针对多种水工建筑物相互作用和影响下的泵站水位预测难题，提出基于GRA-NARX（grey relation analysis-nonlinear autoregressive model with exogenous inputs）神经网络的泵站站前水位预测模型。该模型包括灰色关联分析(GRA)和NARX神经网络两部分，利用3种训练算法和不同时间延迟分别对密云水库调蓄工程屯佃泵站站前水位进行2 h预测，并与NARX模型和GRA-BP(grey relation analysis-back propagation)模型的预测结果进行比较。研究结果表明，GRA-NARX-BR(grey relation analysis-nonlinear autoregressive model with exogenous inputs-bayesian regularization)模型用于水位预测能够比较全面地考虑影响因子，预测精度高，相关系数最高达0.986 62，均方根误差最小为0.008 6 m，预测效果比NARX模型和GRA-BP模型好，且时间延迟越长，均方根误差越小。模型也可在其他调水工程中推广使用。

The uneven distribution of water resources is a long-term and trend problem faced by many countries.The water transfer project is the main way to solve this problem.When long-distance water conveyance dispatching is carried out,hydraulic structures such as pumping stations are often set in the channels to remove the influence of topographic conditions on water conveyance restrictions.During operation,it is required to keep the water level balance among pumping stations as much as possible to avoid problems caused by sharp rises or falls in water levels.If the water level changes sharply with time,it may not only cause water abandonment among pumping stations,but also cause water supply damage or hydraulic oscillation of the whole system.Therefore,processing the water level information and establishing an appropriate water level prediction model of the pumping station,especially the water level prediction model in front of the pumping station,are of great significance to the management of the pumping station,water transfer,building safety and so on.However,up to now,it is still difficult to accurately predict the water level of the pumping station due to the interaction of various hydraulic structures. A lot of studies have reported the research progress of water level prediction based on physical mechanism and machine learning.The water level simulation based on physical mechanism mainly uses the hydrodynamic model with Saint Venant equation as the control equation to simulate one-dimensional channel flow.It requires complete information in the study area,but usually some data is missing.Therefore,this method has certain limitations.Machine learning methods include vector machine RVM model,grey system GM (1,1) model,multiple linear regression model,neural network model,etc.The advantages of vector machine RVM model,grey system GM(1,1) model and multiple linear regression model are suitable for complex prediction tasks,but the disadvantages are that the prediction accuracy of these methods need to be improved.In recent years,with the development of artificial intelligence,neural network has got plentiful results in water level prediction.NARX neural network is a nonlinear dynamic network structure.Based on linear regression model,it has the functions of input delay and feedback memories,and can better approximate and simulate complex multi input and multi output systems. In order to further improve the accuracy of water level prediction,a water level prediction model based on GRA-NARX neural network was proposed,which included grey relational analysis (GRA) and NARX neural network.At present,when using NARX neural network to predict time series,Levenberg Marquardt (LM) algorithms is the most commonly used training algorithm,while the other two algorithms are rarely evaluated.Taking Tundian pumping station of Miyun reservoir storage project as a research case,firstly,the water level information was cleaned by boxplot method,and then interpolated by mean filling method;secondly,the main factors were screened out by grey correlation analysis;thirdly,the water level prediction model of NARX neural network based on grey correlation analysis was constructed;finally,an analysis was performed in order to assess the impact on the water level prediction of different training algorithms and time delays,and compared with GRA-BP neural network. The results show that the Bayesian Regularization (BR) algorithm leads to prediction model with better forecasting accuracy of the highest correlation coefficient and the smallest mean square error among the three different training algorithms.In GRA-NARX-BR model,with the increase of time delay,the correlation coefficient is basically the same,the mean square error is smaller and smaller,and the training time is longer and longer.Compared with the prediction results of GRA-BP model,it is found that among the three training algorithms,GRA-NARX model can comprehensively consider the influencing factors in water level prediction,has better network prediction accuracy,and GRA-NARX-BR model has the highest prediction accuracy,which reflects the superiority of GRA-NARX model structure and strong network generalization ability,and can be used as an effective water level prediction method.