Abstract
Accurate and reliable monthly runoff predictions are crucial for dispatching, allocation, and planning management of water resources. This research provides a hybrid forecasting model to increase the precision of monthly runoff predictions. Firstly, a series of intrinsic mode functions (IMF) and residual values are obtained from raw monthly runoff time series by applying complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). Secondly, variational mode decomposition (VMD) is used to perform a secondary decomposition of high-frequency IMFs. Thirdly, to determine the input–output relationships for all IMFs, Harris Hawks Optimization (HHO) algorithm is used to optimize least squares support vector machine (LSSVM) model. Finally, each IMF output is superimposed and reconstructed to obtain the final result. Five evaluation indicators are utilized to evaluate the effectiveness of the proposed hybrid model on monthly runoff data from Manwan and Hongjiadu Hydropowers in China. MAE, RMSE, MAPE, NSEC, and R of CEEMDAN-VMD-HHO-LSSVM model are 103.25, 137.29, 10.84, 0.98, and 0.99 in Manwan Hydropower and 18.28, 23.58, 28.49, 0.97 and 0.98 in Hongjiadu Hydropower, respectively. The five performance evaluation indicators of the proposed model exhibit excellent results when compared to those of other benchmarking models, demonstrating that the secondary decomposition can successfully extract the complex runoff sequence information so as to significantly increase the hybrid model's prediction accuracy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
Adnan RM, Yuan X, Kisi O, Adnan M, Mehmood A (2018) Stream Flow Forecasting of Poorly Gauged Mountainous Watershed by Least Square Support Vector Machine, Fuzzy Genetic Algorithm and M5 Model Tree Using Climatic Data from Nearby Station. Water Resour Manage 32:4469–4486. https://doi.org/10.1007/s11269-018-2033-2
Anctil F, Perrin C, Andréassian V (2004) Impact of the length of observed records on the performance of ANN and of conceptual parsimonious rainfall-runoff forecasting models. Environ Model Softw 19:357–368. https://doi.org/10.1016/S1364-8152(03)00135-X
Barzegar R, Ghasri M, Qi Z, Quilty J, Adamowski J (2019) Using bootstrap ELM and LSSVM models to estimate river ice thickness in the Mackenzie River Basin in the Northwest Territories. Canada. Journal of Hydrology 577:123903. https://doi.org/10.1016/j.jhydrol.2019.06.075
Ben Seghier MEA, Carvalho H, de Faria CC, Correia JAFO, Fakury RH (2023) Numerical analysis and prediction of lateral-torsional buckling resistance of cellular steel beams using FEM and least square support vector machine optimized by metaheuristic algorithms. Alex Eng J 67:489–502. https://doi.org/10.1016/j.aej.2022.12.062
Bi F, Li X, Liu C, Tian C, Ma T, Yang X (2019) Knock detection based on the optimized variational mode decomposition. Measurement 140:1–13. https://doi.org/10.1016/j.measurement.2019.03.042
Chau KW, Wu CL, Li YS (2005) Comparison of Several Flood Forecasting Models in Yangtze River. J Hydrol Eng 10:485–491. https://doi.org/10.1061/(ASCE)1084-0699(2005)10:6(485)
Chen S, Ren M, Sun W (2021) Combining two-stage decomposition based machine learning methods for annual runoff forecasting. Journal of Hydrology 603:126945. https://doi.org/10.1016/j.jhydrol.2021.126945
Dragomiretskiy K, Zosso D (2014) Variational Mode Decomposition. IEEE Trans Signal Process 62:531–544. https://doi.org/10.1109/tsp.2013.2288675
Feng Z-k, Niu W-j, Tang Z-y, Jiang Z-q, Xu Y, Liu Y, Zhang H-r (2020) Monthly runoff time series prediction by variational mode decomposition and support vector machine based on quantum-behaved particle swarm optimization. Journal of Hydrology 583:124627. https://doi.org/10.1016/j.jhydrol.2020.124627
Yang X-S Firefly Algorithms for Multimodal Optimization. In: Watanabe O, Zeugmann T (eds) Stochastic Algorithms: Foundations and Applications, Berlin, Heidelberg, 2009// 2009. Springer Berlin Heidelberg, pp 169–178.
