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Parameter Identification Methods for an Additive Nonlinear System

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Abstract

This paper deals with parameter identification methods for an additive nonlinear system with a preload nonlinearity and a piece-wise nonlinearity. By using a switching function, we transfer the model of the additive nonlinear system into an identification model, and propose a recursive least squares algorithm and two modified stochastic gradient (SG) algorithms to estimate the parameters of the identification model. The simulation results indicate that the proposed methods converge faster than the SG algorithm.

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References

  1. E.W. Bai, Identification of nonlinear additive FIR systems. Automatica 41(7), 1247–1253 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. E.W. Bai, K.S. Chan, Identification of an additive nonlinear system and its applications in generalized Hammerstein models. Automatica 44(2), 430–436 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Chen, R. Ding, An auxiliary-model-based stochastic gradient algorithm for dual-rate sampled-data Box–Jenkins systems. Circuits Syst. Signal Process. 32(5), 2475–2485 (2013)

    Article  MathSciNet  Google Scholar 

  4. J. Chen, F. Ding, Modified stochastic gradient algorithms with fast convergence rates. J. Vib. Control 17(9), 1281–1286 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Chen, X.L. Lu, R. Ding, Parameter identification of systems with preload nonlinearities based on the finite impulse response model and negative gradient search. Appl. Math. Comput. 219(5), 2498–2505 (2012)

    Article  MathSciNet  Google Scholar 

  6. J. Chen, X.L. Lu, R.F. Ding, Gradient-based iterative algorithm for Wiener systems with saturation and dead-zone nonlinearities. J. Vib. Control 20(4), 634–640 (2014)

    Article  MathSciNet  Google Scholar 

  7. C.J. Curtis, G.L. Simpson, Trends in bulk deposition of acidity in the UK, 1988–2007, assessed using additive models. Ecol. Indic. 37(Part B), 274–286 (2014)

    Article  Google Scholar 

  8. F. Ding, System Identification—New Theory and Methods (Science Press, Beijing, 2013)

    Google Scholar 

  9. F. Ding, Combined state and least squares parameter estimation algorithms for dynamic systems. Appl. Math. Model. 38(1), 403–412 (2014)

    Article  MathSciNet  Google Scholar 

  10. F. Ding, State filtering and parameter identification for state space systems with scarce measurements. Signal Process. (2014). doi:10.1016/j.sigpro.2014.03.031

  11. F. Ding, Hierarchical parameter estimation algorithms for multivariable systems using measurement information. Inf. Sci. (2014). doi:10.1016/j.ins.2014.02.103

  12. F. Ding, K.P. Deng, X.M. Liu, Decomposition based Newton iterative identification method for a Hammerstein nonlinear FIR system with ARMA noise. Circuits Syst. Signal Process. 33 (2014). doi:10.1007/s00034-014-9772-y

  13. J. Ding, C.X. Fan, J.X. Lin, Auxiliary model based parameter estimation for dual-rate output error systems with colored noise. Appl. Math. Model. 37(6), 4051–4058 (2013)

    Article  MathSciNet  Google Scholar 

  14. J. Ding, L.L. Han, X.M. Chen, Time series AR modeling with missing observations based on the polynomial transformation. Math. Comput. Model. 51(5–6), 527–536 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. F. Ding, Y. Gu, Performance analysis of the auxiliary model-based least-squares identification algorithm for one-step state-delay systems. Int. J. Comput. Math. 89(15), 2019–2028 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. F. Ding, Y. Gu, Performance analysis of the auxiliary model-based stochastic gradient parameter estimation algorithm for state-space systems with one-step state delay. Circuits Syst. Signal Process. 32(2), 585–599 (2013)

    Article  MathSciNet  Google Scholar 

  17. J. Ding, J.X. Lin, Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique. Circuits Syst. Signal Process. 33 (2014). doi:10.1007/s00034-013-9704-2

  18. F. Ding, X.M. Liu, H.B. Chen, G.Y. Yao, Hierarchical gradient based and hierarchical least squares based iterative parameter identification for CARARMA systems. Signal Process. 97, 31–39 (2014)

    Article  Google Scholar 

  19. F. Ding, X.P. Liu, G. Liu, Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 21(2), 215–238 (2011)

    Article  Google Scholar 

  20. C.W. Duan, R. Singh, Dynamic analysis of preload nonlinearity in a mechanical oscillator. J. Sound Vib. 301(3–5), 963–978 (2007)

    Article  Google Scholar 

  21. Y. Gu, F. Ding, Auxiliary model based least squares identification method for a state space model with a unit time-delay. Appl. Math. Model. 36(12), 5773–5779 (2012)

