Please wait a minute...
Journal of ZheJiang University (Engineering Science)  2026, Vol. 60 Issue (7): 1567-1576    DOI: 10.3785/j.issn.1008-973X.2026.07.018
    
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
Download: HTML     PDF(4953KB) HTML
Export: BibTeX | EndNote (RIS)      

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 wordsrunoff prediction      long short-term memory network      multi-feature fusion      variational mode decomposition      Newton-Raphson-based optimizer     
Received: 10 March 2025      Published: 23 May 2026
CLC:  TP 391.4  
Fund:  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).
Cite this article:

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.

URL:

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


基于多特征融合和牛顿-拉夫逊优化算法的LSTM日径流预测

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 
Fig.1 Topography and distribution of hydrological stations in Yellow River Basin
站名经度纬度
花园口113.6634.90
利津118.2637.49
Tab.1 Latitude and longitude coordinates of sites
Fig.2 Dataset partition of Huayuankou and Lijin stations
Fig.3 Forecasting framework of multi-feature fusion and LSTM
Fig.4 Flowchart of NRBO-based LSTM Optimization
Fig.5 Correlation analysis of hydrological data between Huayuankou and Lijin Stations
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
Tab.2 Performance evalution results of multiple models with one-day lead time on test set
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
Tab.3 Performance evalution results of multiple models with two- and three- day lead time on test set
Fig.6 Scatter plots of forecasted vs. observed values with one-day lead time at Huayuankou station
Fig.7 Scatter plots of forecasted vs. observed values with one-day lead time at Lijin station
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
Tab.4 Ablation experiment results of multiple models with one-day lead time on test set
[24]   GAUCH M, KRATZERT F, KLOTZ D, et al Rainfall–runoff prediction at multiple timescales with a single long short-term memory network[J]. Hydrology and Earth System Sciences, 2021, 25 (4): 2045- 2062
doi: 10.5194/hess-25-2045-2021
[25]   黄华, 赵秋舸, 何再兴, 等 基于LSTM与牛顿迭代的两轴系统轮廓误差控制[J]. 浙江大学学报: 工学版, 2023, 57 (1): 10- 20
HUANG Hua, ZHAO Qiuge, HE Zaixing, et al Contour error control of two-axis system based on LSTM and Newton iteration[J]. Journal of Zhejiang University: Engineering Science, 2023, 57 (1): 10- 20
[26]   NI L, WANG D, SINGH V P, et al Streamflow and rainfall forecasting by two long short-term memory-based models[J]. Journal of Hydrology, 2020, 583: 124296
doi: 10.1016/j.jhydrol.2019.124296
[27]   王万良, 胡明志, 张仁贡, 等 改进时间卷积网络和长短时记忆网络的泸水河流域月径流量预测模型[J]. 计算机集成制造系统, 2022, 28 (11): 3558- 3575
WANG Wanliang, HU Mingzhi, ZHANG Rengong, et al Monthly runoff prediction model for the lushui river basin based on Improved Temporal Convolution Network and Long Short-Term Memory Network[J]. Computer Integrated Manufacturing Systems, 2022, 28 (11): 3558- 3575
[28]   DAI R, WANG W L, ZHANG R G, et al Multimodal deep learning water level forecasting model for multiscale drought alert in Feiyun River basin[J]. Expert Systems with Applications, 2024, 244: 122951
doi: 10.1016/j.eswa.2023.122951
[29]   MUHAMMAD S, LI X S, BASHIR H, et al A hybrid model for runoff prediction using variational mode decomposition and artificial neural network[J]. Water Resources, 2021, 48 (5): 701- 712
doi: 10.1134/S0097807821050171
[30]   LI B J, SUN G L, LIU Y, et al Monthly runoff forecasting using variational deconposition coupled with gray wolf optimizer-based long short-term memory neural networks[J]. Water Resources Management, 2022, 36: 2095- 2115
