Novel hybrid and weighted ensemble models to predict river discharge series with outliers

Abstract

In this study, a novel hybrid framework named HVK/HVA-HEM was designed to predict river discharge with outliers. Firstly, the Hampel filter (HF) identifies and corrects outliers in the discharge series. Next, this series was denoised and decomposed using ensemble empirical mode decomposition (EEMD) and variational mode decomposition (VMD) respectively. The HF-VMD components were employed to K-nearest neighbor (KNN) and autoregressive integrated moving average (ARIMA) models, while the HF-EEMD series was applied to the multilayer perceptron (MLP) model to obtain the predictions of the proposed HVK(HF-VMD-KNN), HVA(HF-VMD-ARIMA), and HEM(HF-EEMD-MLP) hybrid models. Lastly, using the mean absolute error (MAE) weights of HVK, HVA and HEM predictions, the HVK-HEM and HVA-HEM models were formulated. The application of the new hybrid framework was displayed using the discharge of four rivers in Pakistan. In terms of the RMSE of Kabul River, the HEM hybrid model had better performance than MLP (175.2053 m3/s), HF-MLP (156.1853 m3/s), EEMD-MLP (133.4049 m3/s) and VMD-MLP (170.1337 m3/s). Similarly, the proposed HVK and HEM hybrid models are more efficient than their respective single, HF, EEMD, and VMD-based models. Overall, the proposed HVA-HEM hybrid model outperformed all competing and proposed models.