Abstract
In this paper, we present a damage identification method for small damages based on topology optimization and Lasso regularization. In particular, this work extends the applicability of the previously developed damage identification method using frequency response functions and topology optimization, by conducting rigorous parametric studies in terms of damping, measurement noise, and damage size. It is shown that the presented method successfully identifies small damaged regions with a reasonable accuracy. To evaluate the effectiveness of the proposed method, we applied the method to identify the damages in cantilevered plates that are subject to static or dynamic loads. The method succeeded in detecting the locations and shapes of damages more accurately than the method without Lasso regularization. Furthermore, in most cases we have considered, spurious damages generated during the optimization were successfully suppressed.
Similar content being viewed by others
References
Shull, P.J.: Nondestructive Evaluation: Theory, Techniques, and Application. CRC Press, Boca Raton (2000)
Fan, W., Qiao, P.: Vibration-based damage identification methods: a review and comparative study. Struct. Health Monit. 10(1), 83–111 (2011)
Fan, W., Qiao, P.: A 2-D continuous wavelet transform of mode shape data for damage detection of plate structures. Int. J. Solids Struct. 46(25–26), 4379–4395 (2009)
Wang, F., Ling, X., Xu, X., Zhang, F.: Structural stiffness identification based on the extended Kalman filter research. Abstr. Appl. Anal. 2014, 103102 (2014)
Rucevskis, S., Janeliukstis, R., Akishin, P., Chate, A.: Mode shape-based damage detection in plate structure without baseline data. Struct. Control. Health Monit. 23(9), 1180–1193 (2016)
Friswell, M., Mottershead, J., Ahmadian, H.: Finite-element model updating using experimental test data: parametrization and regularization. Philos. Trans. R. Soc. 359, 169–186 (2001)
Fang, S.E., Perera, R., De Roeck, G.: Damage identification of a reinforced concrete frame by finite element model updating using damage parameterization. J. Sound Vib. 313, 544–559 (2008)
Dimarogonas, A.D.: Vibration of cracked structures: a state of the art review. Eng. Fract. Mech. 55(5), 831–857 (1996)
Owolabi, G.M., Swamidas, A.S.J., Seshadri, R.: Crack detection in beams using changes in frequencies and amplitudes of frequency response functions. J. Sound Vib. 265(1), 1–22 (2003)
Khiem, N.T.: Crack detection for structure based on the dynamic stiffness model and the inverse problem of vibration. Inverse Probl. Sci. Eng. 14(1), 85–96 (2006)
Friswell, M.I.: Damage Identification using inverse methods. Phil. Trans. R. Soc. A 365, 393–410 (2007)
Lee, J.S., Kim, J.E., Kim, Y.Y.: Damage detection by the topology design formulation using modal parameters. Int. J. Numer. Meth. Eng. 69(7), 1480–1498 (2007)
Nishizu, T., Takezawa, A., Kitamura, M.: Damage identification in non-destructive testing based on topology optimization and eigenfrequency analysis. J. Jpn. Soc. Naval Arch. Ocean Eng. 18, 73–80 (2013)
Eslami, S.M., Abdollahi, F., Shahmiri, J., Tavakkoli, S.M.: Structural damage detection by using topology optimization for plane stress problems. Int. J. Optim. Civ. Eng. 9(1), 159–176 (2019)
Niemann, H., Morlier, J., Shahdin, A., Gourinat, Y.: Damage localization using experimental modal parameters and topology optimization. Mech. Syst. Signal Process. 24(3), 636–652 (2010)
Zhang, W., Du, Z., Sun, G., Guo, X.: A level set approach for damage identification of continuum structures based on dynamic responses. J. Sound Vib. 386, 100–1555 (2017)
Reumers, P., Van Hoorickx, C., Schevenels, M., Lombaert, G.: Density filtering regularization of finite element model updating problems. Mech. Syst. Signal Process. 128, 282–294 (2019)
Saomoto, H., Kase, Y., Mori, H., Yoshimi, M., Horikawa, H., Abe, S.: Fault shape detection based on topology optimization technique. J. Jpn. Soc. Civ. Eng. Ser. A 71(4), I21–I31 (2015). ((In Japanese))
Saito, A., Sugai, R., Wang, Z., Saomoto, H.: Damage identification using noisy frequency response functions based on topology optimization. J. Sound Vib. 545, 117412 (2023)
Wu, Y.H., Zhou, X.Q.: L1 regularized model updating for structural damage detection. Int. J. Struct. Stab. Dyn. 18(12), 185157 (2018)
Bendsøe, M., Sigmund, O.: Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69(9), 635–654 (1999)
Ma, Z.-D., Kikuchi, N., Cheng, H.-C.: Topological design for vibrating structures. Comput. Methods Appl. Mech. Eng. 121, 259–280 (1995)
Pedersen, N.L.: Maximization of eigenvalues using topology optimization. Struct. Multidiscip. Optim. 20, 2–11 (2000)
Candès, E.J., Romberg, J., Tao, T.: Robust uncertianty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory. 52(2), 489–509 (2006)
Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. B 58(1), 267–288 (1996)
Tibshirani, R.: Regression shrinkage and selection via the Lasso: a retrospective. J. R. Stat. Soc. Ser. B 73(3), 273–282 (2011)
Gill, P.E., Murray, W., Saunders, M.A.: User’s Guide for SNOPT Version 7.5: Software for Large-Scale Nonlinear Programming. Stanford University, Systems Optimization Laboratory (SOL) (2015)
Zargham, S., Ward, T.A., Ramli, R., Badruddin, I.A.: Topology optimization: a review for structural designs under vibration problems. Struct. Multidiscip. Optim. 53, 1157–1177 (2016)
Mei, Y., Goenezen, S.: Quantifying the anisotropic linear elastic behavior of solids. Int. J. Mech. Sci. 163, 105131 (2019)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sugai, R., Saito, A. & Saomoto, H. Damage identification based on topology optimization and Lasso regularization. Arch Appl Mech 93, 3827–3850 (2023). https://doi.org/10.1007/s00419-023-02464-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-023-02464-7