Skip to main content
SpringerLink
Log in

Hybrid identification method for fractional-order nonlinear systems based on the multi-innovation principle

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Aiming at the identification problems arising for fractional-order Hammerstein-Wiener system parameter coupling, namely, the difficulty of estimating the fractional order, low algorithm accuracy and slow convergence, an alternate identification method based on the principle of multiple innovations is proposed. First, a discrete model of a fractional-order Hammerstein-Wiener system is constructed. Second, an information matrix composed of fractional-order variables is used as the system input, combined with the multi-innovation principle, and the multi-innovation recursive gradient descent algorithm and the multi-innovation Levenberg-Marquardt algorithm are used to alternately estimate the parameters and fractional order of the model. The algorithms are executed cyclically and alternately presuppose each other. Finally, the convergence of the overall algorithm is theoretically analyzed, and the fractional-order Hammerstein-Wiener nonlinear system model is used to carry out numerical simulation experiments to verify the effectiveness of the algorithm. Moreover, we apply the proposed algorithm to an actual flexible manipulator system and perform fractional-order modeling and identification with high accuracy. Compared with the methods proposed by other scholars, the method proposed in this paper is more effective.

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

Similar content being viewed by others

References

  1. Matlob MA, Jamali Y (2019) The concepts and applications of fractional order differential calculus in modeling of viscoelastic systems: a primer. Crit Rev Biomed Eng 47(4):249–276

    Article  Google Scholar 

  2. Yavuz M, Sene N, Yıldız M (2022) Analysis of the influences of parameters in the fractional second-grade fluid dynamics. Mathematics 10(7):1125

    Article  Google Scholar 

  3. Failla G, Zingales M (2020) Advanced materials modelling via fractional calculus: challenges and perspectives. Phil Trans R Soc A 378(2172):20200050

    Article  Google Scholar 

  4. Qureshi S, Yusuf A, Shaikh AA, Inc M, Baleanu D (2019) Fractional modeling of blood ethanol concentration system with real data application. Chaos: An Interdisciplinary Journal of Nonlinear Science 29(1):013143

    Article  MathSciNet  MATH  Google Scholar 

  5. Shulin L, Naxin C, Yan L et al (2017) Modeling and state-of-charge estimation of automotive lithium-ion batteries based on fractional-order theory. Chin J Electrotechnical Technol 32(4):189–195

    Google Scholar 

  6. Jajarmi A, Baleanu D (2021) On the fractional optimal control problems with a general derivative operator. Asian Journal of Control 23(2):1062–1071

    Article  MathSciNet  Google Scholar 

  7. Wang S, Takyi-Aninakwa P, Jin S et al (2022) An improved feedforward-long short-term memory modeling method for the whole-life-cycle state of charge prediction of lithium-ion batteries considering current-voltage-temperature variation. Energy 124224

  8. Wang S, Jin S, Bai D, Fan Y, Shi H, Fernandez C (2021) A critical review of improved deep learning methods for the remaining useful life prediction of lithium-ion batteries. Energy Rep 7:5562–5574

    Article  Google Scholar 

  9. Zou C, Zhang L, Hu X, Wang Z, Wik T, Pecht M (2018) A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors. J Power Sources 390:286–296

    Article  Google Scholar 

  10. Zúñiga-Aguilar CJ, Gómez-Aguilar JF, Romero-Ugalde HM, Jahanshahi H, Alsaadi FE (2022) Fractal-fractional neuro-adaptive method for system identification. Eng Comput 38(4):3085–3108

    Article  Google Scholar 

  11. Xiong R, Tian J, Shen W et al (2018) A novel fractional order model for state of charge estimation in lithium ion batteries. IEEE Trans Veh Technol 68(5):4130–4139

    Article  Google Scholar 

  12. Burkovska O, Glusa C, D’elia M (2022) An optimization-based approach to parameter learning for fractional type nonlocal models. Comput Math Appl 116:229–244

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang Q, Wang H, Liu C (2021) Identification of fractional-order Hammerstein nonlinear ARMAX system with colored noise. Nonlinear Dynamics 106(4):3215–3230

    Article  Google Scholar 

  14. Zhang Q, Wang H, Liu C (2022) MILM hybrid identification method of fractional order neural-fuzzy Hammerstein model. Nonlinear Dynamics:1–15

