A Pretest Planning Method for Model Calibration for Nonlinear Systems

  • Yousheng ChenEmail author
  • Andreas Linderholt
  • Thomas Abrahamsson
  • Yuying Xia
  • Michael I. Friswell
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


With increasing demands on more flexible and lighter engineering structures, it has been more common to take nonlinearity into account. Model calibration is an important procedure for nonlinear analysis in structural dynamics with many industrial applications. Pretest planning plays a key role in the previously proposed calibration method for nonlinear systems, which is based on multi-harmonic excitation and an effective optimization routine. This paper aims to improve the pretest planning strategy for the proposed calibration method. In this study, the Fisher information matrix (FIM), which is calculated from the gradients with respect to the chosen parameters with unknown values, is used for determining the locations, frequency range, and the amplitudes of the excitations as well as the sensor placements. This pretest planning based model calibration method is validated by a structure with clearance nonlinearity. Synthetic test data is used to simulate the test procedure. Model calibration and K-fold cross validation are conducted for the optimum configurations selected from the pretest planning as well as three other configurations. The calibration and cross validation results show that a more accurate estimation of parameters can be obtained by using test data from the optimum configuration.


Nonlinear model calibration Pretest planning Clearance Multi-harmonic excitation Fisher information matrix 


  1. 1.
    Meyer, S., Link, M.: Modelling and updating of local non-linearities using frequency response residuals. Mech. Syst. Signal Process. 17(1), 219–226 (2003)CrossRefGoogle Scholar
  2. 2.
    Isasa, I., Hot, A., Cogan, S., Sadoulet-Reboul, E.: Model updating of locally non-linear systems based on multi-harmonic extended constitutive relation error. Mech. Syst. Signal Process. 25, 2413–2425 (2011)CrossRefGoogle Scholar
  3. 3.
    Kurta, M., Eritenb, M., McFarlandc, D., Bergmanc, L., Vakakis, A.: Methodology for model updating of mechanical components with local nonlinearities. J. Sound Vib. 357(24), 331–348 (2015)CrossRefGoogle Scholar
  4. 4.
    Kammer, D.C.: Sensor placement for on-orbit modal identification and correlation of large space structures. J. Guid. Control. Dyn. 14(2), 251–259 (1991)CrossRefGoogle Scholar
  5. 5.
    Papadimitriou, C., Beck, J.L.: Entropy-based optimal sensor location for structural model updating. J. Vib. Control. 6(5), 781–800 (2000)CrossRefGoogle Scholar
  6. 6.
    Penny, J.E.T., Friswell, M.I., Garvey, S.D.: Automatic choice of measurement locations for dynamic testing. AIAA J. 32(2), 407–414 (1994)CrossRefGoogle Scholar
  7. 7.
    Castro-Triguero, R., Friswell, M.I., Gallego Sevilla, R.: Optimal sensor placement for detection of non-linear structural behavior. In: Proceedings of the International Conference on Noise and Vibration Engineering (ISMA), Leuven (2014)Google Scholar
  8. 8.
    Yaghoubi, V., Chen, Y., Linderholt, A., Abrahamsson, T.: Locally non-linear model calibration using multi harmonic responses-applied on ecole de lyon non linear benchmark structure. In: Proceeding of the 31th the IMAC, Garden Grove (2013)Google Scholar
  9. 9.
    Cameron, T., Griffin, J.: An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems. ASME J. Appl. Mech. 56(1), 149–154 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ren, Y., Beards, C.F.: A new receptance-based perturbative multi-harmonic balance method for the calculation of the steady state response of non-linear systems. J. Sound Vib. 172(5), 593–604 (1994)CrossRefzbMATHGoogle Scholar
  11. 11.
    Ferreira, J.V., Ewins, D.J.: Algebraic nonlinear impedance equation using multi-harmonic describing function. In: Processing of the International Modal Analysis Conference, Orlando (1997)Google Scholar
  12. 12.
    Walter, E., Pronzato, L.: Identification of Parametric Models from Experimental Data. Springer, Heidelberg (1997)zbMATHGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2016

Authors and Affiliations

  • Yousheng Chen
    • 1
    Email author
  • Andreas Linderholt
    • 1
  • Thomas Abrahamsson
    • 2
  • Yuying Xia
    • 3
  • Michael I. Friswell
    • 4
  1. 1.Department of Mechanical EngineeringLinnaeus UniversityVäxjöSweden
  2. 2.Department of Applied MechanicsChalmers University of TechnologyGöteborgSweden
  3. 3.Department of Engineering, Design and MathematicsUniversity of the West of EnglandBristolUK
  4. 4.College of EngineeringSwansea UniversitySwanseaUK

Personalised recommendations