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.
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References
Bhatti, M.A.: Fundamental Finite Element Analysis and Applications: with Mathematica and Matlab Computations. Hoboken, New Jersey. Wiley (2005)
Onãte, E.: Structural analysis with the finite element method. Linear statics. In: Basis and Solids, vol. 1. Barcelona, Springer (2009)
Rao, S.S.: The Finite Element Method in Engineering, 4th edn. Elsevier Butterworth Heinemann, Burlington (2004)
Friswell, M.I., Mottershead, J.E.: Finite Element Model Updating in Structural Dynamics. Kluwer Academic Publishers (1995)
Marwala, T.: Finite Element Model Updating Using Computational Intelligence Techniques. Springer Verlag, London, UK (2010)
H.H. Khodaparast. Stochastic finite element model updating and its application in aeroelasticity. Ph.D. Thesis, Department of Civil Engineering, University of Liverpool, (2010).
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)
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.
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.
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)
Moore, R.: Interval analysis. Prentice Hall, Englewood Cliffs (1966)
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)
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)
Zadeh, L.A.: Fuzzy sets. Inf. Control. 8(3), 338–353 (1965)
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)
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)
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)
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)
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).
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)
Adhikari, S., Khodaparast, H.H.: A spectral approach for fuzzy uncertainty propagation in finite element analysis. Fuzzy Sets Syst. 243, 1–24 (2014)
Nguyen, H.T.: A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64(2), 369–380 (1978)
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)
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)
I.C.J. Riadi. Cognitive Ant colony optimization: A new framework in swarm intelligence, Doctoral dissertation, University of Salford, (2014).
J. Kcnncdy, R.C. Eberhart, Particle swarm optimization, Proceedings of the IEEE International Joint Conference on Neural Networks, 4:1942–1948, (1995).
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.
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)
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Boulkaibet, I., Marwala, T., Friswell, M.I., Khodaparast, H.H., Adhikari, S. (2017). Fuzzy Finite Element Model Updating Using Metaheuristic Optimization Algorithms. In: Dervilis, N. (eds) Special Topics in Structural Dynamics, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-53841-9_8
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