Fu W, Wang K, Tan J, Zhang K (2020) A composite framework coupling multiple feature selection, compound prediction models and novel hybrid swarm optimizer-based synchronization optimization strategy for multi-step ahead short-term wind speed forecasting. Energy Convers. Manag. 205:112461. https://doi.org/10.1016/j.enconman.2019.112461
Guang-Bin H, Qin-Yu Z, Chee-Kheong S (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. In: 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541), 25–29 July 2004. 982, 985–990 https://doi.org/10.1109/IJCNN.2004.1380068
Guo X, Sun X, Ma J (2011) Prediction of daily crop reference evapotranspiration (ET 0) values through a least-squares support vector machine model. Hydrol Res 42:268. https://doi.org/10.2166/nh.2011.072
Guo Z, Zhao W, Lu H, Wang J (2012) Multi-step forecasting for wind speed using a modified EMD-based artificial neural network model. Renewable Energy 37:241–249. https://doi.org/10.1016/j.renene.2011.06.023
Guo Y, Xu Y-P, Sun M, Xie J (2021) Multi-step-ahead forecast of reservoir water availability with improved quantum-based GWO coupled with the AI-based LSSVM model. J. Hydrol. 597:125769. https://doi.org/10.1016/j.jhydrol.2020.125769
He C, Chen F, Long A, Qian Y, Tang H (2023) Improving the precision of monthly runoff prediction using the combined non-stationary methods in an oasis irrigation area. Agric. Water Manag. 279:108161. https://doi.org/10.1016/j.agwat.2023.108161
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: Algorithm and applications. Futur Gener Comput Syst 97:849–872. https://doi.org/10.1016/j.future.2019.02.028
Huang NE et al (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond Ser A 454:903–998. https://doi.org/10.1098/rspa.1998.0193
Huang S, Chang J, Huang Q, Chen Y (2014) Monthly streamflow prediction using modified EMD-based support vector machine. J Hydrol 511:764–775. https://doi.org/10.1016/j.jhydrol.2014.01.062
Humphrey GB, Gibbs MS, Dandy GC, Maier HR (2016) A hybrid approach to monthly streamflow forecasting: Integrating hydrological model outputs into a Bayesian artificial neural network. J Hydrol 540:623–640. https://doi.org/10.1016/j.jhydrol.2016.06.026
Jia W et al. (2023) Landslide Displacement Prediction of Shuping Landslide Combining PSO and LSSVM Model. Water 15.
Jiang Z, Che J, He M, Yuan F (2023) A CGRU multi-step wind speed forecasting model based on multi-label specific XGBoost feature selection and secondary decomposition. Renewable Energy 203:802–827. https://doi.org/10.1016/j.renene.2022.12.124
Jin KH, McCann MT, Froustey E, Unser M (2017) Deep Convolutional Neural Network for Inverse Problems in Imaging. IEEE Trans Image Process 26:4509–4522. https://doi.org/10.1109/TIP.2017.2713099
Kadkhodazadeh M, Farzin S (2021) A Novel LSSVM Model Integrated with GBO Algorithm to Assessment of Water Quality Parameters. Water Resour Manage 35:3939–3968. https://doi.org/10.1007/s11269-021-02913-4
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm. J Global Optim 39:459–471. https://doi.org/10.1007/s10898-007-9149-x
Karran D, Morin E, Adamowski J (2014) Multi-step streamflow forecasting using data-driven non-linear methods in contrasting climate regimes. J Hydroinf 16:671–689. https://doi.org/10.2166/hydro.2013.042
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN'95 - International Conference on Neural Networks, 27, 1944, 1942–1948 https://doi.org/10.1109/ICNN.1995.488968
Khashei M, Bijari M (2011) A novel hybridization of artificial neural networks and ARIMA models for time series forecasting. Appl Soft Comput 11:2664–2675. https://doi.org/10.1016/j.asoc.2010.10.015
