A novel GRA-NARX and hydrodynamic coupled model for water level prediction in front of sluice gates

Purpose It is necessary but difficult to accurately predict the water levels in front of sluice gates of an open channel water transfer project due to the complex interactions among hydraulic structures. The existing methods have certain shortcomings. For example, although one-dimensional hydrodynamic simulation is technically feasible, little is known about hydrodynamic models for prediction. Another example is that, neural networks can hardly predict the information of nonmonitoring sections. To these problems, this paper presents a novel GRA-NARX and hydrodynamic coupled prediction model (H-GRA-NARX-HPM) that is based on the GRA-NARX (gray relation analysis-nonlinear auto-regressive exogenous) neural network with automatic hyperparameter calibration. Design/methodology/approach Firstly, the GRA is used to determine the correlations of influencing factors and find the optimal influencing factors. Secondly, the selected factors are taken as the input variables of the NARX neural network. Finally, the GRA-NARX neural network with automatic hyperparameter calibration (H-GRA-NARX model) provides accurate 24-h water level prediction to be used as the boundary condition of the hydrodynamic model, and then the H-GRA-NARX-HPM is constructed. Findings The section from the inlet sluice gate of Tang River aqueduct to the outlet sluice gate of Zhang River inverted siphon in the Middle Route of the South-to-North Water Transfer Project, China, is taken as the study area. The water levels before the outlet sluice gate of Anyang River inverted siphon on February 22, 2018 and February 26, 2018, are predicted by the H-GRA-NARX-HPM and then compared with those of the prediction models (GRA-BP-HPM, GRA-NARX-HPM) that use GRA-BP(gray relation analysis-back-propagation) neural network and GRA-NARX neural network prediction information as boundary conditions. The results show that the H-GRA-NARX-HPM has the highest accuracy with MAE values of 0.0028 m and 0.0141 m and MSE values of 1.636 × 10-5 and 2.658 × 10-4 on February 22 and February 26, respectively. In order to verify the universality and applicability of the model, the section from the inlet sluice gate of Ming River aqueduct to the outlet sluice gate of Qili River inverted siphon is taken as another study area. The water levels before the outlet sluice gate of Nansha River inverted siphon on March 18, 2018 and March 19, 2018, are predicted by the H-GRA-NARX-HPM and then also compared with GRA-BP-HPM and GRA-NARX-HPM. The results show that the H-GRA-NARX-HPM has the highest accuracy as well. Originality/value The main contribution of this paper is to propose a novel GRA-NARX and hydrodynamic coupled prediction model (H-GRA-NARX-HPM) which can overcome the main limitations of the individual modelling approaches.