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Acta Mechanica Solida Sinica

, Volume 32, Issue 1, pp 105–119 | Cite as

A PCA-Based Approach for Structural Dynamics Model Updating with Interval Uncertainty

  • Xueqian ChenEmail author
  • Zhanpeng Shen
  • Xin’en Liu
Article
  • 65 Downloads

Abstract

Uncertainty widely exists in engineering structures, making it necessary to update the finite element (FE) modeling with uncertainty. An updating approach for the FE model of structural dynamics with interval uncertain parameters is proposed in this work. Firstly, the correlations between the updating parameters and the output qualities of interest are uncorrelated by the principal component analysis (PCA), and the massive samples of major principal components are obtained using the Monte Carlo simulation. Then, the massive samples of updating parameters and output qualities are obtained by reversing transformation in the PCA, and the new samples of updating parameters are re-chosen by combining the massive samples with the experimental intervals of the qualities of interest. Next, the 95% CI of the updating parameters is estimated by the nonparametric kernel density estimation approach, which are regarded as the intervals of updating parameters. Lastly, the proposed approach is validated in simple rectangular plates and the transport mirror system. The updating results evidently demonstrate the feasibility and reliability of the proposed approach.

Keywords

PCA-based approach Interval uncertainty Model updating Kernel density estimation 

Notes

Acknowledgements

This work was supported by the Science Challenge Project (Grant No. TZ2018007), the National Key Research and Development Program of China (Grant No. 2016YFB0201005) and the National Natural Science Foundation of China (Grant No. 11472256).

