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A new water level prediction model based on ESMD−VMD−WSD−ESN

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Abstract

Water level prediction is critical for optimizing available water resources and sustainable use. We propose a new deep learning hybrid model for water level prediction. The model uses Extreme−point symmetric mode decomposition (ESMD), Variational Modal Decomposition(VMD), Wavelet Signal Denoising(WSD) and Echo State Network(ESN) to predict water level at four hydrological stations in the lower Yellow River. The model constructs the ESMD−VMD−WSD−ESN hybrid model by using the respective strengths to extract the most important features in the predictor variables. The prediction effectiveness of the combined quadratic decomposition model is explored by comparing it with the ESN, WSD−ESN and ESMD−WSD−ESN models. The results show that the quadratic decomposition−based combined model ESMD−VMD−WSD−ESN has the best prediction, ESMD−WSD−ESN is the second best, WSD−ESN and ESN are relatively poor. The Mean Absolute Error of the ESMD−VMD−WSD−ESN model is only 0.16 m, the Mean Absolute Percentage Error is 0.18% and the Nash–Sutcliffe efficiency coefficient reaches 0.91. In summary, the combined model of quadratic decomposition model has good applicability and stability in monthly water level prediction.

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Data and materials are available from the corresponding author upon request.

References

  • Alsova OC (2016) An adaptive algorithm for hydrological time series forecasting based on the selection of an analogue−period. SPIIRAS Proc 3(46):27–34

    Article  Google Scholar 

  • Bian N (2018) Application of improved gray system in water level prediction of waterways. China Water Transp 05:75–80

    Google Scholar 

  • Cui BB, Chen XY, Song R (2015) Application of EMD threshold filtering in fiber optic gyroscope drift signal denoising. J Opt 35(2):0207001

    Google Scholar 

  • Devi MS, Rahamathulla V (2020) Prediction of groundwater level in district level by implementing machine learning and advanced softcomputing techniques. Artif Intell Syst Mach Learn 12:11–13

    Google Scholar 

  • Dragomiretskiy K, Zosso D (2014) Variational mode decomposition. IEEE Trans Signal Process 62(3):531–544

    Article  Google Scholar 

  • Gu QH, Hu Y, Tu ZY (2021a) Research on PSO−SVR−LSTM based water level prediction model. Jiangxi Hydraul Sci Technol 47(4):278–284

    Google Scholar 

  • Gu QH, Hu Y, Tu ZY (2021b) Research on water level prediction model based on PSO−SVR−LSTM. Jiangxi Hydraul Sci Technol 47(4):278–284

    Google Scholar 

  • Huang N, Long S, Wu M, Hh S, Zheng Q, Nc Y (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non−stationary time series analysis. Proceedings of the Royal Society. Mathematical, physical and engineering sciences. 454: 903–99595

  • Jaeger H (2001) The “echo state” approach to analysing and training recurrent neural networks−with an erratum note. Bonn, Ger: Ger Nat Res Cent Inform Technol GMD Tech Rep 148(34):13

    Google Scholar 

  • Jiang X, Wang J, Shi J, Shen C, Huang W, Zhu Z (2019) A coarse−to−fine decomposing strategy of VMD for extraction of weak repetitive transients in fault diagnosis of rotating machines. Mech Syst Signal Process 116:668–692

    Article  Google Scholar 

  • Liu Y, Yang G, Li M, Yin H (2016) Variational mode decomposition denoising combined the detrended fluctuation analysis. Signal Process 125:349–364

    Article  Google Scholar 

  • Liu Z, Tan M, Zha X (2017) Hydrological time series forecasting based on WD−RSPA model—a case study of Makou station and Shenzhen station. Acta Entiarum Nat Univ Sunyatseni 56(5):119–126

    Google Scholar 

  • Liu YX, Fan QX, Shang YZ, Fan QM, Liu ZW (2019) Short−term water level prediction method for hydropower station based on LSTM neural network. Adv Sci Technol Water Resour 39(2):56–60

    Google Scholar 

  • Mehmet Ö, Eyyup EB, Ömer E, Volkan H (2020) Comparison of wavelet and empirical mode decomposition hybrid models in drought prediction. Comput Electr Agric. https://doi.org/10.1016/j.compag.2020.105851

    Article  Google Scholar 

  • Miao Y, Zhao M, Lin J (2019) Identification of mechanical compound−fault based on the improved parameter−adaptive variational mode decomposition. ISA Trans 84:82–95

    Article  Google Scholar 

  • Mital U, Dwivedi D, Brown J, Faybishenko B, Painter S, Steefel C (2020) Sequential imputation of missing spatio−temporal precipitation data using random forests. Front Water. https://doi.org/10.3389/frwa.2020.00020

    Article  Google Scholar 

  • Nigam R, Nigam S, Mittal SK (2014) Modelling tropical river runoff: a time dependent approach. Sci Cold Arid Reg 3:247–256

    Google Scholar 

  • Páliz LP, Zapata−Ríos X, Campozano PL (2021) Application of neural network models and ANFIS for water level forecasting of the salve Faccha dam in the Andean zone in northern Ecuador. Water 13:2011

    Article  Google Scholar 

  • Roy DK, Biswas SK, Saha KK, Khandakar FIM (2021) Groundwater level forecast via a discrete space−state modelling approach as a surrogate to complex groundwater simulation modelling. Water Resour Manag 35:1653–1672

