[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Identification of nonlinear discrete systems using a new Hammerstein model with Volterra neural network

  • Optimization
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

For identifying nonlinear discrete systems, a new Hammerstein model consisting of Volterra neural network (VNN) and infinite impulse response (IIR) digital system is developed in this paper. The nonlinear static part of Hammerstein model is the proposed VNN structure that is a combination of the Volterra digital system and feedforward neural network. Another linear dynamic part in the model is expressed by the IIR digital filter. To design weights and thresholds contained in VNN and filter coefficients in IIR, a popular particle swarm optimization (PSO) algorithm is adopted such that the model output is able to approximate the actual nonlinear system output. Finally, many examinations including different population sizes and initial conditions are performed for two nonlinear system examples. All of simulation data including the mean squared error and sum of squared error derived by the proposed method are superior to those by other existing design methods. These sufficiently show the excellent performance of the developed Hammerstein model with PSO tuning on the nonlinear discrete systems modeling.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

Enquiries about data availability should be directed to the authors.

References

  • Abbasi E, Ghatee M, Shiri ME (2013) FRAN and RBF-PSO as two components of a hyper framework to recognize protein folds. Comput Biol Med 43:1182–1191

    Article  Google Scholar 

  • Abrahamsson R, Kay SM, Stoica P (2007) Estimation of the parameters of a bilinear model with applications to submarine detection and system identification. Digital Signal Process 17:756–773

    Article  Google Scholar 

  • Ahn CK (2014) Receding horizon disturbance attenuation for Takagi–Sugeno fuzzy switched dynamic neural networks. Inf Sci 280:53–63

    Article  MathSciNet  Google Scholar 

  • Amer M, Namaane A, M’Sirdi NK (2013) Optimization of hybrid renewable energy systems (HRES) using PSO for cost reduction. Energy Procedia 42:318–327

    Article  Google Scholar 

  • Casenave C (2011) Time-local formulation and identification of implicit Volterra models by use of diffusive representation. Automatica 47:2273–2278

    Article  MathSciNet  Google Scholar 

  • Chang WD (2012) Differential evolution-based nonlinear system modeling using a bilinear series model. Appl Soft Comput 12:3401–3407

    Article  Google Scholar 

  • Chen J, Wang X, Ding R (2012) Gradient based estimation algorithm for Hammerstein systems with saturation and dead-zone nonlinearities. Appl Math Model 36:238–243

    Article  Google Scholar 

  • Cheng Y, Zhang H, Zhang W, Zhang H (2021) Novel algebraic criteria on global Mittag-Leffler synchronization for FOINNs with the Caputo derivative and delay. J Appl Math Comput. https://doi.org/10.1007/s12190-021-01672-0

    Article  Google Scholar 

  • Couchman IJ, Kerrigan EC, Bohm C (2011) Model reduction of homogeneous-in-the-state bilinear systems with input constraints. Automatica 47:761–768

    Article  MathSciNet  Google Scholar 

  • Cui M, Liu H, Li Z, Tang Y, Guan X (2014) Identification of Hammerstein model using functional link artificial neural network. Neurocomputing 142:419–428

    Article  Google Scholar 

  • Ding F, Liu XP, Liu G (2011) Identification methods for Hammerstein nonlinear systems. Digital Signal Process 21:215–238

    Article  Google Scholar 

  • El-Abbasy MS, Senouci A, Zayed T, Mirahadi F, Parvizsedghy L (2014) Artificial neural network models for predicting condition of offshore oil and gas pipelines. Autom Constr 45:50–65

    Article  Google Scholar 

  • Figueiredo EMN, Ludermir TB (2014) Investigating the use of alternative topologies on performance of the PSO-ELM. Neurocomputing 127:4–12

    Article  Google Scholar 

  • Hong X, Chen S (2012) The system identification and control of Hammerstein system using non-uniform rational B-spline neural network and particle swarm optimization. Neurocomputing 82:216–223

    Article  Google Scholar 

  • Hsieh YZ, Su MC, Wang PC (2014) A PSO-based rule extractor for medical diagnosis. J Biomed Inform 49:53–60

    Article  Google Scholar 

  • Huo HB, Zhu XJ, Hu WQ, Tu HY, Li J, Yang J (2008) Nonlinear model predictive control of SOFC based on a Hammerstein model. J Power Sources 185:338–344

    Article  Google Scholar 

  • Le F, Markovsky I, Freeman CT, Rogers E (2012) Recursive identification of Hammerstein systems with application to electrically stimulated muscle. Control Eng Pract 20:386–396

