Parameter estimation and model selection for a class of hysteretic systems using Bayesian inference

Mechanical Systems and Signal Processing

Volumn 32, Issue , 2012, Pages 153-169

  Worden, K ^a   Hensman, J J ^b  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Bayesian inference; Bouc Wen hysteresis; Deviance Information Criterion (DIC); Duffing oscillator; Markov Chain Monte Carlo (MCMC); Nonlinear system identification

Indexed keywords

APPROPRIATE MODELS; BAYESIAN APPROACHES; BAYESIAN INFERENCE; BOUC WEN MODEL; CONFIDENCE BOUNDS; CONFIDENCE INTERVAL; DIFFERENTIAL EVOLUTION ALGORITHMS; DUFFING OSCILLATOR; HYSTERETIC SYSTEMS; IDENTIFICATION SCHEME; INDIVIDUAL MODELS; INFORMATION CRITERION; INFORMED DECISION; MARKOV CHAIN MONTE CARLO; MODEL PREDICTION; MODEL SELECTION; MODEL SELECTION CRITERIA; NEW APPLICATIONS; OBSERVED DATA; OPTIMISATIONS; PARAMETER ESTIMATE; POINT ESTIMATE; SIMULATED SYSTEM;

BAYESIAN NETWORKS; DAMPING; FORECASTING; HYSTERESIS; INFERENCE ENGINES; MODEL STRUCTURES; NONLINEAR SYSTEMS; OPTIMIZATION; OSCILLATORS (MECHANICAL); PROBABILITY DENSITY FUNCTION; STRUCTURAL DYNAMICS;

PARAMETER ESTIMATION;

EID: 84865011898     PISSN: 08883270     EISSN: 10961216     Source Type: Journal    
DOI: 10.1016/j.ymssp.2012.03.019     Document Type: Article

References (36)

1. L. Ljung System Identification: Theory for the User second ed. 1999 Prentice-Hall
2. T. Soderstrom, and P. Stoica System Identification New ed. 1994 Prentice-Hall
3. I.J. Leontaritis, and S.A. Billings Input-output parametric models for nonlinear systems. Part I: deterministic nonlinear systems Int. J. Control: Deter. Nonlinear Syst. 41 1985 303 328
4. I.J. Leontaritis, and S.A. Billings Input-output parametric models for nonlinear systems. Part II: stochastic nonlinear systems Int. J. Control 41 1985 329 344
5. M.J.C. Mackay Information Theory, Inference and Learning Algorithms 2003 Cambridge University Press
6. C.M. Bishop Pattern Recognition and Machine Learning 2007 Springer
7. C.M. Bishop Neural Networks for Pattern Recognition 1998 Oxford University Press
8. C.E. Rasmussen, C.K.I. Williams, Gaussian Processes for Machine Learning, MIT Press.
9. J.D. Collins, G.C. Hart, T.K. Hasselman, and B. Kennedy Statistical identification of structures AIAA J. 12 1974 185 190
10. J.L. Beck, Statistical system identification of structures, in: Proceedings of the Fifth International Conference on Structural Safety and Reliability, ASCE, New York, 1989, pp. 1395-1402.
11. J.L. Beck, and L.S. Katafygiotis Updating models and their uncertainties. I: Bayesian statistical framework ASCE J. Eng. Mech. 124 1998 455 461
12. J.L. Beck, and S.-K. Au Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation ASCE J. Eng. Mech. 128 2002 380 391
13. J.L. Beck, and K.-V. Yuen Model selection using response measurements: Bayesian probabilistic approach ASCE J. Eng. Mech. 130 2004 192 203
14. M. Muto, and J.L. Beck Bayesian updating and model class selection for hysteretic structural models using stochastic simulation J. Vib. Control 14 2008 7 34
15. M. Girolami Bayesian inference for differential equations Theoret. Comput. Sci. 408 2008 4 16
16. B. Calderhead, M. Girolami, D.J. Higham, Is It Safe to Go Out Yet? Statistical Inference in a Zombie Outbreak Model, University of Strathclyde, Department of Mathematics and Statistics, 2010, Preprint.
17. Y. Bard Nonlinear Parameter Estimation 1974 Academic Press
18. J. Ching, J.L. Beck, and K.A. Porter Bayesian state and parameter estimation of uncertain dynamical systems Probab. Eng. Mech. 21 2006 81 96
19. S.J. Ghosh, C.S. Manohar, and D. Roy A sequential importance sampling filter with a new proposal distribution for state and parameter estimation of nonlinear dynamical systems Proc. R. Soc.: Ser. A 464 2008 25 47
20. S.J. Li, Y. Suzuki, and M. Noori Identification of hysteretic systems with slip using a bootstrap filter Mech. Syst. Signal Process. 18 2004 781 795
21. E.N. Chatzi, A.W. Smyth, and S.F. Masri Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty Struct. Safety 32 2010 326 337
22. K.-V. Yuen Bayesian Methods for Structural Dynamics and Civil Engineering 2010 John Wiley and Sons
23. K. Worden, and G.R. Tomlinson Nonlinearity in Structural Dynamics: Detection, Modelling and Identification 2001 Institute of Physics
24. G. Kerschen, K. Worden, J.-C. Golinval, and A.K. Vakakis Past, present and future of nonlinear system identification in structural dynamics Mech. Syst. Signal Process. 20 2006 505 592
25. A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin Bayesian Data Analysis second ed. 2004 Chapman and Hall, CRC
26. G. Kerschen, J.-C. Golinval, and F.M. Hemez Bayesian model screening for the identification of nonlinear mechanical structures ASME J. Vib. Acoust. 125 2003 389 397
27. The Mathworks 2004. Matlab v7.
28. W.h. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery Numerical Recipes: The Art of Scientific Computing third ed. 2007 Cambridge University Press
29. A. Patil, D. Huard, and C.J. Fonnesbeck PyMC: Bayesian stochastic modelling in Python J. Statist. Software 35 2010 81
30. A. Visitin Differential Models of Hysteresis 1994 Springer Berlin
31. R. Bouc, Forced vibration of mechanical system with hysteresis, in: Proceedings of the Fourth Conference on Nonlinear Oscillation, Prague, Czechoslovakia, 1967.
32. Y. Wen Method for random vibration of hysteretic systems ASCE J. Eng. Mech. Div. XX 1976 249 263
33. F. Ikhouane, and J. Rodellar Systems with Hysteresis: Analysis, Identification and Control using the Bouc-Wen Model 2007 Wiley-Blackwell
34. B.P. Deacon, K. Worden, Identification of hysteretic systems using genetic algorithms, in: Proceedings of the EUROMECH - Second European Nonlinear Oscillations Conference, Prague, 1996, pp. 55-58.
35. A. Kyprianou, K. Worden, and M. Panet Identification of hysteretic systems using the differential evolution algorithm J. Sound Vib. 248 2001 289 314
36. M. Yar, and J.K. Hammond Parameter estimation for hysteretic systems J. Sound Vib. 117 1987 161 172