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An Auxiliary-Model-Based Stochastic Gradient Algorithm for Dual-Rate Sampled-Data Box–Jenkins Systems

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Abstract

This paper presents an identification algorithm for Box–Jenkins systems by combining the auxiliary model identification idea and the gradient search principle. The proposed algorithm can estimate all unknown parameters of the Box–Jenkins systems. Furthermore, to improve the convergence rate of the stochastic gradient algorithm, a modified stochastic gradient algorithm is given. The simulation results indicate that the proposed algorithm can work well.

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References

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

    Article  MathSciNet  Google Scholar 

  2. J. Chen, Y. Zhang, R.F. Ding, Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems. Math. Comput. Model. 52(9–10), 1428–1434 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. F. Ding, Several multi-innovation identification methods. Digit. Signal Process. 20(4), 1027–1039 (2010)

    Article  Google Scholar 

  4. F. Ding, Decomposition based fast least squares algorithm for output error systems. Signal Process. 93(5), 1235–1242 (2013)

    Article  Google Scholar 

  5. F. Ding, Coupled-least-squares identification for multivariable systems. IET Control Theory Appl. 7 (2013). doi:10.1049/iet-cta.2012.0171

  6. F. Ding, Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle. IET Control Theory Appl. 7 (2013). doi:10.1049/iet-cta.2012.0313

  7. F. Ding, Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Model. 37(4), 1694–1704 (2013)

    Article  MathSciNet  Google Scholar 

  8. F. Ding, Two-stage least squares based iterative estimation algorithm for CARARMA system modeling. Appl. Math. Model. 37(7), 4798–4808 (2013)

    Article  MathSciNet  Google Scholar 

  9. F. Ding, T. Chen, Combined parameter and output estimation of dual-rate systems using an auxiliary model. Automatica 40(10), 1739–1748 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. F. Ding, T. Chen, Parameter estimation of dual-rate stochastic systems by using an output error method. IEEE Trans. Autom. Control 50(9), 1436–1441 (2005)

    Article  MathSciNet  Google Scholar 

  11. F. Ding, T. Chen, Hierarchical identification of lifted state-space models for general dual-rate systems. IEEE Trans. Circuits Syst. I, Regul. Pap. 52(6), 1179–1187 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Ding, F. Ding, The residual based extended least squares identification method for dual-rate systems. Comput. Math. Appl. 56(6), 1479–1487 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. F. Ding, J. Ding, Least squares parameter estimation with irregularly missing data. Int. J. Adapt. Control Signal Process. 24(7), 540–553 (2010)

    MATH  Google Scholar 

  15. F. Ding, X.P. Liu, H.Z. Yang, Parameter identification and intersample output estimation for dual-rate systems. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 38(4), 966–975 (2008)

    Article  Google Scholar 

  16. F. Ding, X.P. Liu, G. Liu, Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Process. 89(10), 1883–1890 (2009)

    Article  MATH  Google Scholar 

  17. F. Ding, L. Qiu, T. Chen, Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica 45(2), 324–332 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. F. Ding, G. Liu, X.P. Liu, Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Trans. Autom. Control 55(8), 1976–1981 (2010)

    Article  MathSciNet  Google Scholar 

  19. F. Ding, X.P. Liu, G. Liu, Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digit. Signal Process. 20(3), 664–677 (2010)

    Article  Google Scholar 

  20. F. Ding, X.P. Liu, G. Liu, Multi-innovation least squares identification for linear and pseudo-linear regression models. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(3), 767–778 (2010)

    Article  Google Scholar 

  21. J. Ding, F. Ding, X.P. Liu, G. Liu, Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans. Autom. Control 56(11), 2677–2683 (2011)

    Article  MathSciNet  Google Scholar 

  22. F. Ding, G. Liu, X.P. Liu, Parameter estimation with scarce measurements. Automatica 47(8), 1646–1655 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  24. 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 

  25. J. Feng, Z. Wang, M. Zeng, Recursive robust filtering with finite-step correlated process noises and missing measurements. Circuits Syst. Signal Process. 30(6), 1355–1368 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. L.L. Han, F. Ding, Parameter estimation for multirate multi-input systems using auxiliary model and multi-innovation. J. Syst. Eng. Electron. 21(6), 1079–1083 (2010)

    Google Scholar 

  27. H.Q. Han, L. Xie, X.G. Liu, Hierarchical least squares based iterative identification for multivariable systems with moving average noises. Mathematical and Computer Modelling 51(9–10), 1213–1220 (2010)

    Article  MATH  Google Scholar 

  28. S.C. Kadu, M. Bhushan, R.D. Gudi, Optimal sensor network design for multirate systems. J. Process Control 18(6), 594–609 (2008)

    Article  Google Scholar 

  29. D. Li, S.L. Shah, T. Chen, Analysis of dual-rate inferential control systems. Automatica 38(6), 1053–1059 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  30. J.H. Li, F. Ding, G.W. Yang, Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. Math. Comput. Model. 55(3–4), 442–450 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  31. 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 

