Abstract
This paper investigates the parameter estimation of fractional order Wiener-Hammerstein (FWH) nonlinear systems with colored noises. By employing data filtering, the original system with autoregressive moving average noise is filtered to the system with moving average noise; then, particle swarm optimization (PSO) is applied to identify the filtered system. To enhance the algorithm’s performance, the adaptively variable weight, dynamic learning factors and fuzzy control are introduced to construct the data filtering-based adaptively fuzzy PSO (DF-AFPSO) method. For a FWH system with known fractional order, DF-AFPSO is employed to identify the parameter vector, which consists of linear and nonlinear parameters. Furthermore, for a FWH system with unknown fractional order, DF-AFPSO can simultaneously estimate the parameter vector and fractional order by utilizing its parallel search ability. Finally, two simulation cases are designed to test the effectiveness of the proposed algorithm. The results illustrate that the DF-AFPSO method has higher accuracy in identifying FWH systems than the standard PSO and data filtering-based PSO methods.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-04220-w/MediaObjects/10489_2022_4220_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-04220-w/MediaObjects/10489_2022_4220_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-04220-w/MediaObjects/10489_2022_4220_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-04220-w/MediaObjects/10489_2022_4220_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-04220-w/MediaObjects/10489_2022_4220_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-04220-w/MediaObjects/10489_2022_4220_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-04220-w/MediaObjects/10489_2022_4220_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-04220-w/MediaObjects/10489_2022_4220_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-04220-w/MediaObjects/10489_2022_4220_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10489-022-04220-w/MediaObjects/10489_2022_4220_Fig10_HTML.png)
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data Availability
This manuscript has no associated data.
References
Guo W, Xu P, Dai F, Hou Z (2022) Harris hawks optimization algorithm based on elite fractional mutation for data clustering. Applied Intelligence. https://doi.org/10.1007/s10489-021-02985-0https://doi.org/10.1007/s10489-021-02985-0
George T, Ganesan V (2022) Optimal tuning of FOPID controller for higher order process using hybrid approach. Applied Intelligence. https://doi.org/10.1007/s10489-022-03167-2
Xia ZQ, Wang XY, Wang CP, Wang CX, Ma B, Li Q, Wang MX, Zhao TT (2022) A robust zero-watermarking algorithm for lossless copyright protection of medical images. Appl Intell 52:607–621
Zhang Q, Wang HW, Liu CL (2021) Identification of fractional-order Hammerstein nonlinear ARMAX system with colored noise. Nonlinear Dyn 106(4):3215–3230
Galvão RKH, Teixeira MCM, Assunção E, Paiva HM, Hadjiloucas S (2020) Identification of fractional-order transfer functions using exponentially modulated signals with arbitrary excitation waveforms. ISA Trans 103:10–18
Wang JW, Ji Y, Zhang C (2021) Iterative parameter and order identification for fractional-order nonlinear finite impulse response systems using the key term separation. Int J Adapt Control Signal Process 35 (8):1562–1577
Li LW, Ren XM (2020) Parameter identification based on prescribed estimation error performance for extended Wiener-Hammerstein systems. IET Control Theory Appl 14(2):304–312
S̆krjanc I (2021) An evolving concept in the identification of an interval fuzzy model of Wiener-Hammerstein nonlinear dynamic systems. Inf Sci 581:73–87
Liu Q, Tang XM, Li JH, Zeng JX, Zhang K, Chai Y (2021) Identification of Wiener-Hammerstein models based on variational bayesian approach in the presence of process noise. J Frankl Inst 358 (10):5623–5638
Shaikh MAH, Barbé K (2021) Study of random forest to identify Wiener-Hammerstein system. IEEE Trans Instrum Meas 70:1–12
Yu WN, Shao YM, Xu J, Mechefske C (2022) An adaptive and generalized Wiener process model with a recursive filtering algorithm for remaining useful life estimation. Reliab Eng Syst Saf 217:09518320
