Two-stage hybrid model for hydrological series prediction based on a new method of partitioning datasets

Abstract

• A new method of dividing datasets based on PSO is proposed. • BNN incorporates Langevin dynamics in the parameter update step (LDBNN). • Integration of LDBNN, CEEMDAN, VMD and the proposed method yield the hybrid model. • The new data dividing method performs better than the traditional dividing method. • The hybrid model yields excellent point and interval predictions. Obtaining accurate point estimates and reliable interval prediction results for rainfall and runoff series is important to aid in water resource decision-making and planning management in a changing environment. In this paper, we propose a two-stage hybrid model (P-CVEE-LDBNN). The model uses the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD) methods for data preprocessing and a Bayesian neural network (LDBNN) based on Langevin dynamics as a prediction model. Then, a new dataset partitioning method based on a particle swarm optimization algorithm, which is different from the traditional dataset partitioning method, is applied. A one-stage hybrid model (T-CEE-LDBNN) that integrates the CEEMDAN method and the traditional method of partitioning datasets, a one-stage hybrid model (P-CEE-LDBNN) that integrates the CEEMDAN method and the new method of partitioning datasets, and the two-stage hybrid P-CVEE-LDBNN model were compared. These models were applied to monthly runoff and monthly precipitation series from seven hydrological and meteorological stations in the Yellow River basin. The mean absolute error (MAE), absolute root mean squared error (RMSE), Nash–Sutcliffe efficiency (NSE), and correlation coefficient (R) were used to evaluate the predictive ability of the models. The containment ratio (CR), the average bandwidth (IW), and the average asymmetry degree (S) were used to evaluate the interval prediction results of the models. The results show that (1) the subset obtained with the new method of data partitioning considering statistical properties is more favorable for model prediction. (2) The second decomposition approach based on VMD is a reliable method that can significantly improve the prediction accuracy of the final model. (3) Compared with traditional neural networks that can only obtain deterministic point prediction results, Bayesian methods can provide intervals with prediction results, making the results of the two-stage hybrid P-CVEE-LDBNN model highly reliable.