Skip to main content
SpringerLink
Log in

Recurrent neural network modeling combined with bilinear model structure

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

Abstract

In this paper, we propose a neural network modeling scheme for nonlinear systems. The proposed architecture is a new combination of neural network and bilinear system model in which the terms of cross-products of input and output signals within the bilinear model are taken as the inputs into the neural network. Compared with the original bilinear system, this kind of network model possesses much more adjustable parameters to fulfill the system identification. Moreover, instead of the general back-propagation method an evolutionary computation called the differential evolution algorithm is presented to update the network parameters. This algorithm is with multiple direction searches toward the global optimal solution for given optimization problem. To show the feasibility of the proposed scheme, a nonlinear chemical process system of continuously stirred tank reactor is illustrated. Many simulations and examinations are considered to verify the robustness of the proposed neural network structure on the modeling performance, including different sets of initial conditions of the algorithm and model orders.

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

Similar content being viewed by others

References

  1. Khasei M, Bijari M (2011) A novel hybridization of artificial neural networks and ARIMA models for time series forecasting. Appl Soft Comput 11:2664–2675

    Article  Google Scholar 

  2. Luan X, Liu F, Shi P (2010) Robust finite-time H ∞ control for nonlinear jump systems via neural networks. Circuits Syst Signal Process 29:481–498

    Article  MATH  MathSciNet  Google Scholar 

  3. He H, Zhu Z, Makinen E (2009) A neural network model to minimize the connected dominating set for self-configuration of wireless sensor networks. IEEE Trans Neural Netw 20:973–982

    Article  Google Scholar 

  4. Song X, Gao H, Ding L, Liu D, Hao M (2012) The globally asymptotic stability analysis for a class of recurrent neural networks with delays. Neural Comput Appl. doi:10.1007/s00521-012-0888-3

  5. Nourafza N, Setayeshi S, Khadem-Zadeh A (2012) A novel approach to accelerate the convergence speed of a stochastic multi-agent system using recurrent neural nets. Neural Comput Appl. doi:10.1007/s00521-011-0624-4

  6. Ahn KK, Anh HPH (2010) Inverse double NARX fuzzy modeling for system identification. IEEE Trans Mechatron 15:136–148

    Article  Google Scholar 

  7. Huang CJ, Li THS, Chen CC (2009) Fuzzy feedback linearization control for MIMO nonlinear system and its application to full-vehicle suspension system. Circuits Syst Signal Process 28:959–991

    Article  MATH  Google Scholar 

  8. Jassar S, Liao Z, Zhao L (2011) A recurrent neuro-fuzzy system and its application in inferential sensing. Appl Soft Comput 11:2935–2945

    Article  Google Scholar 

  9. Razavi-Far R, Davilu H, Palade V, Lucas C (2009) Model-based fault detection and isolation of a steam generator using neuro-fuzzy networks. Neurocomputing 72:2939–2951

    Article  Google Scholar 

  10. Balasubramaniam P, Chandran R (2011) Delay decomposition approach to stability analysis for uncertain fuzzy Hopfield neural networks with time-varying delay. Commun Nonlinear Sci Numer Simul 16:2098–2108

    Article  MATH  MathSciNet  Google Scholar 

  11. Guo NR, Li THS (2011) Construction of a neuro-fuzzy classification model based on feature-extraction approach. Expert Syst Appl 38:682–691

    Article  Google Scholar 

  12. Abiyev RH, Kaynak O (2010) Type 2 fuzzy neural structure for identification and control of time-varying plants. IEEE Trans Ind Electron 57:4147–4159

    Article  Google Scholar 

  13. Nounou MN, Nounou HN (2007) Improving the prediction and parsimony of ARX models using multiscale estimation. Appl Soft Comput 7:711–721

    Article  Google Scholar 

  14. Rojas I, Valenzuela O, Rojas F, Herrera LJ, Pomares H, Marquez L, Pasadas M (2008) Soft-computing techniques and ARMA model for time series prediction. Neurocomputing 71:519–537

    Article  Google Scholar 

  15. Tsai JSH, Wang CT, Kuang CC, Guo SM, Shieh LS, Chen CW (2010) A NARMAX model-based state-space self-tuning control for nonlinear stochastic hybrid systems. Appl Math Model 34:3030–3054

    Article  MATH  MathSciNet  Google Scholar 

  16. Campello RJGB, Favier G, do Amaral WC (2004) Optimal expansions of discrete-time Volterra models using Laguerre functions. Automatica 40:815–822

    Article  MATH  MathSciNet  Google Scholar 

  17. Zhang J, Zhao H (2010) A novel adaptive bilinear filter based on pipelined architecture. Digit Signal Process 20:23–38

    Article  Google Scholar 

  18. dos Santos PL, Ramos JA, Martins de Carvalho JL (2009) Identification of bilinear systems with white noise inputs: an iterative deterministic-stochastic subspace approach. IEEE Trans Control Syst Technol 17:1145–1153

    Article  Google Scholar 

  19. Subudhi B, Jena D (2011) A differential evolution based neural network approach to nonlinear system identification. Appl Soft Comput 11:861–871

    Article  Google Scholar 

  20. Narendra KS, Parthasarathy K (1990) Identification and control of dynamical systems using neural networks. IEEE Trans Neural Netw 1:4–27

    Article  Google Scholar 

  21. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous. J Global Optim 11:341–359

    Article  MATH  MathSciNet  Google Scholar 

  22. Hachicha NH, Jarboui B, Siarry P (2011) A fuzzy logic control using a differential evolution algorithm aimed at modeling the financial market dynamics. Inf Sci 181:79–91

    Article  Google Scholar 

  23. Bhattacharya A, Chattopadhyay PK (2011) Solving economic emission load dispatch problems using hybrid differential evolution. Appl Soft Comput 11:2526–2537

    Article  Google Scholar 

  24. Babu BV, Angira R (2006) Modified differential evolution (MDE) for optimization of non-linear chemical processes. Comput Chem Eng 30:989–1002

    Article  Google Scholar 

  25. Maulik U, Saha I (2010) Automatic fuzzy clustering using modified differential evolution for image classification. IEEE Trans Geosci Remote Sens 48:3503–3510

    Article  Google Scholar 

  26. Karaboga N, Cetinkaya B (2006) Design of digital FIR filters using differential evolution algorithm. Circuits Syst Signal Process 25:649–660

    Article  MATH  MathSciNet  Google Scholar 

  27. Chen CT, Peng ST (1999) Learning control of process systems with hard input constraints. J Process Control 9:151–160

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work was partially supported by the National Science Council of Taiwan under Grant NSC 99-2221-E-366-011.

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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chang, WD. Recurrent neural network modeling combined with bilinear model structure. Neural Comput & Applic 24, 765–773 (2014). https://doi.org/10.1007/s00521-012-1295-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-012-1295-5

Keywords

Search

Navigation