Polynomial Chaos in Bootstrap Filtering for System Identification

  • P. RangarajEmail author
  • Abhijit Chaudhuri
  • Sayan Gupta
Conference paper


The objective of this chapter is to develop a computationally efficient approach for system identification. An algorithm, the bootstrap filter in conjunction with polynomial chaos expansion, is proposed for identification of system parameters. The central idea of the proposed method is the introduction of response through polynomial chaos expansion in the filtering algorithm. Appreciable performance of the proposed algorithm is been provided by considering the problem of the identification of the properties of a single degree of freedom system.


System identification Polynomial chaos Spectral representation Particle filter Probabilistic collocation 


  1. 1.
    Cameron RH, Martin WT (1947) The orthogonal development of nonlinear functionals in series of Fourier–Hermite functionals. Ann Math 48:385–392MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Desai A, Sarkar S (2010) Analysis of a nonlinear aeroelastic system with parametric uncertainties using polynomial chaos expansion. Math Probl Eng 2010:1–2. Article ID 379472Google Scholar
  3. 3.
    Doucet A, de Freitas JF, Gordon NJ (2001) An introduction to sequential Monte Carlo methods. In: Sequential Monte Carlo methods in practice. Springer, New YorkGoogle Scholar
  4. 4.
    Ghanem R, Spanos P (1991) Stochastic finite elements: a spectral approach. Springer, New YorkzbMATHCrossRefGoogle Scholar
  5. 5.
    Ghanem R, Spanos P (1993) A stochastic Galerkin expansion for nonlinear random vibration analysis. Probab Eng Mech 8:255–264CrossRefGoogle Scholar
  6. 6.
    Gordon NJ, Salmond DJ, Smith AFM (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc F 140:107–113Google Scholar
  7. 7.
    Grewal MS, Andrews AP (2001) Kalman filtering: theory and practice using matlab, 2nd edn. Wiley, New YorkGoogle Scholar
  8. 8.
    Kalman RE (1960) A new approach to linear filtering and prediction problems. ASME J Basic Eng 82:34–45Google Scholar
  9. 9.
    Morla L (2011) Parameter estimation in vibrating structures using particle filtering algorithm vibration analysis. M.Tech thesis, Indian Institute of Technology, MadrasGoogle Scholar
  10. 10.
    Nasrellah HA, Manohar CS (2010) A particle filtering approach for structural system identification in vehicle structure interaction problems. J Sound Vib 329:1289–1309CrossRefGoogle Scholar
  11. 11.
    Wiener N (1938) The homogeneous chaos. Am J Math 60(4):897–936MathSciNetCrossRefGoogle Scholar
  12. 12.
    Xiu D, Karniadakis GE (2002) The Weiner-Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24:619–644MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer India 2013

Authors and Affiliations

  1. 1.Department of Applied MechanicsIndian Institute of Technology MadrasChennaiIndia

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