doi: 10.1007/s11269-022-03133-0
[31]   ALYASSERI A, KHADER T, Al A, et al. EEG signal denoising using hybridizing method between wavelet transform with genetic algorithm [C]// Proceedings of the 11th National Technical Seminar on Unmanned System Technology. Singapore: Springer, 2021: 449–469.
[32]   YU L J, WANG Z, DAI R, et al Daily runoff prediction based on the adaptive fourier deconposition method and mutiscale temporal convolutional network[J]. Envionmental Science and Pollution Research, 2023, 30 (42): 95449- 95463
doi: 10.1007/s11356-023-28936-5
[33]   水利部黄河水利委员会. 黄河实时水情[EB/OL]. (2024-09-30)[2024-09-30]. http://61.163.88.227:8006/hwsq2.aspx?sr=0nkRxv6s9CTRMlwRgmfFF6jTpJPtAv87.
[1]   ISLAM M, KASHEM S, MOMTAZ Z, et al An application of the participatory approach to develop an integrated water resources management (IWRM) system for the drought-affected region of Bangladesh[J]. Heliyon, 2023, 9 (3): e14260
doi: 10.1016/j.heliyon.2023.e14260
[2]   ZHOU Y L, GUO S L, Xu C Y, et al Probabilistic interval estimation of design floods under non-stationary conditionsby an integrated approach[J]. Hydrology Research, 2022, 53 (2): 259- 278
doi: 10.2166/nh.2021.007
[34]   RAHMAN M A, LOU Y S, SULTANA N Analysis and prediction of rainfall trends over Bangladesh using Mann–Kendall, Spearman’s rho tests and ARIMA model[J]. Meteorology and Atmospheric Physics, 2017, 129 (4): 409- 424
doi: 10.1007/s00703-016-0479-4
[35]   DRAGOMIRETSKIY K, ZOSSO D Variational mode decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62 (3): 531- 544
[36]   SOWMYA R, PREMKUMAR M, JANGIR P Newton-Raphson-based optimizer: A new population-based metaheuristic algorithm for continuous optimization problems[J]. Engineering Applications of Artificial Intelligence, 2024, 128: 107532
doi: 10.1016/j.engappai.2023.107532
[37]   XENOCHRISTOU M, HUTTON C, HOFMAN J, et al Short-term forecasting of household water demand in the UK using an interpretable machine learning approach[J]. Journal of Water Resources Planning and Management, 2021, 147 (4): 04021004
doi: 10.1061/(ASCE)WR.1943-5452.0001325
[38]   王俊陆, 李素, 纪婉婷, 等 基于Gram矩阵的T-CNN时间序列分类方法[J]. 浙江大学学报: 工学版, 2023, 57 (2): 267- 276
WANG Junlu, LI Su, JI Wanting, et al T-CNN time series classification method based on Gram matrix[J]. Journal of Zhejiang University: Engineering Science, 2023, 57 (2): 267- 276
[3]   SHEN Y S, WANG S, ZHANG B, et al Development of a stochastic hydrological modeling system for improving ensemble streamflow prediction[J]. Journal of Hydrology, 2022, 608: 127683
doi: 10.1016/j.jhydrol.2022.127683
[4]   FIDAL J, KJELDSEN T R Accounting for soil moisture in rainfall-runoff modelling of urban areas[J]. Journal of Hydrology, 2020, 589: 125122
doi: 10.1016/j.jhydrol.2020.125122
[5]   HAN H, MORRISON R R Data-driven approaches for runoff prediction using distributed data[J]. Stochastic Environmental Research and Risk Assessment, 2022, 36: 2153- 2171
doi: 10.1007/s00477-021-01993-3
[6]   GAO S, HUANG Y F, ZHANG S, et al Short-term runoff prediction with GRU and LSTM networks without requiring time step optimization during sample generation[J]. Journal of Hydrology, 2020, 589: 125188
doi: 10.1016/j.jhydrol.2020.125188
[7]   YAO Z Y, WANG Z C, WANG D W, et al An ensemble CNN-LSTM and GRU adaptive weighting model based improved sparrow search algorithm for predicting runoff using historical meteorological and runoff data as input[J]. Journal of Hydrology, 2023, 625: 129977
doi: 10.1016/j.jhydrol.2023.129977