Kisi O (2015) Streamflow Forecasting and Estimation Using Least Square Support Vector Regression and Adaptive Neuro-Fuzzy Embedded Fuzzy c-means Clustering. Water Resour Manage 29:5109–5127. https://doi.org/10.1007/s11269-015-1107-7
Kratzert F, Klotz D, Brenner C, Karsten S, Herrnegger M (2018) Rainfall-Runoff modelling using Long-Short-Term-Memory (LSTM) networks. https://doi.org/10.31223/osf.io/qv5jz
Lin W, Zhang B, Li H, Lu R (2022) Multi-step prediction of photovoltaic power based on two-stage decomposition and BILSTM. Neurocomputing 504:56–67. https://doi.org/10.1016/j.neucom.2022.06.117
Liu Z, Zhou P, Chen G, Guo L (2014) Evaluating a coupled discrete wavelet transform and support vector regression for daily and monthly streamflow forecasting. J Hydrol 519:2822–2831. https://doi.org/10.1016/j.jhydrol.2014.06.050
Liu G, Tang Z, Qin H, Liu S, Shen Q, Qu Y, Zhou J (2022) Short-term runoff prediction using deep learning multi-dimensional ensemble method. J. Hydrol. 609:127762. https://doi.org/10.1016/j.jhydrol.2022.127762
Liu G et al (2023) Assessing spatial connectivity effects on daily streamflow forecasting using Bayesian-based graph neural network. Sci. Total Environ. 855:158968. https://doi.org/10.1016/j.scitotenv.2022.158968
Malakoutian MMA, Samaei SY, Khaksar M, Malakoutian Y (2022) A prediction of future flows of ephemeral rivers by using stochastic modeling (AR autoregressive modeling). Sustainable Operations and Computers 3:330–335. https://doi.org/10.1016/j.susoc.2022.05.003
Man Y, Yang Q, Shao J, Wang G, Bai L, Xue Y (2022) Enhanced LSTM Model for Daily Runoff Prediction in the Upper Huai River Basin, China. Engineering. https://doi.org/10.1016/j.eng.2021.12.022
Mohammadi K, Eslami HR, Kahawita R (2006) Parameter estimation of an ARMA model for river flow forecasting using goal programming. J Hydrol 331:293–299. https://doi.org/10.1016/j.jhydrol.2006.05.017
Napolitano G, Serinaldi F, See L (2011) Impact of EMD decomposition and random initialisation of weights in ANN hindcasting of daily stream flow series: An empirical examination. J Hydrol 406:199–214. https://doi.org/10.1016/j.jhydrol.2011.06.015
Niu D, Ji Z, Li W, Xu X, Liu D (2021) Research and application of a hybrid model for mid-term power demand forecasting based on secondary decomposition and interval optimization. Energy 234:121145. https://doi.org/10.1016/j.energy.2021.121145
Noori N, Kalin L (2016) Coupling SWAT and ANN models for enhanced daily streamflow prediction. J Hydrol 533:141–151. https://doi.org/10.1016/j.jhydrol.2015.11.050
Qiao W, Fu Z, Du M, Nan W, Liu E (2023) Seasonal peak load prediction of underground gas storage using a novel two-stage model combining improved complete ensemble empirical mode decomposition and long short-term memory with a sparrow search algorithm. Energy 274:127376. https://doi.org/10.1016/j.energy.2023.127376
Qin Y, Li B, Sun X, Chen Y, Shi X (2019b) Nonlinear response of runoff to atmospheric freezing level height variation based on hybrid prediction models. Hydrol Sci J 64:1556–1572. https://doi.org/10.1080/02626667.2019.1662023
Qin J, Liang J, Chen T, Lei X, Kang A (2019a) Simulating and Predicting of Hydrological Time Series Based on TensorFlow Deep Learning. Pol. J. Environ. Stud. 28:795–802. https://doi.org/10.15244/pjoes/81557
Rezaie-Balf M, Naganna SR, Kisi O, El-Shafie A (2019) Enhancing streamflow forecasting using the augmenting ensemble procedure coupled machine learning models: case study of Aswan High Dam. Hydrol Sci J 64:1629–1646. https://doi.org/10.1080/02626667.2019.1661417