References

  1. 1.
    Mottershead J, Friswell M. Model updating in structural dynamics: a survey. J Sound Vib. 1993;167(2):347–75.zbMATHGoogle Scholar
  2. 2.
    Fritzen CP, Jennewein D, Kiefer T. Damage detection based on model updating methods. Mech Syst Signal Process. 1998;11(1):163–86.Google Scholar
  3. 3.
    Ren R, Beards CF. Identification of ‘effective’ linear joints using coupling and joint identification techniques. ASME J Vib Acoust. 1998;121:331–8.Google Scholar
  4. 4.
    Li WL. A new method for structural model updating and joint stiffness identification. Mech Syst Signal Process. 2002;16(1):155–67.Google Scholar
  5. 5.
    Bakir PG, Reynders E, Roeck GD. Sensitivity-based finite element model updating using constrained optimization with a trust region algorithm. J Sound Vib. 2007;305:211–25.Google Scholar
  6. 6.
    Mottershead J, Link M, Friswell M. The sensitivity method in finite element model updating: a tutorial. Mech Syst Signal Process. 2011;25:2275–96.Google Scholar
  7. 7.
    Oberkampf WL, Roy CJ. Verification and validation in scientific computing. Cambridge: Cambridge University Press; 2010. p. 1–15.zbMATHGoogle Scholar
  8. 8.
    Simoen Ellen, De Roeck Guido, Lombaert Geert. Dealing with uncertainty in model updating for damage assessment: a review. Mech Syst Signal Process. 2015;56–57:123–49.Google Scholar
  9. 9.
    Friswell M. The adjustment of structural parameters using a minimum variance estimator. Mech Syst Signal Process. 1989;3(2):143–55.zbMATHGoogle Scholar
  10. 10.
    Beck JL, Katafygiotis LS. Updating models and their uncertainties i: Bayesian statistical framework. J Eng Mech. 1998;124(4):455–61.Google Scholar
  11. 11.
    Beck JL, Au SK. Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation. J Eng Mech. 2002;128(4):380–91.Google Scholar
  12. 12.
    Kennedy MC, Hagan AO’. Bayesian calibration of computer models. J R Stat Soc Ser B Stat Methodol. 2001;63(3):425–64.MathSciNetzbMATHGoogle Scholar
  13. 13.
    Wan HP, Ren WX. Stochastic model updating utilizing Bayesian approach and Gaussian process model. Mech Syst Signal Process. 2016;70–71:245–68.Google Scholar
  14. 14.
    Khodaparast H, Mottershead J, Friswell M. Perturbation methods for the estimation of parameter variability in stochastic model updating. Mech Syst Signal Process. 2008;22(8):1751–73.Google Scholar
  15. 15.
    Husain NA, Khodaparast H, Ouyang HH. Parameter selection and stochastic model updating using perturbation methods with parameter weighting matrix assignment. Mech Syst Signal Process. 2012;32:135–52.Google Scholar
  16. 16.
    Hua XG, Wen Q, Ni YQ. Assessment of stochastically updated finite element models using reliability indicator. Mech Syst Signal Process. 2017;82:217–29.Google Scholar
  17. 17.
    Fang SE, Ren WX, Perera R. A stochastic model updating method for parameter uncertainty quantification based on response surface models and Monte Carlo simulation. Mech Syst Signal Process. 2012;33(4):83–96.Google Scholar
  18. 18.
    Rao SS, Berke L. Analysis of uncertain structural systems using interval analysis. AIAA J. 1997;35(4):727–35.zbMATHGoogle Scholar
  19. 19.
    Zhang DQ, Han X, Jiang C. The interval PHI2 analysis method for time-dependent reliability. Sci Sin. 2015;45(5):054601.Google Scholar
  20. 20.
    Liu J, Meng X, Jiang C. Time-domain Galerkin method for dynamic load identification. Int J Numer Methods Eng. 2016;105(8):620–40.MathSciNetGoogle Scholar
  21. 21.
    Li SL, Li H, Ou JP. Model updating for uncertain structures with interval parameters. In: Proceedings of the Asia-Pacific workshop on structural health monitoring, Yokohama, Japan; 2006.Google Scholar
  22. 22.
    Jiang C, Han X, Liu GR. Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval. Comput Methods Appl Mech Eng. 2007;196(49–52):4791–800.zbMATHGoogle Scholar
  23. 23.
    Qiu ZP, Wang XJ, Friswell M. Eigenvalue bounds of structures with uncertain-but-bounded parameters. J Sound Vib. 2005;282(1):297–312.MathSciNetzbMATHGoogle Scholar
  24. 24.
    Gabriele S, Valente C. An interval-based technique for FE model updating. Int J Reliab Saf. 2009;3(1–3):79–103.Google Scholar
  25. 25.
    Khodaparast H, Mottershead J, Badcock K. Interval model updating with irreducible uncertainty using the Kriging predictor. Mech Syst Signal Process. 2011;25(4):1204–26.Google Scholar
  26. 26.
    Fang SE, Zhang QH, Ren WX. An interval model updating strategy using interval response surface models. Mech Syst Signal Process. 2015;60–61:909–27.Google Scholar
  27. 27.
    Jolliffe I. Principal component analysis. New York: Springer; 1986.zbMATHGoogle Scholar
  28. 28.
    Jackson J. A user’s guide to principal components. New York: Wiley; 1991.zbMATHGoogle Scholar
  29. 29.
    Silverman B. Density estimation for statistics and data analysis. New York: Chapman & Hall/CRC; 1986.zbMATHGoogle Scholar
  30. 30.
    McFarland John, Mahadevan Sankaran. Error and variability characterization in structural dynamics modeling. Comput Methods Appl Mech Eng. 2008;197(29):2621–31.zbMATHGoogle Scholar
  31. 31.
    Wang GG. Adaptive response surface method using inherited Latin hypercube design points. J Mech Des. 2003;125(2):210–20.Google Scholar
  32. 32.
    Husain NA, Khodaparast H, Ouyang HH. Parameter selections for stochastic uncertainty in dynamic models of simple and complicated structures. In: Proceedings of the 10th international conference on recent advances in structural dynamics, Southampton, UK: University of Southampton; 2010.Google Scholar
  33. 33.
    Chen XJ, Wang MC, Wu WK. Structural design of beam transport system in SGIII facility target area. Fusion Eng Des. 2014;89(12):3095–100.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2018

Authors and Affiliations

  1. 1.Institute of Systems EngineeringChina Academy of Engineering Physics(CAEP)MianyangChina
  2. 2.Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan ProvinceMianyangChina

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