Skip to main content
SpringerLink
Log in

Weighted Parameter Estimation for Hammerstein Nonlinear ARX Systems

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper proposes parameter estimation algorithms for Hammerstein nonlinear ARX systems. By making full use of the current and previous input–output data of the system, a weighted multi-innovation stochastic gradient algorithm is presented to improve the convergence rate of identification. The innovation term in the traditional identification algorithms can be treated as a particle in the particle-filtering technique, and the weight of each innovation then can be computed according to their importance. The simulation results indicate that the algorithm can improve the accuracy of parameter estimation.

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

Similar content being viewed by others

References

  1. R.B. Abdennour, M. Ksouri, F.M. Sahli, Nonlinear model-based predictive control using a generalised Hammerstein model and its application to a semi-batch reactor. Int. J. Adv. Manuf. Technol. 20(11), 844–852 (2002)

    Article  Google Scholar 

  2. T. Cui, F. Ding, A. Alsaadi, et al., Joint multi-innovation recursive extended least squares parameter and state estimation for a class of state-space systems. Int. J. Control Autom. 18 (2020)

  3. F. Ding, T. Chen, Performance analysis of multi-innovation gradient type identification methods. Automatica 43(1), 1–14 (2007)

    Article  MathSciNet  Google Scholar 

  4. J. Ding, J.Z. Chen, J.X. Lin, G.P. Jiang, Particle filtering-based recursive identification for controlled auto-regressive systems with quantised output. IET Control Theory Appl. 13(14), 2181–2187 (2019)

    Article  Google Scholar 

  5. J. Ding, J.Z. Chen, J.X. Lin, L.J. Wan, Particle filtering based parameter estimation for systems with output-error type model structures. J. Frankl. Inst. 356(10), 5521–5540 (2019)

    Article  MathSciNet  Google Scholar 

  6. F. Ding, Y.J. Liu, B. Bao, Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 226(1), 43–55 (2012)

    Article  Google Scholar 

  7. F. Ding, L. Lv, J. Pan, et al., Two-stage gradient-based iterative estimation methods for controlled autoregressive systems using the measurement data. Int. J. Control Autom. 18 (2020)

  8. F. Ding, J. Pan, A. Alsaedi et al., Gradient-based iterative parameter estimation algorithms for dynamical systems from observation data. Mathematics 7(5), Article Number: 428 (2019). https://doi.org/10.3390/math7050428

  9. F. Ding, F.F. Wang, T. Hayat et al., Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique. IET Control Theory Appl. 11(3), 390–400 (2017)

    Article  MathSciNet  Google Scholar 

  10. F. Ding, L. Xu, F.E. Alsaadi et al., Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique. IET Control Theory Appl. 12(7), 892–899 (2018)

    Article  MathSciNet  Google Scholar 

  11. B. Fu, C.X. Ouyang, C.S. Li, J.W. Wang, E. Gul, An improved mixed integer linear programming approach based on symmetry diminishing for unit commitment of hybrid power system. Energies 12(5), Article Number: 833 (2019). https://doi.org/10.3390/en12050833

  12. S. Gibson, B. Ninness, Robust maximum-likelihood estimation of multivariable dynamic systems. Automatica 41(10), 1667–1682 (2005)

    Article  MathSciNet  Google Scholar 

  13. P.C. Gong, W.Q. Wang, F.C. Li, H. Cheung, Sparsity-aware transmit beamspace design for FDA-MIMO radar. Signal Process. 144, 99–103 (2018)

    Article  Google Scholar 

  14. P.C. Gong, W.Q. Wang, X.R. Wan, Adaptive weight matrix design and parameter estimation via sparse modeling for MIMO radar. Signal Process. 139, 1–11 (2017)

    Article  Google Scholar 

  15. Y. Gu, Y. Chou, J. Liu, Y. Ji, Moving horizon estimation for multirate systems with time-varying time-delays. J. Frankl. Inst. 356(4), 2325–2345 (2019)

    Article  MathSciNet  Google Scholar 

  16. Y. Gu, J. Liu, X. Li, Y. Chou, Y. Ji, State space model identification of multirate processes with time-delay using the expectation maximization. J. Frankl. Inst. 356(3), 1623–1639 (2019)

    Article  MathSciNet  Google Scholar 

  17. M.H. Li, X.M. Liu, The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique. Signal Process. 147, 23–34 (2018)

    Article  Google Scholar 

  18. M.H. Li, X.M. Liu, F. Ding, The filtering-based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle. Int. J. Adapt. Control Signal Process. 33(7), 1189–1211 (2019)

    Article  MathSciNet  Google Scholar 

  19. J.H. Li, W. Zheng, J.P. Gu, L. Hua, A recursive identification algorithm for Wiener nonlinear systems with linear state-space subsystem. Circuits Syst. Signal Process. 37(6), 2374–2393 (2018)