    Article  MathSciNet  Google Scholar 

  22. M.I. Krastanov, M. Quincampoix, On the small-time controllability of discontinuous piece-wise linear systems. Syst. Control Lett. 62(2), 218–223 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. J.H. Li, Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Appl. Math. Lett. 26(1), 91–96 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  24. Y.J. Liu, F. Ding, Y. Shi, An efficient hierarchical identification method for general dual-rate sampled-data systems. Automatica 50(3), 962–973 (2014)

    Article  MathSciNet  Google Scholar 

  25. Y.J. Liu, L. Yu et al., Multi-innovation extended stochastic gradient algorithm and its performance analysis. Circuits Syst. Signal Process. 29(4), 649–667 (2010)

    Article  MATH  Google Scholar 

  26. Y.J. Liu, J. Sheng, R.F. Ding, Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems. Comput. Math. Appl. 59(8), 2615–2627 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  27. Y.J. Liu, Y.S. Xiao, X.L. Zhao, Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model. Appl. Math. Comput. 215(4), 1477–1483 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. X.L. Luan, P. Shi, F. Liu, Stabilization of networked control systems with random delays. IEEE Trans. Ind. Electron. 58(9), 4323–4330 (2011)

    Article  Google Scholar 

  29. X.L. Luan, S.Y. Zhao, F. Liu, H-infinity control for discrete-time markov jump systems with uncertain transition probabilities. IEEE Trans. Autom. Control 58(6), 1566–1572 (2013)

    Article  MathSciNet  Google Scholar 

  30. P. Shi, X.L. Luan, F. Liu, H-infinity filtering for discrete-time systems with stochastic incomplete measurement and mixed delays. IEEE Trans. Ind. Electron. 59(6), 2732–2739 (2012)

    Article  Google Scholar 

  31. E.B. Sockett, D. Daneman et al., Factors patterns of residual insulin secretion during the first year of type I diabetes mellitus in children. Diabete 30, 453–459 (1987)

    Article  Google Scholar 

  32. J. Vörös, Parameter identification of Wiener systems with discontinuous nonlinearities. Syst. Control Lett. 44(5), 363–372 (2001)

    Article  MATH  Google Scholar 

  33. D.Q. Wang, F. Ding, Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 91(5), 1182–1189 (2011)

    Article  MATH  Google Scholar 

  34. D.Q. Wang, F. Ding, Hierarchical least squares estimation algorithm for Hammerstein–Wiener systems. IEEE Signal Process. Lett. 19(12), 825–828 (2012)

    Article  Google Scholar 

  35. D.Q. Wang, F. Ding, Y.Y. Chu, Data filtering based recursive least squares algorithm for Hammerstein systems using the key-term separation principle. Inf. Sci. 222, 203–212 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  36. D.Q. Wang, F. Ding, X.M. Liu, Least squares algorithm for an input nonlinear system with a dynamic subspace state space model. Nonlinear Dyn. 75(1–2), 49–61 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  37. W. Wang, T. Tang, Recursive least squares estimation algorithm applied to a class of linear-in-parameters output error moving average systems. Appl. Math. Lett. 29, 36–41 (2014)

    Article  MathSciNet  Google Scholar 

  38. C. Wang, T. Tang, Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique. Nonlinear Dyn. (2014). doi:10.1007/s11071-014-1338-9

  39. B. Yu, H. Fang et al., Identification of Hammerstein output-error systems with two-segment nonlinearities: algorithm and applications. Control Intell. Syst. 38(4), 194–201 (2010)

    MathSciNet  MATH  Google Scholar 

  40. Y. Zhang, Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods. Math. Comput. Model. 53(9–10), 1810–1819 (2011)

    Article  MATH  Google Scholar 

  41. Y. Zhang, G.M. Cui, Bias compensation methods for stochastic systems with colored noise. Appl. Math. Model. 35(4), 1709–1716 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  42. C. Zoppou, S. Roberts, M. Hegland, Spatial and temporal rainfall application using additive models. Anziam J. 42, 1599–1611 (2000)

    Google Scholar 

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Authors and Affiliations

  1. Wuxi Professional College of Science and Technology, Wuxi , 214028, People’s Republic of China

    Jing Chen & Yunxia Ni

Authors
  1. Jing Chen
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  2. Yunxia Ni
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Corresponding author

Correspondence to Jing Chen.

Additional information

This work was supported by the National Natural Science Foundation of China and supported by the Natural Science Foundation of Jiangsu Province (No. BK20131109).

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Chen, J., Ni, Y. Parameter Identification Methods for an Additive Nonlinear System. Circuits Syst Signal Process 33, 3053–3064 (2014). https://doi.org/10.1007/s00034-014-9793-6

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  • DOI: https://doi.org/10.1007/s00034-014-9793-6

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