Advertisement

Interval Uncertainty Analysis Using CANDECOMP/PARAFAC Decomposition

  • Jinchun Lan
  • Zhike PengEmail author
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

A new interval uncertain analysis method is proposed based on CANDECOMP/PARAFAC (CP) decomposition. In interval uncertain analysis of structural dynamics, we need to evaluate the lower and upper bounds of uncertain responses. To avoid the overestimation of the lower and upper bounds caused by the wrapping effect, the CP decomposition is used to approximate the interval functions. In CP decomposition, the interval functions are represented with only a few terms, and the energy of each term usually decays fast. In this way, we can achieve shaper and tighter bounds of the interval functions. CP decomposition can be obtained using different methods. Some numerical examples are demonstrated to compare the method with other methods and illustrate the effectiveness of this method.

Keywords

Interval uncertainty quantification Dynamical response CANDECOMP/PARAFAC decomposition Tensor decomposition Low-rank decomposition 

References

  1. 1.
    Chandrashekhar, M., Ganguli, R.: Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic. J. Sound Vib. 326, 939–957 (2009)CrossRefGoogle Scholar
  2. 2.
    Zhang, X.-M., Ding, H.: Design optimization for dynamic response of vibration mechanical system with uncertain parameters using convex model. J. Sound Vib. 318, 406–415 (2008)CrossRefGoogle Scholar
  3. 3.
    Qiu, Z.P., Lihong, M., Xiaojun, W.: Interval analysis for dynamic response of nonlinear structures with uncertainties (in Chinese). Chin. J. Theor. Appl. Mech. 38, 645–651 (2006)Google Scholar
  4. 4.
    Kaminski Jr., J., Riera, J., de Menezes, R., Miguel, L.F.: Model uncertainty in the assessment of transmission line towers subjected to cable rupture. Eng. Struct. 30, 2935–2944 (2008)CrossRefGoogle Scholar
  5. 5.
    Ding, C.-T., Yang, S.-X., Gan, C.-B.: Input torque sensitivity to uncertain parameters in biped robot. Acta Mech. Sinica 29, 452–461 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Guo, S.-X., Li, Y.: Non-probabilistic reliability method and reliability-based optimal LQR design for vibration control of structures with uncertain-but-bounded parameters. Acta Mech. Sinica 29, 864–874 (2013)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Wang, J., Qiu, Z.-P.: Fatigue reliability based on residual strength model with hybrid uncertain parameters. Acta Mech. Sinica 28, 112–117 (2012)CrossRefzbMATHGoogle Scholar
  8. 8.
    Jia, Y.-H., Hu, Q., Xu, S.-J.: Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters, Acta Mech. Sinica 112–124 (2014)Google Scholar
  9. 9.
    Moens, D., Vandepitte, D.: Interval sensitivity theory and its application to frequency response envelope analysis of uncertain structures. Comput. Methods Appl. Mech. Eng. 196, 2486–2496 (2007)CrossRefzbMATHGoogle Scholar
  10. 10.
    Impollonia, N., Muscolino, G.: Interval analysis of structures with uncertain-but-bounded axial stiffness. Comput. Methods Appl. Mech. Eng. 200, 1945–1962 (2011)CrossRefzbMATHGoogle Scholar
  11. 11.
    Qiu, Z.: Convex models and interval analysis method to predict the effect of uncertain-but-bounded parameters on the buckling of composite structures. Comput. Methods Appl. Mech. Eng. 194, 2175–2189 (2005)CrossRefzbMATHGoogle Scholar
  12. 12.
    Qiu, Z., Wang, X.: Parameter perturbation method for dynamic responses of structures with uncertain-but-bounded parameters based on interval analysis. Int. J. Solids Struct. 42, 4958–4970 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Qiu, Z., Ma, L., Wang, X.: Non-probabilistic interval analysis method for dynamic response analysis of nonlinear systems with uncertainty. J. Sound Vib. 319, 531–540 (2009)CrossRefGoogle Scholar
  14. 14.
    Wu, J., Zhang, Y., Chen, L., Luo, Z.: A Chebyshev interval method for nonlinear dynamic systems under uncertainty. Appl. Math. Model. 37, 4578–4591 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Wu, J., Luo, Z., Zhang, Y., Zhang, N.: An interval uncertain optimization method for vehicle suspensions using Chebyshev metamodels. Appl. Math. Model. 38, 3706–3723 (2014)CrossRefGoogle Scholar
  16. 16.
    Ganapathysubramanian, B., Zabaras, N.: Sparse grid collocation schemes for stochastic natural convection problems. J. Comput. Phys. 225, 652–685 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Lars, G., Daniel, K., Christine, T.: A literature survey of low-rank tensor approximation techniques. GAMM-Mitteilungen 36, 53–78 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51, 455–500 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Khoromskij, B.N.: Tensor numerical methods for multidimensional PDES: theoretical analysis and initial applications. ESAIM Proc. Surv. 48, 1–28 (2015)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2016

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanical System and VibrationSchool of Mechanical Engineering, Shanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations