect of the VMD and the particle swarm optimisation (PSO) algorithm was used to optimise the VMD parameters. Then, using orthogonal triangular decomposition (QR), redefining the hidden layer output of BL model and adding forgettable online sequence learning mechanism (FOS) to construct online sequence BL (FOS-QR-RBL), which can significantly improve the computational efficiency of BL model. Finally, a flood forecasting method based on improved VMD-FOS-QR-RBL was constructed by combining the FOS-QR-RBL with the improved VMD and applying it to regional flood forecasting. The experimental results show that the computational efficiency of FOS-QR-RBL is improved by 35% and 23.68% compared with RBL and QR-RBL, respectively. The mean absolute error (MAE) of the coupling model of VMD and FOS-QR-RBL is reduced by 80.30% and 84.10% respectively, and the nash efficiency coefficient (Ens) is increased by 15.51% and 28.16% respectively, compared with that of the coupling model of FOS-QR-RBL with ensemble empirical mode decomposition (EEMD) and adaptive noise complete ensemble empirical mode decomposition (CEEMDAN). The results of the optimal operation based on VMD-FOS-OR-RBL show that the model can effectively reduce the economic losses caused by regional flooding.

The strong randomness exhibited by the runoff series makes the accuracy of the flood forecasting still needs to be improved. Mode mixing can be dealt with using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), and the endpoint effect of CEEMDAN can be successfully dealt with using the mutual information criterion. To increase the computational effectiveness of broad learning (BL), orthogonal triangular matrix decomposition (QR) was used. A novel improved coupled CEEMDAN-QRBL flood forecasting model was created and applied to the prediction of daily runoff in Xiaolangdi reservoir based on the benefit of quick calculation of the model output layer. The findings indicate that the enhanced QRBL is 28.92% more computationally efficient than the BL model, and that the reconstruction error of CEEMDAN has been decreased by 48.22%. The MAE of the improved CEEMDAN-QRBL model is reduced by 12.36% and 16.31%, and the Ens is improved by 8.81% and 3.96%, respectively, when compared to the EMD-LSTM and CEEMDAN-GRU model. The predicted values of CEEMDAN-QRBL model have a suitable fluctuation range thanks to the use of nonparametric kernel density estimation (NPKDE), which might serve as a useful benchmark for the distribution of the regional water resources.