  15. Rahmani MR, Farrokhi M (2018) Identification of neuro-fractional Hammerstein systems: a hybrid frequency−/time-domain approach. Soft Comput 22(24):8097–8106

    Article  MATH  Google Scholar 

  16. Ze D, Ning M (2019) Parameter estimation of fractional-order chaotic systems by differential quantum particle swarm optimization. Journal of System. Simulation 31(08):1664–1673. https://doi.org/10.16182/j.issn1004731x.joss.17-0265

    Article  Google Scholar 

  17. Guo H, Gu W, Khayatnezhad M, Ghadimi N (2022) Parameter extraction of the SOFC mathematical model based on fractional order version of dragonfly algorithm. Int J Hydrog Energy 47(57):24059–24068

    Article  Google Scholar 

  18. Lai X, He L, Wang S, Zhou L, Zhang Y, Sun T, Zheng Y (2020) Co-estimation of state of charge and state of power for lithium-ion batteries based on fractional variable-order model. J Clean Prod 255:120203

    Article  Google Scholar 

  19. Hammar K, Djamah T, Bettayeb M (2015) Fractional hammerstein system identification using particle swarm optimization //2015 7th international conference on modelling, identification and control (ICMIC). IEEE, 1–6

  20. Sersour L, Djamah T, Bettayeb M (2015) Identification of wiener fractional model using self-adaptive velocity particle swarm optimization//2015 7th international conference on modelling, identification and control (ICMIC). IEEE, 1–6

  21. Jin QB, Wang Z, Liu XP (2015) Auxiliary model-based inter-varying multi-innovation least squares identification for multivariable OE-like systems with scarce measurements. J Process Control 35(1):154–168

    Article  Google Scholar 

  22. Chaudhary NI, Raja MAZ, He Y, Khan ZA, Tenreiro Machado JA (2021) Design of multi innovation fractional LMS algorithm for parameter estimation of input nonlinear control autoregressive systems. Appl Math Model 93:412–425

    Article  MathSciNet  MATH  Google Scholar 

  23. Xu L, Ding F, Zhu Q (2022) Separable synchronous multi-innovation gradient-based iterative signal modeling from on-line measurements. IEEE Trans Instrum Meas 71:1–13

    Google Scholar 

  24. Ding F (2016) System identification: multi-innovation identification theory and method. Science Press, Beijing

    Google Scholar 

  25. Mohammad JM, Hamed M, Mohammad T (2018) Recursive identification of multiple-input single-output fractional-order Hammerstein model with time delay. Appl Soft Comput 70(3):486–500

    Google Scholar 

  26. Qi ZD, Sun Q, Ge WP, He YK (2020) Nonlinear modeling of PEMFC based on fractional order subspace identification. Asian J Control 22(5):1892–1900

    Article  MathSciNet  Google Scholar 

  27. Wang JC, Wei YH, Liu TY, Li A, Wang Y (2020) Fully parametric identification for continuous time fractional order Hammerstein systems. J Franklin Inst 357(1):651–666

    Article  MathSciNet  MATH  Google Scholar 

  28. Hammar K, Djamah T, Bettayeb M (2019, Published online) Nonlinear system identification using fractional Hammerstein-wiener models. Nonlinear Dyn 98:2327–2338

    Article  MATH  Google Scholar 

  29. Feng D (2014) System identification-performance analysis of identification methods. Science Press. (in Chinese)

  30. De Moor B, De Gersem P, De Schutter B et al (1997) DAISY: a database for identification of systems. Journal A 38:4–5

    Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (Grant number 61863034).

Author information

Authors and Affiliations

  1. School of Electrical Engineering, Xinjiang University, Urumqi, 830047, People’s Republic of China

    Zhang Qian, Wang Hongwei & Liu Chunlei

  2. School of Control Science and Engineering, Dalian University of Technology, Dalian, 110024, People’s Republic of China

    Wang Hongwei

Authors
  1. Zhang Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wang Hongwei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liu Chunlei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wang Hongwei.

Ethics declarations

Conflict of interests

The authors declare that there is no conflict of interests with respect to the research, authorship, and/or publication of this article.

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

Qian, Z., Hongwei, W. & Chunlei, L. Hybrid identification method for fractional-order nonlinear systems based on the multi-innovation principle. Appl Intell 53, 15711–15726 (2023). https://doi.org/10.1007/s10489-022-04309-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-022-04309-2

Keywords

Search

Navigation