    Article  MathSciNet  Google Scholar 

  20. H.J. Liang, Z.X. Zhang, C.K. Ahn, Event-triggered fault detection and isolation of discrete-time systems based on geometric technique. IEEE Trans. Circuits Syst. II, Exp. Briefs. (2019). https://doi.org/10.1109/TCSII.2019.2907706

  21. H.J. Liang, Y.H. Zhang, T.W. Huang et al., Prescribed performance cooperative control for multiagent systems with input quantization. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2893645

  22. Y. Liu, W.E. Bai, Iterative identification of Hammerstein systems. Automatica 43(2), 346–354 (2007)

    Article  MathSciNet  Google Scholar 

  23. S.Y. Liu, F. Ding, L. Xu, T. Hayat, Hierarchical principle-based iterative parameter estimation algorithm for dual-frequency signals. Circuits Syst. Signal Process. 38(7), 3251–3268 (2019)

    Article  Google Scholar 

  24. N. Liu, S. Mei, D. Sun et al., Effects of charge transport materials on blue fluorescent organic light-emitting diodes with a host-dopant system. Micromachines 10(5), Article Number: 344 (2019). https://doi.org/10.3390/mi10050344

  25. H. Ma, J. Pan, F. Ding et al., Partially-coupled least squares based iterative parameter estimation for multivariable output-error-like autoregressive moving average systems. IET Control Theory Appl. 14, (2020). https://doi.org/10.1049/iet-cta.2019.0112

  26. H. Ma, J. Pan, L. Lv et al., Recursive algorithms for multivariable output-error-like ARMA systems. Mathematics 7(6), Article Number: 558 (2019). https://doi.org/10.3390/math7060558

  27. J. Pan, X. Jiang, X.K. Wan, W. Ding, A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems. Int. J. Control Autom. Syst. 15(3), 1189–1197 (2017)

    Article  Google Scholar 

  28. J. Pan, W. Li, H.P. Zhang, Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control. Int. J. Control Autom. Syst. 16(6), 2878–2887 (2018)

    Article  Google Scholar 

  29. L.B. Pence, K.H. Fathy, L.J. Stein, Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory. Automatica 47(11), 2420–2424 (2011)

    Article  MathSciNet  Google Scholar 

  30. W.X. Shi, N. Liu, Y.M. Zhou, X.A. Cao, Effects of postannealing on the characteristics and reliability of polyfluorene organic light-emitting diodes. IEEE Trans. Electron Devices 66(2), 1057–1062 (2019)

    Article  Google Scholar 

  31. J. Voros, Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones. IEEE Trans. Autom. Control 48(12), 2203–2206 (2003)

    Article  MathSciNet  Google Scholar 

  32. L.J. Wan, F. Ding, Decomposition- and gradient-based iterative identification algorithms for multivariable systems using the multi-innovation theory. Circuits Syst. Signal Process. 38(7), 2971–2991 (2019)

    Article  Google Scholar 

  33. X.K. Wan, Y. Li, C. Xia et al., A T-wave alternans assessment method based on least squares curve fitting technique. Measurement 86, 93–100 (2016)

    Article  Google Scholar 

  34. L.J. Wan, X.M. Liu, F. Ding et al., Decomposition least-squares-based iterative identification algorithms for multivariable equation-error autoregressive moving average systems. Mathematics 7(7), Article Number: 609 (2019). https://doi.org/10.3390/math7070609

  35. Y.J. Wang, F. Ding, A filtering based multi-innovation gradient estimation algorithm and performance analysis for nonlinear dynamical systems. IMA J. Appl. Math. 82(6), 1171–1191 (2017)

    Article  MathSciNet  Google Scholar 

  36. L. Wang, H. Liu, L.V. Dai, Y.W. Liu, Novel method for identifying fault location of mixed lines. Energies 11(6), Article Number: 1529 (2018). https://doi.org/10.3390/en11061529

  37. A.G. Wu, R.Q. Dong, F.Z. Fu, Weighted stochastic gradient identification algorithms for ARX models. IFAC 48(28), 1076–1081 (2015)

    Google Scholar 

  38. T.Z. Wu, X. Shi, L. Liao, C.J. Zhou, H. Zhou, Y.H. Su, A capacity configuration control strategy to alleviate power fluctuation of hybrid energy storage system based on improved particle swarm optimization. Energies 12(4), Article Number: 642 (2019). https://doi.org/10.3390/en12040642

  39. X.P. Xie, D. Yue, C. Peng, Relaxed real-time scheduling stabilization of discrete-time Takagi–Sugeno fuzzy systems via an alterable-weights-based ranking switching mechanism. IEEE Trans. Fuzzy Syst. 26(6), 3808–3819 (2018)