  32. Y.J. Liu, L. Xie et al., An auxiliary model based recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems. Proceedings of the Institution of Mechanical Engineers, Part I. Proc. Inst. Mech. Eng., Part I, J. Syst. Control Eng. 223(4), 445–454 (2009)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  34. Y.J. Liu, D.Q. Wang et al., Least-squares based iterative algorithms for identifying Box–Jenkins models with finite measurement data. Digit. Signal Process. 20(5), 1458–1467 (2010)

    Article  Google Scholar 

  35. 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 

  36. Y.J. Liu, F. Ding, Y. Shi, Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle. Circuits Syst. Signal Process. 31(6), 1985–2000 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  37. S. Nakamori, A. Hermoso-Carazo, J. Linares-Pérez, Suboptimal estimation of signals from uncertain observations using approximations of mixtures. Digit. Signal Process. 17(1), 4–16 (2007)

    Article  Google Scholar 

  38. M.F. Sägfors, H.T. Toivonen, H ∞ and LQG control of asynchronous sampled-data systems. Automatica 33(9), 1663–1668 (1997)

    Article  MathSciNet  Google Scholar 

  39. Y. Shi, F. Ding, T. Chen, Multirate crosstalk identification in xDSL systems. IEEE Trans. Commun. 54(10), 1878–1886 (2006)

    Article  Google Scholar 

  40. A.K. Tanc, A.H. Kayran, Maximum entropy power spectrum estimation for 2-D multirate systems. Circuits Syst. Signal Process. 31(1), 271–281 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  41. R.M. Udrea, D.N. Vizireanu, S. Ciochina, An improved spectral subtraction method for speech enhancement using a perceptual weighting filter. Digit. Signal Process. 18(4), 581–587 (2008)

    Article  Google Scholar 

  42. R.M. Udrea, D.N. Vizireanu, S. Ciochina, S. Halunga, Nonlinear spectral subtraction method for colored noise reduction using multi-band Bark scale. Signal Process. 88(5), 1299–1303 (2008)

    Article  MATH  Google Scholar 

  43. D.N. Vizireanu, S.V. Halunga, Simple, fast and accurate eight points amplitude estimation method of sinusoidal signals for DSP based instrumentation. J. Instrum. 7, P04001 (2012)

    Article  Google Scholar 

  44. D.N. Vizireanu, R.O. Preda, Is “five-point” estimation better than “three-point” estimation? Measurement 46(1), 840–842 (2013)

    Article  Google Scholar 

  45. J. Vörös, Modeling and identification of systems with backlash. Automatica 46(2), 369–374 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  46. D.Q. Wang, Least squares-based recursive and iterative estimation for output error moving average systems using data filtering. IET Control Theory Appl. 5(14), 1648–1657 (2011)

    Article  MathSciNet  Google Scholar 

  47. D.Q. Wang, F. Ding, Input-output data filtering based recursive least squares parameter estimation for CARARMA systems. Digit. Signal Process. 20(4), 991–999 (2010)

    Article  Google Scholar 

  48. D.Q. Wang, F. Ding, Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems. Digit. Signal Process. 20(3), 750–762 (2010)

    Article  Google Scholar 

  49. 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 

  50. 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 

  51. D.Q. Wang, G.W. Yang, R.F. Ding, Gradient-based iterative parameter estimation for Box–Jenkins systems. Comput. Math. Appl. 60(5), 1200–1208 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  52. W. Wang, F. Ding, J.Y. Dai, Maximum likelihood least squares identification for systems with autoregressive moving average noise. Appl. Math. Model. 36(5), 1842–1853 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  53. D.Q. Wang, R. Ding, X.Z. Dong, Iterative parameter estimation for a class of multivariable systems based on the hierarchical identification principle and the gradient search. Circuits Syst. Signal Process. 31(6), 2167–2177 (2012)

    Article  MathSciNet  Google Scholar 

  54. L. Xie, Y.J. Liu et al., Modelling and identification for non-uniformly periodically sampled-data systems. IET Control Theory Appl. 4(5), 784–794 (2010)

    Article  MathSciNet  Google Scholar 

  55. Z.N. Zhang, F. Ding, X.G. Liu, Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems. Comput. Math. Appl. 61(3), 672–682 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61273194), the University Graduate Scientific Research Innovation Program of Jiangsu Province, the Ph.D. Candidate Scientific Research Foundation of Jiangnan University (JUDCF11001), and the 111 Project (B12018).

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Authors and Affiliations

  1. Wuxi Professional College of Science and Technology, Wuxi, 214028, PR China

    Jing Chen

  2. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, 214122, PR China

    Jing Chen

  3. School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, PR China

    Rui Ding

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  1. Jing Chen
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  2. Rui Ding
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Correspondence to Rui Ding.

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Chen, J., Ding, R. An Auxiliary-Model-Based Stochastic Gradient Algorithm for Dual-Rate Sampled-Data Box–Jenkins Systems. Circuits Syst Signal Process 32, 2475–2485 (2013). https://doi.org/10.1007/s00034-013-9563-x

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  • DOI: https://doi.org/10.1007/s00034-013-9563-x

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