    Article  Google Scholar 

  • Modares H, Alfi A, Sistani MBN (2010) Parameter estimation of bilinear systems based on an adaptive particle swarm optimization. Eng Appl Artif Intell 23:1105–1111

    Article  Google Scholar 

  • Mosleh M (2013) Fuzzy neural network for solving a system of fuzzy differential equations. Appl Soft Comput 13:3597–3607

    Article  Google Scholar 

  • Namda SJ, Panda G, Majhi B (2010) Improved identification of Hammerstein plants using new CPSO and IPSO algorithms. Expert Syst Appl 37:6818–6831

    Article  Google Scholar 

  • Nguyen SD, Ngo LN, Tran QT, Choi SB (2013) A new method for beam-damage-diagnosis using adaptive fuzzy neural structure and wavelet analysis. Mech Syst Signal Process 39:181–194

    Article  Google Scholar 

  • Otadi M (2014) Fully fuzzy polynomial regression with fuzzy neural networks. Neurocomputing 142:486–493

    Article  Google Scholar 

  • Panda S, Mohanty B, Hota PK (2013) Hybrid BFOA–PSO algorithm for automatic generation control of linear and nonlinear interconnected power systems. Appl Soft Comput 13:4718–4730

    Article  Google Scholar 

  • Schmidt CA, Biagiola SI, Cousseau JE, Figueroa JL (2014) Volterra-type models for nonlinear systems identification. Appl Math Model 38:2414–2421

    Article  MathSciNet  Google Scholar 

  • Senouci A, Boukabou A (2014) Predictive control and synchronization of chaotic and hyperchaotic systems based on a T-S fuzzy model. Math Comput Simul 105:62–78

    Article  MathSciNet  Google Scholar 

  • Solis AR, Panoutsos G (2013) Granular computing neural-fuzzy modeling: a neutrosophic approach. Appl Soft Comput 13:4010–4021

    Article  Google Scholar 

  • Stamova IM, Stamov T, Simeonova N (2014) Impulsive effects on the global exponential stability of neural network models with supremums. Eur J Control 20:199–206

    Article  MathSciNet  Google Scholar 

  • Tang Y, Li Z, Guan X (2014) Identification of nonlinear system using extreme learning machine based Hammerstein model. Commun Nonlinear Sci Numer Simul 19:3171–3183

    Article  MathSciNet  Google Scholar 

  • Van de Vegte J (2001) Fundamentals of digital signal processing. Prentice Hall, New Jersey

    Google Scholar 

  • Yang YS, Chang WD, Liao TL (2012) Volterra system-based neural network modeling by particle swarm optimization approach. Neurocomputing 82:179–185

    Article  Google Scholar 

  • Zhang C, Huang N, O’Regan D (2013) Almost periodic solutions for a Volterra model with mutual interference and Holling type III functional response. Appl Math Comput 225:503–511

    MathSciNet  MATH  Google Scholar 

  • Zhang C, Feng G, Qiu J, Zhang WA (2014) T-S fuzzy-model-based piecewise output feedback controller design for networked nonlinear systems with medium access constraint. Fuzzy Sets Syst 248:86–105

    Article  MathSciNet  Google Scholar 

  • Zhang H, Ye M, Ye R, Cao J (2018a) Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks. Physica A 508:155–165

    Article  MathSciNet  Google Scholar 

  • Zhang H, Ye R, Liu S, Cao J, Alsaedi A, Li X (2018b) LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays. Int J Syst Sci 49:537–545

    Article  MathSciNet  Google Scholar 

  • Zhang H, Ye R, Cao J, Alsaedi A (2018c) Delay-independent stability of Riemann–Liouville fractional neutral-type delayed neural networks. Neural Process Lett 47:427–442

    Google Scholar 

  • Zhang H, Cheng J, Zhang H, Zhang W, Cao J (2021) Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays. Chaos Solitons Fractals 152:111432

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the Ministry of Science and Technology of Taiwan under Grant MOST 108-2221-E-366-003.

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Department of Computer and Communication, Shu-Te University, Kaohsiung, 824, Taiwan

    Wei-Der Chang

Authors
  1. Wei-Der Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei-Der Chang.

Ethics declarations

Conflict of interest

The author declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by the author.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chang, WD. Identification of nonlinear discrete systems using a new Hammerstein model with Volterra neural network. Soft Comput 26, 6765–6775 (2022). https://doi.org/10.1007/s00500-022-07089-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-022-07089-6

Keywords

Search

Navigation