    Article  Google Scholar 

  • Song YQ, Deng SC, Lu YG (2019) The application of VMD with K value optimization in bearing fault diagnosis. Meas Control Technol 38(04):117–121

    Google Scholar 

  • Su WC, Zhu ST, Liu T, Jin C (2019) Fault diagnosis of motor bearings based on ESMD entropy fusion and PSO−SVM. Large Electr Mach Hydraul Turbine 5:24–28

    Google Scholar 

  • Sun D, Zhang H, Guo Z (2018) Complexity analysis of precipitation and runoff series based on approximate entropy and extreme−point symmetric mode. Decomposition 10:1388

    Google Scholar 

  • Tang M, Long Y, Lei XH, Tan FQ, Zhang Z (2020) Long short term memory network (LSTM) based water level prediction for the south−north water diversion central line. China Rural Water Hydropower 10:189–193

    Google Scholar 

  • Wan YL, Li XC, Zhou HB (2019) Short−term traffic flow prediction based on WPD−PSO−ESN. Highw Traffic Sci Technol 236(8):144–151

    Google Scholar 

  • Wang JL, Li ZJ (2013a) Extreme−point symmetric mode decomposition method for data analysis. Adv Adapt Data Anal 5(3):1350015

    Article  Google Scholar 

  • Wang JL, Li ZJ (2013b) Extreme−point symmetric mode decomposition method for data analysis. Adv Adapt Data Anal 05:1350015

    Article  Google Scholar 

  • Wang YF, Huang YP, Xiao M, Xiong B, Zhou SS, Jin Z (2022) Research on LSTM Yangtze river flood season water level prediction method based on attention mechanism. J China Three Gorges Univ (nat Sci) 44(3):13–19

    Google Scholar 

  • Wen Q, Yu Z (2017) Study on short−term water level forecasting in the middle reaches of Yangtze river. China Water Transp 02:46–52

    Google Scholar 

  • Xie HJ, Li JR, Dong Y, Li J, Sun ZX (2020) Effect of wavelet basis and threshold parameters on the denoising effect of transient electromagnetic signals. J xi’an Univ Sci Technol 40(04):682–690

    Google Scholar 

  • Xu GY, Zhu J, Si CY, Hu WB, Liu F (2019) A combined model for hydrological time series prediction based on CNN and MC. Comput Mod. (11): 23–28+33

  • Xu ML, Wang IW (2021) A study on time series prediction based on improved differential evolution and echo state network. J Autom 7:1589–1597

    Google Scholar 

  • Yang CH, Peng X, Zhao YZ, Wang X, Fu KL, Li YD, Li PL (2019) Prediction model to analyze the performance of VMD desalination process. Comput Chem Eng. https://doi.org/10.1016/j.compchemeng.2019.106619

    Article  Google Scholar 

  • Yao Z, Xu JP, Kong JP, Liu SB (2018a) Research on GA−Elman based river water level prediction method. J Yangtze River Sci Res Inst 35(9):34–37

    Google Scholar 

  • Yao Z, Xu JP, Kong JL, Liu SB (2018b) Research on river water level prediction method based on GA−Elman[J]. J Yangtze River Sci Res Inst 35(9):34–37

    Google Scholar 

  • Yu Z (2018) Research on water level prediction in waterways based on time series analysis. China Water Transp 10:148–150

    Google Scholar 

  • Zhang WY, Qu ZX, Zhang KQ, Mao WQ, Ma Y, Fan X (2017) A combined model based on CEEMDAN and modified flower pollination algorithm for wind speed forecasting. Energy Convers Manag 136:439–451

    Article  Google Scholar 

  • Zhang X, Miao Q, Zhang H, Wang L (2018) A parameter−adaptive VMD method based on grasshopper optimization algorithm to analyze vibration signals from rotating machinery. Mech Syst Sig Process 108:58–72

    Article  Google Scholar 

  • Zhu H, Wang J, Chen X Application of RBF neural network model in groundwater depth prediction. Yellow River. 42(03):50

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Funding

This work was supported by the Key Scientific Research Project of Colleges and Universities in Henan Province (CN) [grant numbers 17A570004].

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Authors and Affiliations

  1. Water Conservancy College, North China University of Water Resources and Electric Power, Zhengzhou, 450046, China

    Xianqi Zhang, Haiyang Chen, Yihao Wen, Jinwen Shi & Yimeng Xiao

  2. Collaborative Innovation Center of Water Resources Efficient Utilization and Protection Engineering, Zhengzhou, 450046, China

    Xianqi Zhang

  3. Technology Research Center of Water Conservancy and Marine Traffic Engineering, Zhengzhou, 450046, Henan, China

    Xianqi Zhang

Authors
  1. Xianqi Zhang
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  2. Haiyang Chen
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  3. Yihao Wen
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  4. Jinwen Shi
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  5. Yimeng Xiao
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Contributions

All authors contributed to the study conception and design. writing and editing: XZ and HC; chart editing: YW; preliminary data collection: JS, Yx. All authors read and approved the final manuscript.

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Correspondence to Haiyang Chen.

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Zhang, X., Chen, H., Wen, Y. et al. A new water level prediction model based on ESMD−VMD−WSD−ESN. Stoch Environ Res Risk Assess 37, 3221–3241 (2023). https://doi.org/10.1007/s00477-023-02446-9

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