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浙江大学学报(工学版)  2026, Vol. 60 Issue (7): 1567-1576    DOI: 10.3785/j.issn.1008-973X.2026.07.018
土木与水利工程     
基于多特征融合和牛顿-拉夫逊优化算法的LSTM日径流预测
王铮1,2(),张梦君1,姜楠1,王万良3,屠杭垚2
1. 华东交通大学 信息工程与软件学院,江西 南昌 330013
2. 浙大城市学院 计算机与计算科学学院,浙江 杭州 310015
3. 浙江工业大学 计算机科学与技术学院,浙江 杭州 310023
Daily runoff prediction using LSTM based on multi-feature fusion and Newton-Raphson-based optimizer
Zheng WANG1,2(),Mengjun ZHANG1,Nan JIANG1,Wanliang WANG3,Hangyao TU2
1. College of Information and Software Engineering, East China Jiaotong University, Nanchang 330013, China
2. College of Computer Science and Technology, Hangzhou City University, Hangzhou 310015, China
3. College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China
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摘要:

为了提高日径流预测的精度,解决现有预测模型在多特征数据提取方面的不足,提出基于多特征融合(MFF)和牛顿-拉夫逊优化算法(NRBO)的长短期记忆网络(LSTM)模型. 该模型使用变分模态分解(VMD)技术将原始径流序列分解成若干个固有模态函数(IMF),降低径流序列的非平稳性和复杂性. 引入相关性分析,筛选出与径流高度相关的水文特征值,并将其与IMF分量进行融合,构建特征矩阵作为模型输入. 新模型通过NRBO对LSTM模型的关键超参数进行优化,以获得模型最佳配置. 为了验证模型性能,选取黄河流域的花园口和利津2个站点的数据集进行实验. 结果表明,新模型在预见期为1、2、3 d的情况下,2个测站的纳什效率系数(NSE)均大于0.97. 与随机森林、卷积神经网络、时间卷积网络等模型的预测结果对比表明,该模型在充分融合多特征数据的基础上,于2个测站1 d内,RMSE平均降低了61.42%,NSE 平均提升了4.20%,可以有效提高日径流预测的精度.

关键词: 径流预测长短期记忆网络多特征融合变分模态分解牛顿-拉夫逊优化算法    
Abstract:

Based on multi-feature fusion (MFF) and Newton-Raphson-based optimizer (NRBO), a long short-term memory (LSTM) model was proposed to improve the accuracy of daily runoff prediction and address the limitations of existing models in extracting multi-feature data. Variational mode decomposition (VMD) was applied to decompose the original runoff series into several intrinsic mode functions (IMFs) in the spectral domain, reducing the non-stationarity and complexity of the runoff series. Hydro-meteological features highly correlated with runoff were selected by correlation analysis. These selected features were integrated with IMF components, which could be used to construct the feature matrix serving as the model input. The NRBO algorithm was utilized to optimize the key hyperparameters of the LSTM model to achieve the optimal configuration. Datasets from Huayuankou and Lijin stations in the Yellow River Basin were selected for experiments to validate the model performance. Results showed that for the novel model, Nash-Sutcliffe efficiency (NSE) values at two stations were all higher than 0.97 under forecast horizons of 1, 2, and 3 days. Compared with Random Forest, CNN, TCN and other models, the proposed model —— by fully fusing multi-feature data —— achieved an average 61.42% reduction in RMSE and 4.20% increase in NSE over a 1-day forecast horizon at two stations, effectively improving the daily runoff prediction accuracy.

Key words: runoff prediction    long short-term memory network    multi-feature fusion    variational mode decomposition    Newton-Raphson-based optimizer
收稿日期: 2025-03-10 出版日期: 2026-05-23
CLC:  TP 391.4  
基金资助: 浙江省“尖兵领雁”研发攻关计划资助项目(2023C03189);国家自然科学基金资助项目(61873240).
作者简介: 王铮(1986—),男,副教授,从事智能系统优化与调度研究. orcid.org/0000-0003-3896-000X. E-mail:wangz@hzcu.edu.cn
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引用本文:

王铮,张梦君,姜楠,王万良,屠杭垚. 基于多特征融合和牛顿-拉夫逊优化算法的LSTM日径流预测[J]. 浙江大学学报(工学版), 2026, 60(7): 1567-1576.

