Finite Element Model Updating Based on Least Squares Support Vector Machines

  • Yue Zhu
  • Lingmi Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5552)


Finite element model updating based on the design parameter is a kind of inverse problem in structural dynamics, whose theoretical foundation is using the features of the structure to be a function of design parameters. According to the first-order derivative of the features with respect to design parameters, iterative solution is made. This paper presents a new method which treats the model updating as a positive problem. Features are independent variables and design parameters are dependent variables. The least squares support vector machines (LS-SVM) is utilized as a map function. The objective value of the design parameters can be directly estimated due to the generalization character of the LS-SVM. The method avoids solving the complicated nonlinear optimization problem which is difficult in the reported methods. Finite element model updating based on LS-SVM about the GARTEUR aircraft model is studied. Simulation results show the errors of design parameters and modal frequencies are less than 2% and 1%, respectively.


Support Vector Machine Inverse Problem Finite Element Model Design Parameter Little Square Support Vector Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Mottershead, J.E., Friswell, M.I.: Model Updating in Structural Dynamics. Journal of Sound and Vibration 167, 347–375 (1993)CrossRefzbMATHGoogle Scholar
  2. 2.
    Zhang, L.M.: A Unified Approach & Assessment of Analytical Model Updating using Dynamic Test Data. In: Proceedings of 13th IMAC, USA, pp. 532–537 (1995)Google Scholar
  3. 3.
    VAPNIK, V.N.: Statistical Learning Theory. Wiley, New York (1998)Google Scholar
  4. 4.
    Montgomery, D.C.: Design and Analysis of Experiments. Wiley, New York (2003)Google Scholar
  5. 5.
    Vapnik, V.N.: The Nature Statistical Learning Theory. Springer, Berlin (1995)CrossRefzbMATHGoogle Scholar
  6. 6.
    Balmes, E.: GARTEUR Group on Ground Vibration Testing, Results from The Test of a Single Structure by 12 Laboratories in Europe [A]. In: Proceedings of 15th IMAC, USA, pp. 1346–1352 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yue Zhu
    • 1
  • Lingmi Zhang
    • 1
  1. 1.College of Aerospace EngineeringNanjing University of Aeronautics & AstronauticsNanjingChina

Personalised recommendations