基于变分模态分解的分频径流预测模型

准确的径流预测对于流域防洪减灾、农业灌溉、水库调度等具有重要意义。针对径流序列具有较强的非线性和非平稳性特征，提出一种月径流预测混合模型VMD-(CNN-LSTM, ELMAN)。首先运用VMD将径流序列分解为多个模态分量，并计算各个模态分量的样本熵值(SE),将其划分为高频和中低频分量；然后运用CNN-LSTM模型预测高频分量，运用ELMAN模型预测中低频分量；最后将预测结果相加得到最终预测结果。将模型应用于黄河流域中下游段白马寺和黑石关水文站的月径流预测，并与CNN-LSTM、ELMAN、VMD-CNN-LSTM模型的预测结果进行对比与评价。研究结果表明：本文模型预测结果的NSE值均大于0.99,优于其他模型，表明VMD-(CNN-LSTM, ELMAN)模型具有较高的预测精度，可应用于实际研究区的径流预测。

Runoff prediction model of frequency division based on variational mode decomposition

Accurate runoff prediction is of great significance for agricultural irrigation, reservoir scheduling, flood control and disaster mitigation in the basin. Aiming at the strong nonlinearity and non-stationarity of the runoff series, a hybrid model for monthly runoff prediction, VMD-(CNN-LSTM, ELMAN), is proposed. Firstly, VMD is used to decompose the runoff sequence into multiple modal components, and the sample entropy (SE) of each modal component is calculated, according to which the components are divided into high-frequency and medium-low frequency components. Then the CNN-LSTM model is used for the prediction of high-frequency components, the ELMAN model for the medium-low frequency components. Finally the predictions results are summed up. The model is then applied to the monthly runoff prediction of Baimasi Station and Heishiguan Station in the middle and lower reaches of the Yellow River Basin, and the prediction results are evaluated compared with those of CNN-LSTM, ELMAN, VMD-CNN-LSTM models. Research results show that the NSE values of the prediction results of this model are all greater than 0.99, which is superior to other models, indicating that the VMD-(CNN-LSTM, ELMAN) model has high prediction accuracy and can be applied to actual monthly runoff prediction of the basin.