Skip to main content
SpringerLink
Log in

Prediction of Chaotic Time Series Based on SALR Model with Its Application on Heating Load Prediction

  • Research Article-Computer Engineering and Computer Science
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

With the development of nonlinear science, improving the prediction performance of chaotic time series is of great significance in industrial production and daily life. Now, researchers have to develop effective models to achieve accurate prediction performance. The echo state network (ESN) has been proven to be an excellent prediction tool. However, the ESN has been criticized for not being principled enough. Thus, a novel ESN model namely self-join adjacent-feedback loop reservoir (SALR) is proposed. This model achieves the simplest topology structure on the premise of ensuring that all the connection modes of the classic ESN are available. In addition, in order to ensure the prediction performance of the network, the whale optimization algorithm was used to solve the parameter selection problems in the traditional cycle reservoir (SCR) model, the adjacent-feedback loop reservoir (ALR) model, and the SALR model. Finally, we use the proposed SALR model to solve classic benchmark chaotic time series as well as practical heating load prediction problems, and compare the SALR with the ESN, SCR, and ALR, respectively. Experimental results show that the proposed model can obtain higher accuracy with relatively low complexity than the ESN, SCR, and ALR.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Lun, S.X., Yao, X.S., Qi, H.Y., et al.: A novel model of leaky integrator echo state network for time-series prediction. Neurocomputing 159(jul.2), 58–66 (2015)

    Article  Google Scholar 

  2. Al-Shammari, E.T., Keivani, A., Shamshirband, S., et al.: Prediction of heat load in district heating systems by Support Vector Machine with Firefly searching algorithm. Energy 95, 266–273 (2016)

    Article  Google Scholar 

  3. Jaeger, H., Haas, H.: Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science 304, 78–80 (2004)

    Article  Google Scholar 

  4. Strauss, T., Wustlich, W., Labahn, R.: Design strategies for weight matrices of Echo state networks. Neural Comput. 24, 3246 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Najibi, E., Rostami, H.: 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 (2015)

    Article  Google Scholar 

  6. Boccato, L., Attux, R., Von Zuben, F.J.: Self-organization and lateral interaction in echo state network reservoirs. Neurocomputing 138, 297–309 (2014)

    Article  Google Scholar 

  7. Fang, Z., Wang, D.Z.: Optimization of aerodynamic characteristicson the unit body of high-speed train based on GRNN model and GA algorithm. J. Jim Univ. (Nat. Sci.) 95, 56–71 (2018)

    Google Scholar 

  8. Abualigah, L.M., Khader, A.T., Hanandeh, E.S.: Hybrid clustering analysis using improved Krill Herd algorithm. Appl. Intell. 73, 11–125 (2018)

    Google Scholar 

  9. Abualigah, L.M.: Feature selection and enhanced krill herd algorithm for text document clustering. Comput. Rev. 60(8), 318 (2019)

    Google Scholar 

  10. Abualigah, L.M., Khader, A.T., Hanandeh, E.S.: A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J. Comput. Sci. 25, 10 (2017)

    Google Scholar 

  11. Zhang, Y.; Lei, Y.X.: Research on Adaptive Adjustment of Cuckoo Search Algorithm. Software Guide, (2019)

  12. Chouikhi, N., Ammar, B., Rokbani, N., et al.: PSO-based analysis of Echo State Network parameters for time series forecasting. Appl. Soft Comput. 55, 211–225 (2017)

    Article  Google Scholar 

  13. Bala, A.; Ismail, I.; Ibrahim, R.: Cuckoo search based optimization of Echo State Network for time series prediction. In: 7th International Conference on Intelligent and Advanced System. IEEE (2018)

  14. Mirjalili, S., Lewis, A.: The Whale optimization algorithm. Adv. Eng. Softw. 95, 51–67 (2016)

    Article  Google Scholar 

  15. Hof, P.R.; Gucht, E.V.: Structure of the cerebral cortex of the humpback whale, Megaptera novaeangliae (Cetacea, Mysticeti, Balaenopteridae). In: The Anatomical Record: Advances in Integrative Anatomy and Evolutionary Biology, vol. 290, pp. 1–31 (2007)

  16. Jaeger, H.: The “echo state” approach to analyzing and training recurrent neural networks-with an erratum note. Technical report GMD report, 148 (2001)

