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Fuzzy Finite Element Model Updating Using Metaheuristic Optimization Algorithms

  • I. Boulkaibet
  • T. Marwala
  • M. I. Friswell
  • H. H. Khodaparast
  • S. Adhikari
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

In this paper, a non-probabilistic method based on fuzzy logic is used to update finite element models (FEMs). Model updating techniques use the measured data to improve the accuracy of numerical models of structures. However, the measured data are contaminated with experimental noise and the models are inaccurate due to randomness in the parameters. This kind of aleatory uncertainty is irreducible, and may decrease the accuracy of the finite element model updating process. However, uncertainty quantification methods can be used to identify the uncertainty in the updating parameters. In this paper, the uncertainties associated with the modal parameters are defined as fuzzy membership functions, while the model updating procedure is defined as an optimization problem at each α-cut level. To determine the membership functions of the updated parameters, an objective function is defined and minimized using two metaheuristic optimization algorithms: ant colony optimization (ACO) and particle swarm optimization (PSO). A structural example is used to investigate the accuracy of the fuzzy model updating strategy using the PSO and ACO algorithms. Furthermore, the results obtained by the fuzzy finite element model updating are compared with the Bayesian model updating results.

Keywords

Finite Element Model updating Fuzzy logic Fuzzy membership function Ant colony optimization Particle swarm optimization Bayesian 

