基于超参数自动率定的 GRA-NARX（grey?relation?analysis-nonlinear?autoregressive?model?with?exogenous?inputs） 模型是 GRA-NARX 模型的一种有效改进。以南水北调东线一期工程洪泽泵站为例，使用基于超参数自动率定的 GRA-NARX 模型，针对 1?h 和 2?h 时间间隔的输入数据，分别预测 3 个短预见期（2?h、4?h、6?h）和 1 个长预见期（12?h） 的泵站站前水位，并与 GRA-BP（grey?relation?analysis-back?propagation）模型的预测结果进行比较。结果表明：不同 预见期（2?h、4?h、6?h、12?h）下，基于超参数自动率定的 GRA-NARX 模型的相关系数、均方根误差和平均绝对误差 等指标均相差不大，预测精度高，且皆优于 GRA-BP 模型；采用 1?h 时间间隔的输入数据预测结果优于 2?h 时间间 隔的输入数据结果。研究成果可为不同预见期泵站站前水位预测提供理论参考。

Large-scale water transfer projects make a considerable contribution to reducing a country's uneven distribution of water resources. The water level between two neighboring pumping stations should be kept as consistent as feasible in an open-channel water transfer project that includes a wide range of hydraulic structures for various purposes to prevent potential channel overflow or drying-up of the pumping station forebay. A sharp change in water level may impair water supply and generate significant hydraulic oscillation. As a result, precise prediction of water levels in front of pumping stations is critical to the normal operation of these pumping stations.The GRA-NARX (grey relationship analysis-nonlinear autoregressive model with exogenous inputs) model is a recurrent dynamic network composed of input delay and feedback memory nodes, with advantageous properties such as more rapid calculation, high generalization performance and high accuracy. The GRA-NARX model based on hyper-parameter automatic calibration is an effective improvement of the GRA-NARX model, which significantly improves the accuracy of water level prediction in front of the Tundian pumping station of the Miyun project in the 2 h short forecast period. However, this model did not consider the water level prediction for different short forecast periods (4 h, 6 h) and long forecast period (12 h). Taking the Hongze pumping station of the Eastern Route of South-to-North Water Transfers Project as an example, the model is used to predict the water level in front of the pumping station for three short forecast periods (2 h, 4 h, 6 h) and one long forecast period (12 h) based on input data at 1 hour and 2 hours intervals, and the prediction results are compared with the GRA-BP (grey relationship analysis backpropagation) model. The results show that the prediction accuracy of the GRA-NARX model with automatic calibration of hyper-parameters is better than that of the GRA-BP model under different forecast periods. The coefficient of association (R), root mean square error (ERMS), and mean absolute error (EMA) of the GRA-NARX model with automatic calibration of hyper-parameters are not significantly different under different forecast periods. When the time interval for inputting data is 1 hour, with a long forecast period of 12 hours, the optimal R is 0.990 03, ERMS is 0.018 m, and EMA is 0.013 m. When the time interval for inputting data is 2 hours, with a forecast period of 12 hours, the optimal R is 0.96985,ERMS is 0.033 m, and EMA is 0.02 m.Since the hyper-parameters of the GRA-NARX neural network are automatically calibrated and the optimal combination of time delay and the number of hidden layer neurons is selected, the GRA-NARX neural network based on the automatic calibration of hyper-parameters under different forecast periods has a good prediction effect on the water level prediction in front of the pumping station, which can meet the water level prediction demand of the pumping station in different forecast periods. Under the same forecast period, when the time interval of inputting data is 1 hour, the prediction results of the GRA-NARX model with hyper-parameter automatic calibration are better than those of the model with inputting data time interval of 2 hours, and the prediction accuracy is high. The findings of the study can be used as the groundwork for estimating the water level in front of pumping stations across different forecast periods.