The l1 regularization technique has been developed for damage detection by utilizing the sparsity feature of structural damage. However, the sensitivity matrix in the damage identification exhibits a strong correlation structure, which does not suffice the independency criteria of the l1 regularization technique. This study employs the elastic net method to solve the problem by combining the l1 and l2 regularization techniques. Moreover, the proposed method enables the grouped structural damage being identified simultaneously, whereas the l1 regularization cannot. A numerical cantilever beam and an experimental three-story frame are utilized to demonstrate the effectiveness of the proposed method. The results showed that the proposed method is able to accurately locate and quantify the single and multiple damages, even when the number of measurement data is much less than the number of elements. In particular, the present elastic net technique can detect the grouped damaged elements accurately, whilst the l1 regularization method cannot.
SalawuOS. Detection of structural damage through changes in frequency: A review. Eng Struct1997; 19(9): 718–723.
2.
LiJHaoHXiaY, et al.Damage detection of shear connectors in bridge structures with transmissibility in frequency domain. Int J Struct Stab Dyn2014; 14(2): 1350061.
3.
ChenCYuL. A hybrid ant lion optimizer with improved Nelder–Mead algorithm for structural damage detection by improving weighted trace lasso regularization. Adv Struct Eng2020; 23(3): 468–484.
4.
DoeblingSWFarrarCRPrimeMB, et al.Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in Their Vibration Characteristics: A Literature Review. Los Alamos National Laboratory Report, 1996.
5.
SohnHFarrarCRHemezFM, et al.A Review of Structural Health Monitoring Literature: 1996–2001. Los Alamos National Laboratory Report, 2003.
6.
EsfandiariANabiyanMSRofooeiFR. Structural damage detection using principal component analysis of frequency response function data. Struct Health Monit2020; 27(7): e2550.
7.
ZhangFLKimCWGoiY. Efficient Bayesian FFT method for damage detection using ambient vibration data with consideration of uncertainty. Struct Control Health Monit2021; 28: e2659.
8.
GhoulemKKormiTBel Hadj AliN. Damage detection in nonlinear civil structures using kernel principal component analysis. Adv Struct Eng2020; 23(11): 2414–2430.
9.
GuoTWuLWangC, et al.Damage detection in a novel deep-learning framework: A robust method for feature extraction. Struct Health Monit2020; 19(2): 424–442.
10.
PadilKHBakharyNAbdulkareemM, et al.Non-probabilistic method to consider uncertainties infrequency response function for vibration-based damage detection using artificial neural network. J Sound Vib2020; 467: 115069.
11.
Beheshti AvalSBAhmadianVMaldarM, et al.Damage detection of structures using signal processing and artificial neural networks. Adv Struct Eng2020; 23(5): 884–897.
12.
KullaaJ. Robust damage detection in the time domain using Bayesian virtual sensing with noise reduction and environmental effect elimination capabilities. J Sound Vib2020; 473: 115232.
13.
WahWSLChenYTOwenJS. A regression-based damage detection method for structures subjected to changing environmental and operational conditions. Eng Struct2021; 228: 111462.
14.
BaoYChenZWeiS, et al.The state of the art of data science and engineering in structural health monitoring. Engineering2019; 5(2): 234–242.
15.
SunLMShangZQXiaY, et al.Review of bridge structural health monitoring aided by big data and artificial intelligence: From condition assessment to damage detection. J Struct Eng2020; 146(5): 04020073.
16.
HouRXiaY. Review on the new development of vibration-based damage identification for civil engineering structures: 2010-2019. J Sound Vib2021; 491: 115741.
17.
LiXYLawSS. Adaptive Tikhonov regularization for damage detection based on nonlinear model updating. Mech Syst Signal Process2010; 24(6): 1646–1664.
18.
WeberBPaultrePProulxJ. Structural damage detection using nonlinear parameter identification with Tikhonov regularization. Struct Control Health Monit2007; 14(3): 406–427.
19.
TikhonovANArseninVY. Solutions of IL-Posed Problems. New York: Wiley, 1977.
20.
HansenPC. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev1992; 34(4): 561–580.
21.
TheodoridisSKopsinisYSlavakisK. Sparsity-aware learning and compressed sensing: An overview. Acad Press Libr Signal Process2013: 1271–1377.
22.
HouRRXiaYZhouXQ. Structural damage detection based on l1 regularization using natural frequencies and mode shapes. Struct Control Health Monit2018; 25(3): e2107.
23.
DingZHLiJHaoH. Structural damage identification by sparse deep belief network using uncertain and limited data. Struct Control Health Monit2020; 27(5): e2522.
24.
YangYNagarajaiahS. Structural damage identification via a combination of blind feature extraction and sparse representation classification. Mech Syst Signal Process2014; 45(1): 1–23.
25.
LiuHLYuLLuoZW, et al.Multi-strategy structural damage detection based on included angle of vectors and sparse regularization. Struct Eng Mech2020; 75(4): 415–424.
26.
HernandezEM. Identification of isolated structural damage from incomplete spectrum information using l1-norm minimization. Mech Syst Signal Process2014; 46(1): 59–69.
27.
ZhangCHuangJZSongGQ, et al.Structural damage identification by extended Kalman filter with l1-norm regularization scheme. Struct Control Health Monit2017; 24(11): e1999.
28.
YuanMLinY. Model selection and estimation in regression with grouped variables. J R Stat Soc Series B2006; 68(1): 49–67.
29.
GraveEObozinskiGRBachFR. Trace lasso: A trace norm regularization for correlated designs. In: Proceeding advances neural inform process system, Granada, Spain, 12–17 December 2011, pp. 2187–2195.
30.
ZuoWMMengDYZhangL, et al.A generalized iterated shrinkage algorithm for non-convex sparse coding. In: Proceedings of IEEE international conference on computer vision (ICCV), Sydney, Australia, 3–6 December 2013, pp. 217–224.
31.
TibshiraniR. Regression shrinkage and selection via the lasso. J R Stat Soc B1996; 58(1): 267–288.
32.
FuWJ. Penalized regressions: The bridge versus the Lasso. J Comput Graph Stat1998; 7(3): 397–416.
33.
XuHCaramanisCMannorS. Sparse algorithms are not stable: A no-free-lunch theorem. IEEE PAMI2012; 34(1): 187–193.
34.
ZouHHastieT. Regularization and variable selection via the elastic net. J R Stat Soc B2005; 67(2): 301–320.
BakirPGReyndersEDe RoeckG. Sensitivity-based finite element model updating using constrained optimization with a trust region algorithm. J Sound Vib2007; 305(1): 211–225.
37.
ZhouX-QXiaYWengS. L1 regularization approach to structural damage detection using frequency data. Struct Health Monit2015; 14(6): 571–582.
38.
NelsonRB. Simplified calculation of eigenvector derivatives. AIAA J1976; 14(9): 1201–1205.
39.
WengSXiaYXuY-L, et al.An iterative substructuring approach to the calculation of eigen solution and eigen sensitivity. J Sound Vib2011; 330(14): 3368–3380.
40.
HouRXiaYBaoY, et al.Selection of regularization parameter for l1-regularized damage detection. J Sound Vib2018; 423: 141–160.
41.
MATLAB. Optimization Toolbox User’s Guide Version 3. Natick, MA: The Mathworks Inc., 2005.
42.
FormentiDRichardsonM. Parameter estimation from frequency response measurements using rational fraction polynomials (twenty years of progress). In: Proceedings of the 20th international modal analysis conference (IMAC), Los Angeles, California, 4–7 February 2002, pp. 167–181.
