径流预报的极点对称模态分解-Elman网络模型

针对径流序列非线性、非平稳的特点，将极点对称模态分解（ESMD）方法与Elman神经网络模型相结合，建立了ESMD-Elman神经网络组合模型，并应用于长江上游干支流8站的年、月径流预报。首先利用ESMD方法将径流序列分解为各模态分量和趋势余项；然后利用Elman神经网络模型分别预测各平稳序列；最后加和重构得到最终预测结果。结果表明：组合模型预报精度大于单一模型，与ESMD-BP神经网络组合模型比，ESMD-Elman神经网络组合模型的8站年径流预报结果的平均相对误差（MAPE）平均降低3.6%，均方根误差（RMSE）平均降低7.8%，确定性系数平均提高5.0%；8站月径流预报结果的MAPE平均降低3.0%，RMSE平均降低2.8%，具有“分解?预测?重构”特点的组合模型提高了预报精度。

Runoff forecasts using combined model of extreme-point symmetric mode decomposition and Elman neural network

Aiming at the nonlinear and non-stationary characteristics of runoff sequences, we develop a combined model of extreme-point symmetric mode decomposition (ESMD) and Elman neural network, and apply it to annual and monthly runoff forecasts at eight stations in the upper reaches of the Yangtze River. First, ESMD is used to decompose a runoff sequence into modal components and trend remainders; then, the Elman neural network model is used to predict each of the stationary sequences; lastly, final prediction results are obtained by adding and reconstruction. The results show this combined model has forecast accuracy higher than that of a single model. Compared with the ESMD-BP neural network combination model, for annual runoff forecasts, it has an average reduction of 3.6% in mean absolute percentage error (MAPE) and 7.8% in root mean square error (RMSE), and an average increase of 5.0% in determination coefficient for the eight stations; while for monthly runoff forecasts, the MAPE is decreased by an average of 3.0% and the RMSE decreased by an average of 2.8%. Our combined model, characterized by decomposition-prediction-reconstruction, improves prediction accuracy.