Zheng WANG,Mengjun ZHANG,Nan JIANG,Wanliang WANG,Hangyao TU. Daily runoff prediction using LSTM based on multi-feature fusion and Newton-Raphson-based optimizer. Journal of ZheJiang University (Engineering Science), 2026, 60(7): 1567-1576.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2026.07.018        https://www.zjujournals.com/eng/CN/Y2026/V60/I7/1567

图 1  黄河流域地形地貌及水文站分布
站名经度纬度
花园口113.6634.90
利津118.2637.49
表 1  站点经纬度坐标
图 2  花园口和利津站点的数据集划分
图 3  多特征融合和LSTM的预测框架
图 4  NRBO优化LSTM流程图
图 5  花园口和利津站水文数据的相关性分析
模型花园口利津
RMSEMAEMAPENSERMSEMAEMAPENSE
RF301.368 6152.467 20.112 50.907 9261.708 0135.698 80.122 90.933 4
CNN281.343 0141.966 00.108 30.919 7201.703 6106.062 80.106 10.960 4
TCN267.640 8131.018 90.108 60.927 3204.422 5105.637 60.120 70.959 4
TCN-LSTM269.727 5131.594 50.103 30.926 2212.500 0114.145 70.111 20.956 1
LSTM267.388 6131.654 00.110 20.927 5200.944 3104.585 30.105 70.960 7
MFF-LSTM134.740 577.958 80.066 00.979 5116.979 653.791 30.068 80.985 5
MFF-SSA-LSTM80.723 337.219 40.029 40.992 678.314 833.306 10.041 40.993 5
MFF-BKA-LSTM84.636 938.968 80.033 30.991 986.887 834.992 70.029 40.992 0
MFF-NRBO-LSTM61.289 631.822 40.028 30.995 855.684 427.875 00.034 20.996 7
表 2  各模型在测试集上的1 d预见期性能评价结果
模型2 d3 d
花园口利津花园口利津
RMSENSERMSENSERMSENSERMSENSE
RF437.774 40.805 4386.129 40.854 9535.451 50.709 2481.175 60.774 8
CNN398.110 30.839 1340.881 00.886 9487.641 70.758 8433.588 50.817 1
TCN411.112 90.828 4378.179 30.860 8505.366 60.741 0437.845 30.813 5
TCN-LSTM403.074 90.835 1344.661 50.884 4492.761 40.753 7437.448 90.813 9
LSTM409.039 90.830 1335.820 80.830 1500.632 20.745 8433.363 70.817 3
MFF-LSTM136.870 80.972 8121.582 10.972 8215.398 60.947 7217.145 90.950 2
MFF-SSA-LSTM154.234 20.978 9121.582 10.978 9227.501 30.941 6170.716 30.969 2
MFF-BKA-LSTM155.409 70.973 2126.920 30.973 2221.533 30.944 7196.019 80.959 4
MFF-NRBO-LSTM116.784 90.984 6109.921 00.971 4196.854 00.956 3164.402 40.971 4
表 3  各模型在测试集上的2 和 3 d预见期性能评价结果
图 6  花园口预见期为1 d的预测值和实测值的散点分布图
图 7  利津预见期为1 d的预测值和实测值的散点分布图
站点算法RMSEMAEMAPENSE
花园口LSTM267.388 6131.654 00.110 20.927 5
MFF-LSTM134.740 577.958 80.066 00.979 5
NRBO-LSTM216.410 0114.240 00.100 00.954 0
MFF-NRBO-LSTM61.289 631.822 40.028 30.995 8
利津LSTM200.944 3104.585 30.105 70.960 7
MFF-LSTM116.979 653.791 30.068 80.985 5
NRBO-LSTM199.833 0105.086 60.108 70.961 2
MFF-NRBO-LSTM55.684 427.875 00.034 20.996 7
表 4  各模型在测试集上的1 d预见期的消融实验结果
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