[8]   LIU C, SUN B, ZHANG C H, et al A hybrid prediction model for residential electricity consumption using holt-winters and extreme learning machine[J]. Applied Energy, 2020, 275: 115383
doi: 10.1016/j.apenergy.2020.115383
[9]   LU Y K, SHENG B Y, FU G C, et al Prophet-EEMD-LSTM based method for predicting energy consumption in the paint workshop[J]. Applied Soft Computing, 2023, 143: 110447
doi: 10.1016/j.asoc.2023.110447
[10]   LI W, WANG X S, PANG S J, et al A runoff prediction model based on nonhomogeneous markov chain[J]. Water Resources Management, 2022, 36: 1431- 1442
doi: 10.1007/s11269-022-03091-7
[11]   DAI R, WANG Z, WANG W L, et al VTNet: A multi-domain information fusion model for long-term multi-variate time series forecasting with application in irrigation water level[J]. Applied Soft Computing Journal, 2024, 167: 112251
doi: 10.1016/j.asoc.2024.112251
[12]   FAN J J, YUE W J, WU L F, et al Evaluation of SVM, ELM and four tree-based ensemble models for predicting daily reference evapotranspiration using limited meteorological data in different climates of China[J]. Agricultural and Forest Meteorology, 2018, 263: 225- 241
doi: 10.1016/j.agrformet.2018.08.019
[13]   FILIPOVA V, HAMMOND A, LEEDAL D, et al Prediction of flood quantiles at ungauged catchments for the contiguous USA using artificial neural networks[J]. Hydrology Research, 2022, 53 (1): 107- 123
doi: 10.2166/nh.2021.082
[14]   CONTRERAS P, ORELLANA-ALVEAR J, MUNOZ P, et al Influence of random forest hyperparameterization on short-term runoff forecasting in an andean mountain catchment[J]. Atmosphere, 2021, 12 (2): 1- 16
doi: 10.3390/atmos12020238
[15]   DA SILVA R G, MORENO S R, RIBERIO M H D M, et al Multi-step short-term wind speed forecasting based on multi-stage decomposition coupled with stacking-ensemble learning approach[J]. International Journal of Electrical Power and Energy Systems, 2022, 143: 108504
[16]   RIBERIO M H D M, DA Silva R G, RIBERIEL G T, et al Cooperative ensemble learning model improves electric short-term load forecasting[J]. Chaos, Solitons and Fractals, 2023, 166: 112982
[17]   林浩, 李雷孝, 王慧, 等 基于相关向量机和模糊综合评价的路况预测模型[J]. 浙江大学学报: 工学版, 2021, 55 (6): 1072- 1082
LIN Hao, LI Leixiao, WANG Hui, et al Model based onrelevance vector machine and fuzzy comprehensive evaluation forroad condition prediction[J]. Journal of Zhejiang University: Engineering Science, 2021, 55 (6): 1072- 1082
[18]   ZHOU J, HUANG S, WANG M Z, et al Performance evaluation of hybrid GA–SVM and GWO–SVM models to predict earthquake-induced liquefaction potential of soil: a multi-dataset investigation[J]. Engineering with Computers, 2021, (2): 1- 19
[19]   LIU Y, JI Y, LIU D, et al A new method for runoff prediction error correction based on LS-SVM and a 4D copula joint distribution[J]. Journal of Hydrology, 2021, 598: 126223
doi: 10.1016/j.jhydrol.2021.126223
[20]   SEMAN L O, STEFENON S F, MARIAIN V C, et al Ensemble learning methods using the Hodrick–Prescott filter for fault forecasting in insulators of the electrical power grids[J]. International Journal of Electrical Power & Energy Systems, 2023, 152: 109269
[21]   于军琪, 杨思远, 赵安军, 等 基于神经网络的建筑能耗混合预测模型[J]. 浙江大学学报: 工学版, 2022, 56 (6): 1220- 1231
YU Junqi, YANG Siyuan, ZHAO Anjun, et al Hybrid prediction model of building energy consumption based on neural network[J]. Journal of Zhejiang University: Engineering Science, 2022, 56 (6): 1220- 1231
[22]   KAO I F, ZHOU Y L, CHANG L C, et al Exploring a long short-term memory based encoder-decoder framework for muti-step-ahead flood forecasting[J]. Journal of Hydrology, 2020, 583: 124631
doi: 10.1016/j.jhydrol.2020.124631
[39]   温竹鹏, 陈捷, 刘连华, 等 基于小波变换和优化CNN的风电齿轮箱故障诊断[J]. 浙江大学学报: 工学版, 2022, 56 (6): 1212- 1219