    Article  Google Scholar 

  40. X.P. Xie, D. Yue, C. Peng, Observer design of discrete-time fuzzy systems based on an alterable weights method. IEEE Trans. Cybern. (2018). https://doi.org/10.1109/TCYB.2018.2878419

  41. L. Xu, Application of the Newton iteration algorithm to the parameter estimation for dynamical systems. J. Comput. Appl. Math. 288, 33–43 (2015)

    Article  MathSciNet  Google Scholar 

  42. L. Xu, The damping iterative parameter identification method for dynamical systems based on the sine signal measurement. Signal Process. 120, 660–667 (2016)

    Article  Google Scholar 

  43. L. Xu, The parameter estimation algorithms based on the dynamical response measurement data. Adv. Mech. Eng. 9(11), 1–12 (2017). https://doi.org/10.1177/1687814017730003

    Article  Google Scholar 

  44. L. Xu, L. Chen, W.L. Xiong, Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration. Nonlinear Dyn. 79(3), 2155–2163 (2015)

    Article  MathSciNet  Google Scholar 

  45. L. Xu, W.L. Xiong, A. Alsaedi, T. Hayat, Hierarchical parameter estimation for the frequency response based on the dynamical window data. Int. J. Conrol Autom. 16(4), 1756–1764 (2018)

    Article  Google Scholar 

  46. X. Zhang, F. Ding, L. Xu et al., A hierarchical approach for joint parameter and state estimation of a bilinear system with autoregressive noise. Mathematics 7(4), Article Number: 356 (2019). https://doi.org/10.3390/math7040356

  47. X. Zhang, F. Ding, E.F. Yang, State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors. Int. J. Adapt. Control 33(7), 1157–1173 (2019)

    Article  MathSciNet  Google Scholar 

  48. X. Zhang, F. Ding, L. Xu et al., Highly computationally efficient state filter based on the delta operator. Int. J. Adapt. Control 33(6), 875–889 (2019)

    Article  MathSciNet  Google Scholar 

  49. X. Zhang, F. Ding, L. Xu et al., State filtering-based least squares parameter estimation for bilinear systems using the hierarchical identification principle. IET Control Theory Appl. 12(12), 1704–1713 (2018)

    Article  MathSciNet  Google Scholar 

  50. N. Zhao, Joint optimization of cooperative spectrum sensing and resource allocation in multi-channel cognitive radio sensor networks. Circuits Syst. Signal Process. 35(7), 2563–2583 (2016)

    Article  Google Scholar 

  51. N. Zhao, Y. Liang, Y. Pei, Dynamic contract incentive mechanism for cooperative wireless networks. IEEE Trans. Veh. Technol. 67(11), 10970–10982 (2018)

    Article  Google Scholar 

  52. X.L. Zhao, Z.Y. Lin, B. Fu, L. He, C.S. Li, Research on the predictive optimal PID plus second order derivative method for AGC of power system with high penetration of photovoltaic and wind power. J. Electr. Eng. Technol. 14(3), 1075–1086 (2019)

    Article  Google Scholar 

  53. X.L. Zhao, Z.Y. Lin, B. Fu, L. He, F. Na, Research on automatic generation control with wind power participation based on predictive optimal 2-degree-of-freedom PID strategy for multi-area interconnected power system. Energies 11(12), Article Number: 3325 (2018). https://doi.org/10.3390/en11123325

  54. Y. Zhao, G. Liu, R. David, Networked predictive control systems based on the Hammerstein model. IEEE Trans. Circuits Syst. II Express Br. 55(5), 469–473 (2008)

    Article  Google Scholar 

  55. X.L. Zhao, F. Liu, B. Fu, F. Na, Reliability analysis of hybrid multi-carrier energy systems based on entropy-based Markov model. Proc. Inst. Mech. Eng. O-J Risk 230(6), 561–569 (2016)

    Article  Google Scholar 

  56. N. Zhao, M.H. Wu, J.J. Chen, Android-based mobile educational platform for speech signal processing. Int. J. Electr. Eng. Educ. 54(1), 3–16 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 61473158, 61873326, 61203028) and the Natural Science Foundation of NJUPT (No. NY217063).

Author information

Authors and Affiliations

  1. Jiangsu Engineering Lab for IoT Intelligent Robots, School of Automation and Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, 210023, People’s Republic of China

    Jie Ding, Zhengxin Cao, Jiazhong Chen & Guoping Jiang

Authors
  1. Jie Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhengxin Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiazhong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guoping Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jie Ding.

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

Ding, J., Cao, Z., Chen, J. et al. Weighted Parameter Estimation for Hammerstein Nonlinear ARX Systems. Circuits Syst Signal Process 39, 2178–2192 (2020). https://doi.org/10.1007/s00034-019-01261-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-019-01261-4

Keywords

Search

Navigation