References

  1. 1.
    Bhatti, M.A.: Fundamental Finite Element Analysis and Applications: with Mathematica and Matlab Computations. Hoboken, New Jersey. Wiley (2005)Google Scholar
  2. 2.
    Onãte, E.: Structural analysis with the finite element method. Linear statics. In: Basis and Solids, vol. 1. Barcelona, Springer (2009)Google Scholar
  3. 3.
    Rao, S.S.: The Finite Element Method in Engineering, 4th edn. Elsevier Butterworth Heinemann, Burlington (2004)Google Scholar
  4. 4.
    Friswell, M.I., Mottershead, J.E.: Finite Element Model Updating in Structural Dynamics. Kluwer Academic Publishers (1995)Google Scholar
  5. 5.
    Marwala, T.: Finite Element Model Updating Using Computational Intelligence Techniques. Springer Verlag, London, UK (2010)CrossRefMATHGoogle Scholar
  6. 6.
    H.H. Khodaparast. Stochastic finite element model updating and its application in aeroelasticity. Ph.D. Thesis, Department of Civil Engineering, University of Liverpool, (2010).Google Scholar
  7. 7.
    Marwala, T., Boulkaibet, I., Adhikari, S.: Probabilistic Finite ElementModel Updating Using Bayesian Statistics: Applications to Aeronautical and Mechanical Engineering. Pondicherry, India, John Wiley & Sons (2016)CrossRefGoogle Scholar
  8. 8.
    I. Boulkaibet, T. Marwala, M. I. Friswell, and S. Adhikari. An adaptive markov chain monte carlo method for bayesian finite element model updating. In Special Topics in Structural Dynamics, vol. 6, pp. 55–65. Springer International Publishing, 2016.Google Scholar
  9. 9.
    I. Boulkaibet, L. Mthembu, T. Marwala, M. I. Friswell and S. Adhikari. Finite Element Model Updating Using Hamiltonian Monte Carlo Techniques, Inverse Problems in Science and Engineering, 2016.Google Scholar
  10. 10.
    Boulkaibet, I., Mthembu, L., Marwala, T., Friswell, M.I., Adhikari, S.: finite element model updating using the shadow hybrid Monte Carlo technique. Mech. Syst. Signal Process. 52, 115–132 (2015)CrossRefGoogle Scholar
  11. 11.
    Moore, R.: Interval analysis. Prentice Hall, Englewood Cliffs (1966)MATHGoogle Scholar
  12. 12.
    Moens, D., Vandepitte, D.: An interval finite element approach for the calculation of envelope frequency response functions. Int. J. Numer. Methods Eng. 61, 2480–2507 (2004)CrossRefMATHGoogle Scholar
  13. 13.
    Khodaparast, H.H., Mottershead, J.E., Badcock, K.J.: Interval model updating with irreducible uncertainty using the Kriging predictor. Mech. Syst. Signal Process. 25(4), 1204–1226 (2011)CrossRefGoogle Scholar
  14. 14.
    Zadeh, L.A.: Fuzzy sets. Inf. Control. 8(3), 338–353 (1965)CrossRefMATHGoogle Scholar
  15. 15.
    Moens, D., Vandepitte, D.: Recent advances in non-probabilistic approaches for non-deterministic dynamic finite element analysis. Arch. Comput. Methods Eng. 13(3), 389–464 (2006)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Chen, L., Rao, S.S.: Fuzzy finite-element approach for the vibration analysis of imprecisely-defined systems. Finite Elem. Anal. Design. 27(1), 69–83 (1997)CrossRefMATHGoogle Scholar
  17. 17.
    Moens, D., Vandepitte, D.: A fuzzy finite element procedure for the calculation of uncertain frequency response functions of damped structures: part 1 procedure. J. Sound Vib. 288(3), 431–462 (2005)CrossRefGoogle Scholar
  18. 18.
    Erdogan, Y.S., Bakir, P.G.: Inverse propagation of uncertainties in finite element model updating through use of fuzzy arithmetic. Eng. Appl. Artif. Intell. 26(1), 357–367 (2013)CrossRefGoogle Scholar
  19. 19.
    H.H. Khodaparast, Y. Govers, S. Adhikari, M. Link, M. I. Friswell, J. E. Mottershead, and J. Sienz. Fuzzy model updating and its application to the DLR AIRMOD test structure. Proceeding of ISMA 2014 including USD 2014, (2014).Google Scholar
  20. 20.
    Liu, Y., Duan, Z.: Fuzzy finite element model updating of bridges by considering the uncertainty of the measured modal parameters. Sci. China Technol. Sci. 55(11), 3109–3117 (2012)CrossRefGoogle Scholar
  21. 21.
    Adhikari, S., Khodaparast, H.H.: A spectral approach for fuzzy uncertainty propagation in finite element analysis. Fuzzy Sets Syst. 243, 1–24 (2014)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Nguyen, H.T.: A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64(2), 369–380 (1978)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Qiu, Z., Hu, J., Yang, J., Lu, Q.: Exact bounds for the sensitivity analysis of structures with uncertain-but-bounded parameters. Appl. Math. Model. 32(6), 1143–1157 (2008)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Socha, K., Blum, C.: An ant colony optimization algorithm for continuous optimization: application to feed-forward neural network training. Neural Comput. & Applic. 16(3), 235–247 (2007)CrossRefGoogle Scholar
  25. 25.
    I.C.J. Riadi. Cognitive Ant colony optimization: A new framework in swarm intelligence, Doctoral dissertation, University of Salford, (2014).Google Scholar
  26. 26.
    J. Kcnncdy, R.C. Eberhart, Particle swarm optimization, Proceedings of the IEEE International Joint Conference on Neural Networks, 4:1942–1948, (1995).Google Scholar
  27. 27.
    I. Boulkaibet, L. Mthembu, F. De Lima Neto and T. Marwala. Finite Element Model Updating Using Fish School Search Optimization Method, 1st BRICS & 11th CBIC Brazilian Congress on Computational Intelligence, Brazil, 2013.Google Scholar
  28. 28.
    Boulkaibet, I., Mthembu, L., De Lima Neto, F., Marwala, T.: Finite element model updating using fish school search and volitive particle swarm optimization. Integr. Computer-Aided Eng. 22(4), 361–376 (2015)CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2017

Authors and Affiliations

  • I. Boulkaibet
    • 1
  • T. Marwala
    • 1
  • M. I. Friswell
    • 2
  • H. H. Khodaparast
    • 2
  • S. Adhikari
    • 2
  1. 1.Electrical and Electronic Engineering DepartmentUniversity of JohannesburgAuckland ParkSouth Africa
  2. 2.College of EngineeringSwansea University Bay CampusSwanseaUK

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