Skip to main content
SpringerLink
Log in

Multi-state delayed echo state network with empirical wavelet transform for time series prediction

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

In this paper, considering the effect of multiple delayed states on the reservoir itself, based on the advantage of the empirical wavelet transform, an improved ESN with multiple delayed states is proposed, called multi-state delayed echo state network with empirical wavelet transform (EWT-MSD-ESN). Firstly, the empirical wavelet transform is used to decompose the input signal, and then the main features of all decomposed components of the input signal can be extracted. Secondly, considering the multi-state delayed capability of the reservoir, the reservoir state equation of the EWT-MSD-ESN can be adjusted adaptively by using the autocorrelation coefficient of the input signal, such that the intrinsic characteristics of different learning tasks can be fully reflected. Finally, four numerical simulation examples and two actual examples are used to validate the predictive performance of EWT-MSD-ESN.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1
Fig. 1
Fig. 2
Fig. 3
Algorithm 2
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  1. Jaeger H (2001) The ‘echo state’ approach to analysing and training recurrent neural networks-with an erratum note. German National Research Center for Information Technology, GMD Report 148

  2. Li X, Bi FR, Zhang LP, Lin JW, Bi XB, Yang X (2022) Rotating machinery faults detection method based on deep echo state network. Appl Soft Comput 127:109335

    Article  Google Scholar 

  3. Kleyko D, Frady EP, Kheffache M, Osipov E (2022) Integer echo state networks: efficient reservoir computing for digital hardware. IEEE Trans Neural Netw Learn Syst 33(4):1688–1701

    Article  Google Scholar 

  4. Wang ZJ, Zhao H, Zheng MW, Niu SJ, Gao XZ, Li LX (2023) A novel time series prediction method based on pooling compressedsensing echo state network and its application in stock market. Neural Netw 164:216–227

    Article  Google Scholar 

  5. Yao XS, Wang ZS, Huang ZJ (2021) A stability criterion for discrete-time fractional-order echo state network and its application. Soft Comput 25:4823–4831

    Article  Google Scholar 

  6. Zhang GG, Zhang C, Zhang WD (2020) Evolutionary echo state network for long-term time series prediction: on the edge of chaos. Appl Intell 50:893–904

    Article  Google Scholar 

  7. Najibi E, Rostami H (2015) SCESN, SPESN, SWESN: three recurrent neural echo state networks with clustered reservoirs for prediction of nonlinear and chaotic time series. Appl Intell 43:460–472

    Article  Google Scholar 

  8. Zhang HY, Hu B, Wang XY, Xu JP, Wang L, Sun Q et al (2021) Self-organizing deep belief modular echo state network for time series prediction. Knowl-Based Syst 222:107007

    Article  Google Scholar 

  9. Yao XS, Wang ZS (2019) Broad echo state network for multivariate time series prediction. J Frank Inst 356(9):4888–4906

    Article  MathSciNet  Google Scholar 

  10. Yao XS, Shao YN, Fan SY, Cao SX (2022) Echo state network with multiple delayed outputs for multiple delayed time series prediction. J Frank Inst 359(18):11089–11107

    Article  MathSciNet  Google Scholar 

  11. Liao YB, Li HM (2019) Deep echo state network with reservoirs of multiple activation functions for time-series prediction. Sādhanā: Acad Proc Eng Sci 44:1–12

    Article  MathSciNet  Google Scholar 

  12. Gao RB, Du L, Duru O, Yuen KF (2021) Time series forecasting based on echo state network and empirical wavelet transformation. Appl Soft Comput 102:107111

    Article  Google Scholar 

  13. Zhang H, Zheng MW, Zhang YP, Yu X, Li WC, Gao H (2021) Application of ESN prediction model based on compressed sensing in stock market. Commun Nonlinear Sci Numer Simul 101:105857

    Article  MathSciNet  Google Scholar 

  14. Liu ZY, Li SX, Pan MY, Loo CK (2022) Grammatical structure detection by instinct plasticity based echo state networks with genetic algorithm. Neurocomputing 467:173–183

    Article  Google Scholar 

  15. Wang HS, Wu QMJ, Wang DS, Xin JB, Yang YM, Yu KJ (2021) Echo state network with a global reversible autoencoder for time series classification. Inf Sci 570:744–768

    Article  MathSciNet  Google Scholar 

  16. Li N, Tuo JY, Wang YQ, Wang MH (2020) Prediction of blood glucose concentration for type 1 diabetes based on echo state networks embedded with incremental learning. Neurocomputing 378:248–259

  17. Gao RB, Li RL, Hu MH, Suganthan PN, Yuen KF (2023) Dynamic ensemble deep echo state network for significant wave height forecasting. Appl Energy 329:120261

    Article  Google Scholar 

  18. Li FJ, Li Y (2023) Robust echo state network with cauchy loss function and hybrid regularization for noisy time series prediction. Appl Soft Comput 146:110640

    Article  Google Scholar 

  19. Wang ZJ, Zhao H, Zheng MW, Niu SJ, Gao XZ, Li LX (2023) A novel time series prediction method based on pooling compressed sensing echo state network and its application in stock market. Neural Netw 164:216–227

