Updating finite element model using frequency domain decomposition method and bees algorithm

Document Type: Research Paper


1 kiyanpars-12st avenue-no27

2 Shahid Chamran University of Ahwaz, Faculty of Engineering, Mechanical Engineering group.

3 computer &mathematical sciences, chamran university, ahvaz


The following study deals with the updating the finite element model of structures using the operational modal analysis. The updating process uses an evolutionary optimization algorithm, namely bees algorithm which applies instinctive behavior of honeybees for finding food sources. To determine the uncertain updated parameters such as geometry and material properties of the structure, local and global sensitivity analyses have been performed. The sum of the squared errors between the natural frequencies obtained from operational modal analysis and the finite element method is used to define the objective function. The experimental natural frequencies are determined by frequency domain decomposition technique which is considered as an efficient operational modal analysis method. To verify the accuracy of the proposed algorithm, it is implemented on a three-story structure to update its finite element model. Moreover, to study the efficiency of bees algorithm, its results are compared with those particle swarm optimization and Nelder and Mead methods. The results show that this algorithm leads more accurate results with faster convergence. In addition, modal assurance criterion is calculated for updated finite element model and frequency domain decomposition technique. Moreover, finding the best locations of acceleration and shaker mounting in order to accurate experiments are explained.


Main Subjects

[1]          He J., Fu Z. F., 2001, Modal Analysis, Oxford, London, Firsted.

[2]          Heylen W., Lammens S., Sas P., 1997, Modal Analysis Theory and Testing, K.U. Leuven, Belgium, First ed.

[3]          Brincker R., Zhang L., Andersen P., Modal identification from ambient responses using frequency domain decomposition, in 28th International Modal Analysis Conference, San Antonio, TX, USA, 2000.

[4]          Cara .J. F, Juan.J, Alarco´n .E, Reynders .E, DeRoeck .G, Modal contribution and state space order selection in operational modal analysis, Mechanical Systems and Signal Processing, Vol. 38, No. 2, pp. 276–298, 2013.

[5]          James G.H., Carne.T.G., Lauffer. P., The natural excitation technique (NExT) for modal parameter extraction from operating structures modal analysis, The International Journal of Analytical and Experimental Modal Analysis, Vol. 10, pp. 260-277, 1995.

[6]          Ibrahim S.R., Mikulcik. E.C., A method for direct identification of vibration parameters from the free response, Shock and Vibration Bulletin Vol. 47 No. 4, pp. 183-198, 1997.

[7]          Juang J.N., Pappa R.S., An eigensystem realization algorithm for modal parameter identificationand model reduction, Control and Dynamics Vol. 8, No. 4, pp. 620-627, 1985.

[8]          Van Overschee  P., De Moor B., 1996, Subspace Identification for Linear Systems: Theory-Implementations-Applications, Kluwer Academic Publishers, Dordrecht-Netherlands

[9]          Allemang S., Brown D.L., A complete review of the complex mode  indicator function (CMIF) with applications, in Proceeding of ISMA International Conference on Noise and Vibration Engineering, Belgium, 2006.

[10]        Magalhães F., Cunha A., Explaining operational modal analysis with data from an arch bridge, Mech. Syst. Signal Process, Vol. 25, No. 5, pp. 1431–1450, 2010.

[11]        Zhang L., Wang T., Tamura Y., A frequency-spatial domain decomposition(FSDD) technique for operational modal analysis, Mech. Syst. Signal Process, Vol. 24, No. 5, pp. 1227–1239, 2010.

[12]        Pioldi.F, Ferrari.R, Rizzi.E, Output-only modal dynamic identification of frames by a refined FDD algorithm at seismic input and high damping, Mechanical Systemsand Signal Processing, Vol. 68, pp. 265–291, 2016.

[13]        Collins J.D, Hart G.C, Hasselman T.K, Kennedy B., Statistical identification of structures, AIAA Journal Vol. 12, pp. 185-190, 1974.

[14]        Dunn S, Peucker S, Perry J, Genetic algorithm optimisation of mathematical models using distributed computing, Applied Intelligence, Vol. 23, pp. 21-32, 2005.

[15]        Moradi S, Fatahi L, Razi P, Finite element model updating using bees algorithm, Structural and Multidisciplinary Optimization, Vol. 42, pp. 283-291, 2010.

[16]        Malekzehtab H, Golafshani A.A, Damage detection in an offshore Jacket platform using genetic algorithm based finite element model updating with noisy modal data, Procedia Engineering, Vol. 54, 2013.

[17]        Chouksey M., Dutt J.K., Modak S.V., Model updating of rotors supported on ball bearings and its application in response prediction and balancing, Measurement, Vol. 46, pp. 4261-4273, 2013.

[18]        Moradi S., Alimouri P., Crack detection of plate using differential quadrature method, Mechanical Engineering Science, Vol. 227, No. 7, 2013.

[19]        Torres W., Almazán J. L., Sandoval C., Boroschek R., Operational modal analysis and FE model updating of the Metropolitan Cathedral of Santiago, Chile, Engineering Structures, Vol. 143, pp. 169–188, 2017.

[20]        Ebrahimi R, Esfahanian M, Ziaei-rad S, Vibration modeling and modification of cutting platform in a harvest combine by means of operational modal analysis (OMA), Measurement Vol. 46, pp. 3959-3967, 2013.

[21]        Pioldi F., Ferrari R., Rizzi E., A refined FDD algorithm for Operational Modal Analysis of buildings under earthquake loading, in Proceeding of the Conference on Noise and Vibration Engineering (ISMA2014),, Leuven,Belgium, 2014.

[22]        Kennedy J., Eberhart RC., Particle swarm optimization, IEEE international journal on neural networks Vol. 4, pp. 1942–1948, 1995.

[23]        Nelder J.A., Mead R., A simplex method for function minimization, Compute, Vol. 7, pp. 308-313, 1965.