Abstract
This work deals with the crack identification using model reduction based on the proper orthogonal decomposition method. The proposed inverse problem consists of the estimation of the crack length and its position in a plate using boundary displacements as input data. Genetic algorithm and particle swarm optimization were applied for the minimization of the error function expressed as the difference between the boundary displacements of the actual crack and those of the estimated crack. It was found that the proposed approach is able to accurately estimate crack size and detect its location. The stability of the identification algorithm was tested against measurement uncertainty by introducing a white Gaussian noise in the input data. The approach showed high stability for noise levels lower than 5 %. The efficiency of the approach using small number of sensor points was also demonstrated.
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References
Abraham A, Jain L (2005) Evolutionary multiobjective optimization. Springer, London
Alessandri C, Mallardo V (1999) Crack identification in two-dimensional unilateral contact mechanics with the boundary element method. Comput Mech 24:100–109
Amoura N, Kebir H, Rechak S, Roelandt J (2010) Axisymmetric and two-dimensional crack identification using boundary elements and coupled quasi-random downhill simplex algorithms. Eng Anal Bound Elem 34:611–618
Bolzon G, Buljak V (2011) An effective computational tool for parametric studies and identification problems in materials mechanics. Comput Mech 48:675–687
Bolzon G, Buljak V, Maier G, Miller B (2011) Assessment of elastic–plastic material parameters comparatively by three procedures based on indentation test and inverse analysis. Inverse Problems Sci Eng 19:815–837
Bonnet M, Constantinescu A (2005) Inverse problems in elasticity. Inverse Problems 21:R1
Bui HD (2007) Fracture mechanics: inverse problems and solutions, vol 139. Springer Science & Business Media, Dordrecht
Buljak V (2011) Inverse analyses with model reduction: proper orthogonal decomposition in structural mechanics. Springer Science & Business Media, New York
Buljak V, Maier G (2011) Proper orthogonal decomposition and radial basis functions in material characterization based on instrumented indentation. Eng Struct 33:492–501
Burczynski T, Beluch W (2001) The identification of cracks using boundary elements and evolutionary algorithms. Eng Anal Bound Elem 25:313–322
Chatterjee A (2000) An introduction to the proper orthogonal decomposition. Curr Sci 78:808–817
Doebling SW, Farrar CR, Prime MB (1998) A summary review of vibration-based damage identification methods. Shock Vib Dig 30:91–105
Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science. New York, NY, pp 39–43
Galvanetto U, Violaris G (2007) Numerical investigation of a new damage detection method based on proper orthogonal decomposition. Mech Syst Signal Process 21:1346–1361
Gen M, Cheng R (2000) Genetic algorithms and engineering optimization, vol 7. Wiley, New York
Hattori G, Sáez A (2013) Damage identification in multifield materials using neural networks. Inverse Problems Sci Eng 21:929–944
Hoang K, Khoo B, Liu G, Nguyen NC, Patera AT (2013) Rapid identification of material properties of the interface tissue in dental implant systems using reduced basis method. Inverse Problems Sci Eng 21:1310–1334
Kennedy J (2010) Particle swarm optimization. In: Encyclopedia of Machine Learning. Springer, pp 760–766
Lanata F, Del Grosso A (2006) Damage detection and localization for continuous static monitoring of structures using a proper orthogonal decomposition of signals. Smart Mater Struct 15:1811
Liang YC, Lee HP, Lim SP (2002a) Proper orthogonal decomposition and its applications – part I: theory. J Sound Vib 252(3):527–544. doi:10.1006/jsvi.2001.4041
Liang YC, Lin WZ, Lee HP, Lim SP, Lee KH (2002b) Proper orthogonal decomposition and its applications – part II: model reduction for MEMS dynamical analysis. J Sound Vib 256(3):515–532. doi:10.1006/jsvi.5007
Mellings S, Aliabadi M (1995) Flaw identification using the boundary element method. Int J Numer Methods Eng 38:399–419
Ness S, Sherlock CN, Moore PO, McIntire P (1996) Nondestructive testing overview. American Society for Nondestructive Testing, Columbus
Ostrowski Z, Białecki R, Kassab A (2008) Solving inverse heat conduction problems using trained POD-RBF network inverse method. Inverse Problems Sci Eng 16:39–54
Rogers CA, Kassab AJ, Divo EA, Ostrowski Z, Bialecki RA (2012) An inverse POD-RBF network approach to parameter estimation in mechanics. Inverse Problems Sci Eng 20:749–767
Schilders WH, Van der Vorst HA, Rommes J (2008) Model order reduction: theory, research aspects and applications, vol 13. Springer, Berlin
Shane C, Jha R (2011) Proper orthogonal decomposition based algorithm for detecting damage location and severity in composite beams. Mech Syst Signal Process 25:1062–1072
Stavroulakis GE (2000) Inverse and crack identification problems in engineering mechanics, vol 46. Springer Science & Business Media, Dordrecht
Venter G (2010) Review of optimization techniques Encyclopedia of aerospace engineering, vol 8. Wiley, New York
Vossou CG, Koukoulis IN, Provatidis CG (2007) Genetic combined with a simplex algorithm as an efficient method for the detection of a depressed ellipsoidal flaw using the boundary element method. Int J Appl Math Comput Sci 4:122–127
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Benaissa, B., Aït Hocine, N., Belaidi, I. et al. Crack identification using model reduction based on proper orthogonal decomposition coupled with radial basis functions. Struct Multidisc Optim 54, 265–274 (2016). https://doi.org/10.1007/s00158-016-1400-y
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DOI: https://doi.org/10.1007/s00158-016-1400-y