Abstract
This paper presents an application of multiobjective optimization for the damage quantification in beams. The simulation of damage relies on the finite element analysis of Euler-Bernoulli beams and is carried out by considering a reduction in the Young’s modulus of specific elements. The damage is quantified by minimizing two objective functions. These two functions are based on the difference in the Frobenius norm of matrices containing the modal displacements and the modal rotations of a beam in the undamaged and damaged states. The solution of the optimization problem thus defined is solved by a direct multisearch algorithm, which is an extension of the direct search algorithm to multiobjective optimization. This algorithm does not need any derivatives information about the objective functions. The validity, robustness and efficiency of the present application is tested for different boundary conditions of the damaged beam and high levels of noise in the simulated measured data.
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References
Jaishia, B., Ren, W.-X.: Damage detection by finite element model updating using modal flexibility residual. J. Sound Vib. 290, 369–387 (2006). https://doi.org/10.1016/j.jsv.2005.04.006
Au, F.T.K., Cheng, Y.S., Tham, L.G., Bai, Z.Z.: Structural damage detection based on a micro-genetic algorithm using incomplete and noisy modal test data. J. Sound Vib. 259(5), 1081–1094 (2003). https://doi.org/10.1006/jsvi.2002.5116
Perera, R., Fang, S.-E., Huerta, C.: Structural crack detection without updated baseline model by single and multiobjective optimization. Mech. Syst. Signal Process. 23, 752–768 (2009). https://doi.org/10.1016/j.ymssp.2008.06.010
Shabbir, F., Omenzetter, P.: Application of multi-objective optimization to structural damage estimation via model updating. In: Proceedings of SPIE 8348, Health Monitoring of Structural and Biological Systems, 83481C (2012). https://doi.org/10.1117/12.914765
Lopes, H., Ribeiro, J., Araújo dos Santos, J.V.: Interferometric techniques in structural damage identification. Shock Vib. 19, 835–844 (2012). https://doi.org/10.3233/sav-2012-0692
Lopes, H., Ferreira, F., Araújo dos Santos, J.V., Moreno-García, P.: Localization of damage with speckle shearography and higher order spatial derivatives. Mech. Syst. Signal Process. 49(1–2), 24–38 (2014). https://doi.org/10.1016/j.ymssp.2013.12.016
Spagnolo, G.S., Martocchia, A., Papalillo, D., Cozzella, L.: Simple educational tool for digital speckle shearography. Eur. J. Phys. 33, 733–750 (2012). https://doi.org/10.1088/0143-0807/33/4/733
Lemaitre, J.: A Course on Damage Mechanics, 2nd edn. Springer, Berlin, Heidelberg (1996)
Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston (1999)
Custódio, A.L., Madeira, J.F.A., Vaz, A.I.F., Vicente, L.N.: Direct multisearch for multiobjective optimization. SIAM J. Optim. 21, 1109–1140 (2011). https://doi.org/10.1137/10079731X
Custódio, A.L., Emmerich, M., Madeira, J.F.A.: Recent developments in derivative-free multiobjective optimization. Comput. Technol. Rev. 5, 1–30 (2012). https://doi.org/10.4203/ctr.5.1
Araújo dos Santos, J.V., Mota Soares, J.V., Mota Soares, C.M., Maia, N.M.M.: Structural damage identification in laminated structures using FRF data. Compos. Struct. 67, 239–249 (2005). https://doi.org/10.1016/j.compstruct.2004.09.011
Yun, C.-B., Yi, J.-H., Bahng, E.Y.: Joint damage assessment of framed structures using a neural networks technique. Eng. Struct. 23, 425–435 (2001). https://doi.org/10.1016/S0141-0296(00)00067-5
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Araújo dos Santos, J.V., Madeira, J.F.A., Lopes, H., Moreno-García, P. (2019). Application of Multiobjective Optimization Based on Differences of Modal Displacements and Modal Rotations for Damage Quantification in Beams. In: Rodrigues, H., et al. EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization. EngOpt 2018. Springer, Cham. https://doi.org/10.1007/978-3-319-97773-7_87
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DOI: https://doi.org/10.1007/978-3-319-97773-7_87
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