    Article  Google Scholar 

  20. Basterrech S, Rubino G (2023) Evolutionary Echo State Network: A neuroevolutionary framework for time series prediction. Appl Soft Comput 144:110463

    Article  Google Scholar 

  21. Wang L, Su Z, Qiao JF, Deng F (2022) A pseudo-inverse decomposition-based self-organizing modular echo state network for time series prediction. Appl Soft Comput 116:108317

    Article  Google Scholar 

  22. Guo X, Li WJ, Qiao JF (2023) A self-organizing modular neural network based on empirical mode decomposition with sliding window for time series prediction. Appl Soft Comput 145:110559

    Article  Google Scholar 

  23. Nguyen HP, Baraldi P, Zio E (2021) Ensemble empirical mode decomposition and long short-term memory neural network for multi-step predictions of time series signals in nuclear power plants. Appl Energy 283:116346

    Article  Google Scholar 

  24. Abdallah M, Mohammadi B, Nasiri H, Katipoǧlu OM, Abdalla MAA, Ebadzadeh MM (2023) Daily global solar radiation time series prediction using variational mode decomposition combined with multi-functional recurrent fuzzy neural network and quantile regression forests algorithm. Energy Rep 10:4198–4217

    Article  Google Scholar 

  25. Iwabuchi K, Kato K, Watari D, Taniguchi I, Catthoor F, Shirazi E et al (2022) Flexible electricity price forecasting by switching mother wavelets based on wavelet transform and long short-term memory. Energy and AI 10:100192

    Article  Google Scholar 

  26. Anggraeni W, Yuniarno EM, Rachmadi RF, Sumpeno S, Pujiadi P, Sugiyanto S et al (2024) A hybrid EMD-GRNN-PSO in intermittent time-series data for dengue fever forecasting. Expert Syst Appl 237:121438

    Article  Google Scholar 

  27. Zhu Q, Zhang F, Liu S, Wu YQ, Wang L (2019) A hybrid VMD-BiGRU model for rubber futures time series forecasting. Appl Soft Comput 84:105739

    Article  Google Scholar 

  28. Abebe SA, Qin TL, Zhang X, Yan DH (2022) Wavelet transform-based trend analysis of streamflow and precipitation in upper blue nile river basin. J Hydrol Reg Stud 44:101251

    Article  Google Scholar 

  29. Feng ZK, Niu WJ, Tang ZY, Jiang ZQ, Xu Y, Liu Y et al (2020) Monthly runoff time series prediction by variational mode decomposition and support vector machine based on quantum-behaved particle swarm optimization. J Hydrol 583:124627

    Article  Google Scholar 

  30. Liang HT, Gao J, Qiang N (2021) A novel framework based on wavelet transform and principal component for face recognition under varying illumination. Appl Intell 51:1762–1783

    Article  Google Scholar 

  31. Dong HB, Han S, Pang JW, Yu XD (2023) A joint network of non-linear graph attention and temporal attraction force for geo-sensory time series prediction. Appl Intell 53:17346–17362

    Article  Google Scholar 

  32. Gilles J (2013) Empirical wavelet transform. IEEE Trans Signal Process 61(16):3999–4010

    Article  MathSciNet  Google Scholar 

  33. Huang NE, Shen Z, Long SR, Qu MC, Snin HH, Zheng Q et al (1998) The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis. R Soc 454:903–995

    Article  MathSciNet  Google Scholar 

  34. Olkkone JT (2011) Discrete wavelet transforms: theory and applications. BoD-Books on Demand

  35. Dragomiretskiy K, Zosso D (2014) Variational mode decomposition. IEEE Trans Signal Process 62(3)

  36. Jaeger H, Lukoševičius M, Popovici D, Siewert U (2007) Optimization and applications of echo state networks with leaky-integrator neurons. Neural Netwo 20(3):335–352

    Article  Google Scholar 

  37. Lun SX, Yao XS, Hu HF (2016) A new echo state network with variable memory length. Inf Sci 370:103–119

    Article  Google Scholar 

  38. Bo YC, Wang P, Zhang X (2020) An asynchronously deep reservoir computing for predicting chaotic time series. Appl Soft Comput 95:106530

Download references

Acknowledgements

This work is supported in part by the National Natural Science Foundation of China under Grant 62203103 and Grant 62003274, and in part by the Jilin Provincial Department of Education Scientific Research Project under Grant JJKH20240152KJ.

Author information

Authors and Affiliations

  1. School of Automation Engineering, Northeast Electric Power University, Jilin, China

    Xianshuang Yao, Huiyu Wang, Yanning Shao & Shengxian Cao

  2. College of Aeronautics, Northwestern Polytechnical University, Xian, China

    Zhanjun Huang

  3. Shandong Henghui Energy Saving Technology Group Co., Ltd., Yantai, China

    Qingchuan Ma

Authors
  1. Xianshuang Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huiyu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanning Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhanjun Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shengxian Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Qingchuan Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianshuang Yao.

Additional information

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yao, X., Wang, H., Shao, Y. et al. Multi-state delayed echo state network with empirical wavelet transform for time series prediction. Appl Intell 54, 4646–4667 (2024). https://doi.org/10.1007/s10489-024-05386-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-024-05386-1

Keywords

Search

Navigation