  17. Lukosevicius, M., Jaeger, H.: Reservoir computing approaches to recurrent neural network training. Comput. Sci. Rev. 3, 127–149 (2009)

    Article  MATH  Google Scholar 

  18. Deng, Z.D., Zhang, Y.: Collective behavior of a small-world recurrent neural system with scale-free distribution. IEEE Trans. Neural Netw. 18, 1364–1375 (2007)

    Article  Google Scholar 

  19. Liu, X., Cui, H.X., Zhou, T.J., et al.: Performance evaluation of new echo state networks based on complex network. J. China Univ. Posts Telecommun. 19(001), 87–93 (2012)

    Article  Google Scholar 

  20. Song, Q.S., Feng, Z.: Effects of connectivity structure of complex echo state network on its prediction performance for nonlinear time series. Neurocomputing 73, 2177–2185 (2010)

    Article  Google Scholar 

  21. Zhang, B., David, J.M., Wang, Y.: Nonlinear system modeling with random matrices: Echo State Networks revisited. IEEE Trans. Neural Netw. Learn. Syst. 23, 175–182 (2012)

    Article  Google Scholar 

  22. Cui, H.. Y., Liu, X., Li, L.. X.: The architecture of dynamic reservoir in the echo state network. Chaos Interdiscipl. J. Nonlinear Sci. 22, 033–127 (2012)

    MathSciNet  MATH  Google Scholar 

  23. Rodan, A., Tino, P.: Minimum complexity echo state network. IEEE Trans. Neural Netw. 22, 131–44 (2011)

    Article  Google Scholar 

  24. Sun, X.C.; Cui, H.Y.; Liu, R.P.; et al.: Modeling deterministic echo state network with loop reservoir. J. Zhejiang Univ. Part C (Comput. Electron.) (English version) (2012)

  25. Luisa, M., Delgado, P.: Color image quantization using the shuffled-frog leaping algorithm. Eng. Appl. Artif. Intell. 79, 142–158 (2019)

    Article  Google Scholar 

  26. Wang, H., Wang, W.J., Zhou, X.Y., et al.: Firefly algorithm with neighborhood attraction. Inf. Sci. 382–383, 374–387 (2017)

    Article  Google Scholar 

  27. Zhang, Z.Q., Wang, K.P., Zhu, L.X., et al.: A Pareto improved artificial Fish swarm algorithm for solving a multi-objective fuzzy disassembly line balancing problem. Expert Syst. Appl. 86, 165–176 (2017)

    Article  Google Scholar 

  28. Ameur, M.S.B., et al.: FPGA based hardware implementation of Bat Algorithm. Appl. Soft Comput. 58, 378–387 (2017)

    Article  Google Scholar 

  29. Lin, Y., Gong, Y.J., Zhang, J.: An adaptive ant colony optimization algorithm for constructing cognitive diagnosis tests. Appl. Soft Comput. 52, 1–13 (2017)

    Article  Google Scholar 

  30. Jiang, F., Xia, H.. y, Tran, Q.. A., et al.: A new binary hybrid particle swarm optimization with wavelet mutation. Knowl.-Based Syst. 130, 90–101 (2017)

    Article  Google Scholar 

  31. Oliva, D., El Aziz, M.A., Hassanien, A.E.: Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm. Appl. Energy 200, 141–154 (2017)

    Article  Google Scholar 

  32. Sarath, K., Sekar, S.: Modelling and optimal design of LLC resonant converter using whale optimization algorithm. Int. J. Model. Simul. Sci. Comput. 9, 3 (2018)

    Article  Google Scholar 

  33. Abdel-Basset, M., Gunasekaran, M., El-Shahat, D., et al.: A hybrid whale optimization algorithm based on local search strategy for the permutation flow shop scheduling problem. Future Gener. Comput. Syst. 85, 10 (2018)

    Article  Google Scholar 

  34. Cuomo, K.M., Oppenheim, A.V., Strogatz, S.H.: Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circuits Syst. II Analog Digital Signal Process. 40, 626–633 (1993)