Ji Y, Kang Z, Liu X (2021) The data filtering based multiple-stage Levenberg-Marquardt algorithm for Hammerstein nonlinear systems. Int J Robust Nonlinear Control 31(15):7007–7025
Xu H, Ma FY, Ding F, Xu L, Alsaedi A, Hayat T (2020) Data filtering-based recursive identification for an exponential autoregressive moving average model by using the multi-innovation theory. IET Control Theory Appl 14(17):2526–2534
Liu LJ, Liu HB, Ding F, Alsaedi A, Hayat T (2020) Data filtering based maximum likelihood gradient estimation algorithms for a multivariate equation-error system with ARMA noise. J Frankl Inst 357 (9):5640–5662
Cui YY, Meng X, Qiao JF (2022) A multi-objective particle swarm optimization algorithm based on two-archive mechanism. Appl Soft Comput 108532:119
Ajdad H, Baba YF, Mers AA, Merroun O, Bouatem A, Boutammachte N (2019) Particle swarm optimization algorithm for optical-geometric optimization of linear fresnel solar concentrators. Renew Energy 130:992–1001
Moodia M, Ghazvini M, Moodi H (2021) A hybrid intelligent approach to detect Android botnet using smart self-adaptive learning-based PSO-SVM. Knowl-Based Syst 222:106988
Zhang B, Tang Y, Zhang X, Lu Y (2021) Operational matrix based set-membership method for fractional order systems parameter identification. J Frankl Inst 358(18):10141–10164
Victor S, Mayoufi A, Malti R, Chetoui M, Aoun M (2022) System identification of MISO fractional systems: Parameter and differentiation order estimation. Automatica 141:110268
Yang C, Gao Z, Li X, Huang X (2021) Adaptive fractional-order Kalman filters for continuous-time nonlinear fractional-order systems with unknown parameters and fractional-orders. Int J Syst Sci 52 (13):2777–2797
Janjanam L, Saha SK, Kar R, Mandal D (2022) Optimal design of cascaded Wiener-Hammerstein system using a heuristically supervised discrete Kalman filter with application on benchmark problems. Expert Syst Appl 200:117065
Guo J, Zhao YL (2021) Identification for Wiener-Hammerstein systems under quantized inputs and quantized output observations. Asian J Control 23(1):118–127
Hammar K, Djamah T, Bettayeb M (2019) Nonlinear system identification using fractional Hammerstein-Wiener models. Nonlinear Dyn 98(3):2327–2338
Zong TC, Li JH, Lu GP (2021) Auxiliary model-based multi-innovation PSO identification for Wiener-Hammerstein systems with scarce measurements. Eng Appl Artif Intell 106:104470
Ding F, Xu L, Alsaadi FE, Hayat T (2018) Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique. IET Control Theory Appl 12(7):892–899
Li JH, Zong TC, Gu JP, Hua L (2020) Parameter estimation of Wiener systems based on the particle swarm iteration and gradient search principle. Circuits Syst Signal Process 39:3470–3495
Cheng ML, Liu B (2021) Application of an extended VES production function model based on improved PSO algorithm. Soft Comput 25(12):7937–7945
Zou LR (2021) Design of reactive power optimization control for electromechanical system based on fuzzy particle swarm optimization algorithm. Microprocess Microsyst 82:103865
Li J, Zong T, Lu G (2022) Parameter identification of Hammerstein-Wiener nonlinear systems with unknown time delay based on the linear variable weight particle swarm optimization. ISA Trans 120:89–98
Rodrigues F, Molina Y, Silva C, Ñaupari Z (2021) Simultaneous tuning of the AVR and PSS parameters using particle swarm optimization with oscillating exponential decay. Int J Electr Power Energy Syst 133:107251
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (61973176, 62073180), the Six Talent Peaks Project in Jiangsu Province (XYDXX-038), the Natural Science Research Program of Jiangsu Colleges and Universities (20KJA470002), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX21_3083).
Author information
Authors and Affiliations
Corresponding authors
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 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
Zong, T., Li, J. & Lu, G. Identification of fractional order Wiener-Hammerstein systems based on adaptively fuzzy PSO and data filtering technique. Appl Intell 53, 14085–14101 (2023). https://doi.org/10.1007/s10489-022-04220-w
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10489-022-04220-w