Samantaray S, Sawan Das S, Sahoo A, Prakash Satapathy D (2022) Monthly runoff prediction at Baitarani river basin by support vector machine based on Salp swarm algorithm. Ain Shams Eng. 13:101732. https://doi.org/10.1016/j.asej.2022.101732
Song CM (2022) Data construction methodology for convolution neural network based daily runoff prediction and assessment of its applicability. J. Hydrol. 605:127324. https://doi.org/10.1016/j.jhydrol.2021.127324
Sun AY, Wang D, Xu X (2014) Monthly streamflow forecasting using Gaussian Process Regression. J Hydrol 511:72–81. https://doi.org/10.1016/j.jhydrol.2014.01.023
Sun W, Tan B, Wang Q (2021) Multi-step wind speed forecasting based on secondary decomposition algorithm and optimized back propagation neural network. Appl. Soft Comput 113:107894. https://doi.org/10.1016/j.asoc.2021.107894
Suykens J, Vandewalle J (1999) Least Squares Support Vector Machine Classifiers. Neural Process Lett 9:293–300. https://doi.org/10.1023/A:1018628609742
Tan Q-F, Lei X-H, Wang X, Wang H, Wen X, Ji Y, Kang A-Q (2018) An adaptive middle and long-term runoff forecast model using EEMD-ANN hybrid approach. J Hydrol 567:767–780. https://doi.org/10.1016/j.jhydrol.2018.01.015
Tareke KA, Awoke AG (2023) Hydrological drought forecasting and monitoring system development using artificial neural network (ANN) in Ethiopia. Heliyon 9:e13287. https://doi.org/10.1016/j.heliyon.2023.e13287
Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res. Atmos. 106:7183–7192. https://doi.org/10.1029/2000JD900719
Tikhamarine Y, Souag-Gamane D, Ahmed AN, Sammen SS, Kisi O, Huang YF, El-Shafie A (2020) Rainfall-runoff modelling using improved machine learning methods: Harris hawks optimizer vs. particle swarm optimization. J. Hydrol. 589:125133. https://doi.org/10.1016/j.jhydrol.2020.125133
Torres ME, Colominas MA, Schlotthauer G, (2011) Flandrin P A complete ensemble empirical mode decomposition with adaptive noise. In: 2011 IEEE Int Conf Acoust Speech Signal Process (ICASSP), 22–27 4144–4147.https://doi.org/10.1109/ICASSP.2011.5947265
Vu GXM, Zhong ZW (2018) Forecasting Air Passengers of Changi Airport Based on Seasonal Decomposition and an LSSVM Model. Review of Information Engineering and Applications 5:12–30.https://doi.org/10.18488/journal.79.2018.51.12.30
Wang W-C, Chau K-W, Cheng C-T, Qiu L (2009) A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series. J Hydrol 374:294–306. https://doi.org/10.1016/j.jhydrol.2009.06.019
Wang W-c, Chau K-w, Qiu L, Chen Y-b (2015) Improving forecasting accuracy of medium and long-term runoff using artificial neural network based on EEMD decomposition. Environ Res 139:46–54. https://doi.org/10.1016/j.envres.2015.02.002
Wang D, Luo H, Grunder O, Lin Y, Guo H (2017) Multi-step ahead electricity price forecasting using a hybrid model based on two-layer decomposition technique and BP neural network optimized by firefly algorithm. Appl Energy 190:390–407. https://doi.org/10.1016/j.apenergy.2016.12.134
Wang L, Li X, Ma C, Bai Y (2019) Improving the prediction accuracy of monthly streamflow using a data-driven model based on a double-processing strategy. J Hydrol 573:733–745. https://doi.org/10.1016/j.jhydrol.2019.03.101
Wang W-c, Du Y-j, Chau K-w, Xu D-m, Liu C-j, Ma Q (2021) An Ensemble Hybrid Forecasting Model for Annual Runoff Based on Sample Entropy, Secondary Decomposition, and Long Short-Term Memory Neural Network. Water Resour Manage 35:4695–4726. https://doi.org/10.1007/s11269-021-02920-5
Wang Y et al (2022) A new scheme for probabilistic forecasting with an ensemble model based on CEEMDAN and AM-MCMC and its application in precipitation forecasting. Expert Syst. Appl. 187:115872. https://doi.org/10.1016/j.eswa.2021.115872
