Skip to main content
SpringerLink
Log in

Development of adaptive p-step RBF network model with recursive orthogonal least squares training

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

An adaptive p-step prediction model for nonlinear dynamic processes is developed in this paper and implemented with a radial basis function (RBF) network. The model can predict output for multi-step-ahead with no need for the unknown future process output. Therefore, the long-range prediction accuracy is significantly enhanced and consequently is especially useful as the internal model in a model predictive control framework. An improved network structure adaptation is also developed with the recursive orthogonal least squares algorithm. The developed model is online updated to adapt both its structure and parameters, so that a compact model structure and consequently a less computing cost are achieved with the developed adaptation algorithm applied. Two nonlinear dynamic systems are employed to evaluate the long-range prediction performance and minimum model structure and compared with an existing PSC model and a non-adaptive RBF model. The simulation results confirm the effectiveness of the developed model and superior over the existing models.

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

Similar content being viewed by others

References

  1. Hao Y et al (2011) Advantages of radial basis function networks for dynamic system design. IEEE Trans Ind Electron 58(12):5438–5450

    Article  Google Scholar 

  2. Broomhead DS, Lowe D (1988) Multivariable functional interpolation and adaptive networks. Complex Syst 2:321–355

    MathSciNet  MATH  Google Scholar 

  3. Diaconescu E (2008) The use of NARX neural networks to predict chaotic time series. WSEAS Trans Comput Res 3(3):182–191

    Google Scholar 

  4. Su TH, McAvoy TJ (1997) Artificial neural network for nonlinear process identification and control. In: Henson MA, Seborg DE (eds) Nonlinear process control. Prentice Hall, Englewood Cliffs, pp 371–428

    Google Scholar 

  5. Bhartiya S, Whiteley JR (2001) Factorized approach to nonlinear MPC using a radial basis function model. AIChE J 47(2):358–368

    Article  Google Scholar 

  6. Chen S, Grant PM, Cowan CFN (1992) Orthogonal least-square algorithm for training multioutput radial basis function networks. Radar Signal Process IEE Proc F 139(6):378–384

    Article  Google Scholar 

  7. Platt J (1991) A resource-allocating network for function interpolation. Neural Comput 3:213–225

    Article  MathSciNet  Google Scholar 

  8. Karayiannis NB, Mi GW (1997) Growing radial basis neural networks: merging supervised and unsupervised learning with network growth techniques. IEEE Trans Neural Netw 8(6):1492–1506

    Article  Google Scholar 

  9. Todorovic B, Stankovic M (2001) Sequential growing and pruning of radial basis function network. In: Proceedings of the international joint conference on neural networks 2001 (IJCNN’01), IEEE pp 1954–1959

  10. Han H-G, Chen Q-L, Qiao J-F (2011) An efficient self-organizing RBF neural network for water quality prediction. Neural Netw 24(7):717–725

    Article  MATH  Google Scholar 

  11. Chen S, Cowan CFN, Grant PM (1991) Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans Neural Netw 2(2):302–309

    Article  Google Scholar 

  12. Chang E, Yang HH, Bos S (1996) Orthogonal least-squares learning algorithm with local adaptation process for the radial basis function networks. IEEE Signal Process Lett 3(8):253–255

    Article  Google Scholar 

  13. Yu DL, Gomm JB, Williams D (1997) A recursive orthogonal least squares algorithm for training RBF networks. Neural Process Lett 5(3):167–176

    Article  Google Scholar 

  14. Gomm JB, Yu DL (2000) Selecting radial basis function network centres with recursive orthogonal least squares training. IEEE Trans Neural Netw 11(2):306–314

    Article  Google Scholar 

  15. Yu DL, Yu DW (2007) A new structure adaptation algorithm for RBF networks and its application. Neural Comput Appl 16(1):91–100

    Article  Google Scholar 

  16. Tok DKS et al (2015) Adaptive structure radial basis function network model for processes with operating region migration. Neurocomputing 155:186–193

    Article  Google Scholar 

  17. Wang SW et al (2006) Adaptive neural network model based predictive control for air–fuel ratio of SI engines. Eng Appl Artif Intell 19(2):189–200

    Article  Google Scholar 

  18. Yu DL et al (2004) Adaptive RBF model for model-based control. In: Fifth world congress intelligent control and automation on 2004 (WCICA 2004)

  19. Qiao J-F, Han H-G (2012) Identification and modeling of nonlinear dynamical systems using a novel self-organizing RBF-based approach. Automatica 48(8):1729–1734

    Article  MathSciNet  MATH  Google Scholar 

  20. Han H-G, Wu X-L, Qiao J-F (2013) Real-time model predictive control using a self-organizing neural network. IEEE Trans Neural Netw Learn Syst 24(9):1425–1436

    Article  Google Scholar 

  21. Lu CH, Tsai CC (2008) Adaptive predictive control with recurrent neural network for industrial process: an application to temperature control of a variable-frequency oil-cooling machine. IEEE Trans Ind Electron 55(3):1366–1375

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electronic Information, Changchun Architecture and Civil Engineering College, Changchun, China

    Lei Gu

  2. Process Control Group, Liverpool John Moores University, Liverpool, UK

    D. K. Siong Tok & Ding-Li Yu

Authors
  1. Lei Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. K. Siong Tok
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ding-Li Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ding-Li Yu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gu, L., Tok, D.K.S. & Yu, DL. Development of adaptive p-step RBF network model with recursive orthogonal least squares training. Neural Comput & Applic 29, 1445–1454 (2018). https://doi.org/10.1007/s00521-016-2669-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2669-x

Keywords

Search

Navigation