WEN Zhupeng, CHEN Jie, LIU Lianhua, et al Fault diagnosis of wind power gearbox based on wavelet transform and improved CNN[J]. Journal of Zhejiang University: Engineering Science, 2022, 56 (6): 1212- 1219
[23]   YIN H L, GUO Z L, ZHANG X W, et al Runoff predictions in ungauged basins using sequence-to-sequence models[J]. Journal of Hydrology, 2021, 603: 126975
doi: 10.1016/j.jhydrol.2021.126975
[1] Xiaolong WANG,Jili TAO,Xiangxian ZHU,Jianwei LIANG,Daidai CHEN,Zhitao LIU. Convolutional long short-term memory network based lithium battery life prediction and dynamic modeling[J]. Journal of ZheJiang University (Engineering Science), 2026, 60(5): 1027-1036.
[2] Lihong WANG,Xinqian LIU,Jing LI,Zhiquan FENG. Network intrusion detection method based on federated learning and spatiotemporal feature fusion[J]. Journal of ZheJiang University (Engineering Science), 2025, 59(6): 1201-1210.
[3] Qincheng JIANG,Jianfeng TAO,Yangyang WANG,Yulei ZHANG,Chengliang LIU. EWT-LSTM based industrial robot joint anomaly detection[J]. Journal of ZheJiang University (Engineering Science), 2025, 59(5): 982-994.
[4] Guijun WAN,Jianan LI,Dongming FENG. Bridge influence line identification based on variational mode decomposition and piecewise polynomial truncated singular value decomposition[J]. Journal of ZheJiang University (Engineering Science), 2025, 59(3): 460-468.
[5] Haijun WANG,Tao WANG,Cijun YU. CFRP ultrasonic detection defect identification method based on recursive quantitative analysis[J]. Journal of ZheJiang University (Engineering Science), 2024, 58(8): 1604-1617.
[6] Man XU,Dongmei ZHANG,Xiang YU,Jiang LI,Yiping WU. Improved GRU landslide displacement prediction model based on multifractal[J]. Journal of ZheJiang University (Engineering Science), 2024, 58(7): 1407-1416.
[7] Qingjie QIAN,Junhe YU,Hongfei ZHAN,Rui WANG,Jian HU. Dimension prediction method of injection molded parts based on multi-feature fusion of DL-BiGRU[J]. Journal of ZheJiang University (Engineering Science), 2024, 58(3): 646-654.
[8] Xue-qi XING,Yu-tong DING,Tang-bin XIA,Er-shun PAN,Li-feng XI. Integrated modeling of commercial aircraft maintenance plan recommendation system based on knowledge graph[J]. Journal of ZheJiang University (Engineering Science), 2023, 57(3): 512-521.
[9] Lin TONG,Zheng GUAN,Li-wei WANG,Wen-tao YANG,Yang YAO. New energy ramp event prediction based on time series decomposition and error correction[J]. Journal of ZheJiang University (Engineering Science), 2022, 56(2): 338-346.
[10] Wei-qi CHEN,Jing-chang WANG,Ling CHEN,Yong-qin YANG,Yong WU. Prediction model of multi-factor aware mobile terminal replacement based on deep neural network[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(1): 109-115.
[11] Wen-shu LI,Tao-tao ZOU,Hong-yan WANG,Hai HUANG. Traffic accident quantity prediction model based on dual-scale long short-term memory network[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1613-1619.
[12] Jin-hai ZHOU,Yi-chuan WANG,Jing-ping TONG,Shi-yi ZHOU,Xiang-fei WU. Ultra wide band radar gait recognition based on slow-time segmentation[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(2): 283-290.
[13] Mao-xia RAN,Qin-yuan HUANG,Xin LIU,Hong SONG,Hao WU. Internal defect detection of arc magnets based on optimized variational mode decomposition[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(11): 2158-2168.
[14] Ji-jun TONG,Yan-jie BAI,Jian-wei PAN,Jia-feng YANG,Lu-rong JIANG. Ballistocardiogram and respiratory signal separation based on variational mode decomposition[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(10): 2058-2066.