Wang W, Nie X, Qiu L (2010) Support vector machine with particle swarm optimization for reservoir annual inflow forecasting. In: Proceedings - International Conference on Artificial Intelligence and Computational Intelligence, AICI, 2010. pp 184–188.https://doi.org/10.1109/AICI.2010.45
Wen X, Feng Q, Deo RC, Wu M, Yin Z, Yang L, Singh VP (2019) Two-phase extreme learning machines integrated with the complete ensemble empirical mode decomposition with adaptive noise algorithm for multi-scale runoff prediction problems. J Hydrol 570:167–184. https://doi.org/10.1016/j.jhydrol.2018.12.060
Wu Z, Huang NE (2009) Ensemble empirical mode decomposition: A noise-assisted data analysis method. Adv Adapt Data Anal 01:1–41. https://doi.org/10.1142/S1793536909000047
Xu Z, Mo L, Zhou J, Fang W, Qin H (2022) Stepwise decomposition-integration-prediction framework for runoff forecasting considering boundary correction. Sci. Total Environ. 851:158342. https://doi.org/10.1016/j.scitotenv.2022.158342
Yang XS, Suash D (2009) Cuckoo search via Lévy flights. 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC), pp. 210–214. https://doi.org/10.1109/NABIC.2009.5393690
Yin H, Zhang X, Wang F, Zhang Y, Xia R, Jin J (2021) Rainfall-runoff modeling using LSTM-based multi-state-vector sequence-to-sequence model. J. Hydrol 598:126378. https://doi.org/10.1016/j.jhydrol.2021.126378
Yoon H, Jun S-C, Hyun Y, Bae G-O, Lee K-K (2011) A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. J Hydrol 396:128–138. https://doi.org/10.1016/j.jhydrol.2010.11.002
Young C-C, Liu W-C (2015) Prediction and modelling of rainfall–runoff during typhoon events using a physically-based and artificial neural network hybrid model. Hydrol Sci J 60:2102–2116. https://doi.org/10.1080/02626667.2014.959446
Zhang W, Qu Z, Zhang K, Mao W, Ma Y, Fan X (2017) A combined model based on CEEMDAN and modified flower pollination algorithm for wind speed forecasting. Energy Convers Manage 136:439–451. https://doi.org/10.1016/j.enconman.2017.01.022
Zhang X, Wang H, Peng A, Wang W, Li B, Huang X (2020) Quantifying the Uncertainties in Data-Driven Models for Reservoir Inflow Prediction. Water Resour Manage 34:1479–1493. https://doi.org/10.1007/s11269-020-02514-7
Zhao X, Chen X, Xu Y, Xi D, Zhang Y, Zheng X (2017) An EMD-Based Chaotic Least Squares Support Vector Machine Hybrid Model for Annual Runoff Forecasting. Water 9.https://doi.org/10.3390/w9030153
Funding
This work was supported by a Special project for collaborative innovation of science and technology in 2021 (No: 202121206) and Henan Province University Scientific and Technological Innovation Team (No: 18IRTSTHN009).
Author information
Authors and Affiliations
Contributions
All authors contributed to the study Conceptualization and Methodology. Writing—original draft preparation, data collection and analysis were performed by Dong-mei Xu, Xiao-xue Hu, Wen-chuan Wang, Kwok-wing Chau, Bo Wang and Hong-fei Zang. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors have no relevant financial or non-financial interests to disclose.
Additional information
Communicated by H. Babaie.
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Xu, Dm., Hu, Xx., Wang, Wc. et al. An enhanced monthly runoff forecasting using least squares support vector machine based on Harris hawks optimization and secondary decomposition. Earth Sci Inform 16, 2089–2109 (2023). https://doi.org/10.1007/s12145-023-01018-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-023-01018-3