    Article  Google Scholar 

  35. Miranian, A., Abdollahzade, M.: Developing a local least-squares support vector machines-based neuro-fuzzy model for nonlinear and chaotic time series prediction. IEEE Trans. Neural Netw. Learn. Syst. 24, 207–218 (2013)

    Article  Google Scholar 

  36. Victor, M., Torres, Castillo O.: A type-2 fuzzy neural network ensemble to predict chaotic time series. Stud. Comput. Intell. 601, 185–195 (2015)

    Article  Google Scholar 

  37. Ma, Q., Shen, L.F., Chen, W.B., et al.: Functional echo state network for time series classification. Inf. Sci. 373, 1–20 (2016)

    Article  MATH  Google Scholar 

  38. Tian, Z.D., Gao, X.W., Li, S.J., et al.: Prediction method for network traffic based on genetic algorithm optimized Echo State Network. J. Comput. Res. Dev. 52, 1137–1145 (2015)

    Google Scholar 

  39. Huang, J., Qian, J., Liu, L., et al.: Echo state network based predictive control with particle swarm optimization for pneumatic muscle actuator. J. Franklin Inst. 353, 2761–2782 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  40. Zhang, Y.; Qi, W.: Interval forecasting for heating load using support vector regression and error correcting Markov chains. In: Proceedings of the Eighth International Conference on Machine Learning and Cybernetics vol. 2, pp. 1106–1110 (2009)

  41. Werner, S.E.: The Heat Load in District Heating System. Chalmers University of Technology, Goteborg (1984)

    Google Scholar 

  42. Stevenson, W.: Using artificial neural nets to predict building energy parameters. ASHRAE Trans. 100, 1076–1087 (1994)

    Google Scholar 

  43. Dong, B., Cao, C., Lee, S.: Applying support vector machines to predict building energy consumption in tropical region. Energy Build. 37, 545–553 (2005)

    Article  Google Scholar 

  44. Nielsen, H.A., Madsen, H.: Modelling the heat consumption in district heating systems using a grey-box approach. Energy Build. 38, 63–71 (2006)

    Article  Google Scholar 

  45. Yetemen, O., Yalcin, T.: Climatic parameters and evaluation of energy consumption of the Afyon geothermal district heating system. Renew. Energy 34, 706–710 (2009)

    Article  Google Scholar 

  46. Bacher, P.; Madsen, H.; Nielsen, H.A.: Online short-term heat load forecasting for single family houses. In: 39th Annual Conference of the IEEE Industrial Electronics Society, pp. 5741-5746 (2013)

  47. Al-Shammari, E.T., Keivani, A., Shamshirband, S., et al.: Prediction of heat load in district heating systems by support vector machine with firefly searching algorithm. Energy 95, 266–273 (2015)

    Article  Google Scholar 

  48. Takens, F.: Detecting strange attractors in fluid turbulence. In: Rand, D., Young, L.S. (eds.) Dynamical Systems and Turbulence, pp. 366–381. Springer, Berlin (1981)

    Google Scholar 

  49. Rossler, O.E.: An equation for continuous chaos. Phys. Lett. A 57, 397–398 (1976)

    Article  MATH  Google Scholar 

  50. Chatzis, S.P., Demiris, Y.: Echo State Gaussian process. IEEE Trans. Neural Netw. 22, 1435–1445 (2011)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Sub-Project of Intelligent Robot under National Key \( R \& D\) Program of China (No. 2019YFB1312102), Hebei Province Natural Science Foundation (No. F2019202364), and Humanity and Social Science Foundation of Ministry of Education of China (No. 15YJA630108).

Author information

Authors and Affiliations

  1. School of Electronics and Information Engineering, Hebei University of Technology, 5340 Xiping Road, Beichen District, Tianjin, 300401, People’s Republic of China

    Minghui Zhang, Baozhu Wang, Yatong Zhou, Jihao Gu & Yuheng Wu

Authors
  1. Minghui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Baozhu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yatong Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jihao Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yuheng Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yatong Zhou.

Ethics declarations

Conflict of interest

This paper has no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, M., Wang, B., Zhou, Y. et al. Prediction of Chaotic Time Series Based on SALR Model with Its Application on Heating Load Prediction. Arab J Sci Eng 46, 8171–8187 (2021). https://doi.org/10.1007/s13369-021-05407-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-021-05407-y

Keywords

Search

Navigation