It is known that in finite element model updating (FEMU), an important yet challenging problem is how to preserve the structural connectivity and adjust only the inaccurate elements in the coefficient matrices using measured modal data, without altering the accurate elements in the analytical matrices (i.e., local model updating (LMU)). In this paper, an iterative method for solving this problem by using the acceleration-velocity-displacement feedback (AVDF) technique is developed. With this method, the physical connectivity of the original model is preserved, and only the erroneous elements in the analysis matrices are corrected, while the error-free ones remain unchanged, achieving LMU. Numerical examples confirm the effectiveness of the introduced method.
BaiZJChuDSunD (2011) A dual optimization approach to inverse quadratic eigenvalue problems with partial eigenstructure. SIAM Journal on Scientific Computing29: 2531–2561. https://doi.org/10.1137/060656346
2.
BansalSCheungSH (2017) A new stochastic simulation algorithm for updating robust reliability of linear structural dynamic systems subjected to future Gaussian excitations. Computer Methods in Applied Mechanics and Engineering326: 481–504. https://doi.org/10.1016/j.cma.2017.07.032
3.
Ben-IsraelAGrevilleTNE (2003) Generalized Inverses: Theory and Applications. Springer.
4.
BermanANagyEJ (1983) Improvement of a large analytical model using test data. American Institute of Aeronautics and Astronautics (AIAA) Journal21: 1168–1173. https://doi.org/10.2514/3.60140
5.
ChaPDSwitkesJP (2002) Enforcing structural connectivity to update damped systems using frequency response. American Institute of Aeronautics and Astronautics (AIAA) Journal40: 1197–1203. https://doi.org/10.2514/2.1771
6.
ChingJMutoMBeckJL (2006) Structural model updating and health monitoring with incomplete modal data using Gibbs sampler. Computer-Aided Civil and Infrastructure Engineering21: 242–257. https://doi.org/10.1111/j.1467-8667.2006.00432.x
7.
CobbRGLiebstBS (1997) Structural damage identification using assigned partial eigenstructure. American Institute of Aeronautics and Astronautics (AIAA) Journal35: 152–158.
8.
DattaBN (2002) Finite–element model updating, eigenstructure assignment and eigenvalue embedding techniques for vibrating systems. Mechanical Systems and Signal Processing16: 83–96. https://doi.org/10.1006/mssp.2001.1443
9.
DattaBNRamYMSarkissianDR (2000) Multi-input partial pole placement for distribued parameter gyroscopic systems. In Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 5 December, 2000, pp. 4661–4665.
DingYYLiuH (2002) A method for updating damped gyroscopic systems by using output feedback control. Numerical Mathematics–A Journal of Chinese Universities44: 230–242.
12.
EreizSDuvnjakIJiménez-AlonsoJF (2022) Review of finite element model updating methods for structural applications. Structures41: 684–723. https://doi.org/10.1016/j.istruc.2022.05.041
13.
FarhatCHemezFM (1993) Updating finite element dynamic models using an element-by-element sensitivity methodology. American Institute of Aeronautics and Astronautics (AIAA) Journal31: 1702–1711. https://doi.org/10.2514/3.11833
14.
FarshadiMEsfandiariAVahediM (2017) Structural model updating using incomplete transfer function and modal data. Structural Control & Health Monitoring24: 1–13. https://doi.org/10.1002/stc.1932
15.
FriswellMIInmanDJPilkeyDF (1998) Direct updating of damping and stiffness matrices. American Institute of Aeronautics and Astronautics (AIAA) Journal36: 491–493. https://doi.org/10.2514/3.13851
16.
GhannadiPKourehliSS (2020) Multiverse optimizer for structural damage detection: numerical study and experimental validation. Structural Design of Tall and Special Buildings213: 1–27. https://doi.org/10.1002/tal.1777
17.
GhannadiPKourehliSS (2022) Efficiency of the slime mold algorithm for damage detection of large-scale structures. Structural Design of Tall and Special Buildings213: 1–36. https://doi.org/10.1002/tal.1967
18.
GhannadiPKourehliSSNooriM, et al. (2020) Efficiency of grey wolf optimization algorithm for damage detection of skeletal structures via expanded mode shapes. Advances in Structural Engineering213: 1–16. https://doi.org/10.1177/1369433220921000
19.
GhannadiPKhatirSKourehliSS, et al. (2023) Finite element model updating and damage identification using semi-rigidly connected frame element and optimization procedure: an experimental validation. Structures50: 1173–1190. https://doi.org/10.1016/j.istruc.2023.02.008
20.
GhannadiPKourehliSSNguyenA (2025) Experimental validation of an efficient strategy for FE model updating and damage identification in tubular structures. Nondestructive Testing and Evaluation40: 3424–3463. https://doi.org/10.1080/10589759.2024.2402887
21.
HeLReyndersEGarcía-PalaciosJH, et al. (2020) Wireless-Based identification and model updating of a skewed highway bridge for structural health monitoring. Applied Sciences10: 2347. https://doi.org/10.3390/app10072347
22.
HuSLJLiH (2007) Simultaneous mass, damping, and stiffness updating for dynamic systems. American Institute of Aeronautics and Astronautics (AIAA) Journal45: 2529–2537. https://doi.org/10.2514/1.28605
23.
JiaZWeiM (2011) A real-valued spectral decompostion of the undamped gyroscopic system with applications. SIAM Journal on Matrix Analysis and Applications32: 584–604. https://doi.org/10.1137/100792020
24.
KavehA (2014) Computational Structural Analysis and Finite Element Methods. Springer.
25.
KuoYCLinWWXuSF (2005) New model correcting method for quadratic eigenvalue problems using symmetric eigenstructure assignment. American Institute of Aeronautics and Astronautics (AIAA) Journal43: 2593–2598. https://doi.org/10.2514/1.16258
26.
KuoYCLinWWXuSF (2006) New methods for finite element model updating problems. American Institute of Aeronautics and Astronautics (AIAA) Journal44: 1310–1316. https://doi.org/10.2514/1.15654
27.
LinCS (1990) Location of modeling errors using modal test data. American Institute of Aeronautics and Astronautics (AIAA) Journal28: 1650–1654. https://doi.org/10.2514/3.25264
28.
LiuHLiRDingY (2020) Partial eigenvalue assignment for gyroscopic second–order systems with time delay. Mathematics8: 1235. https://doi.org/10.3390/math8081235
29.
López-DíezJMarco-GómezVLuengoP (1999) Modal effective mass applied to error localization of finite element models. 40th Structures, Structural Dynamics, and Materials Conference and Exhibit, St. Louis, MO, U.S.A. 1999, pp. 970–977.
MinasCInmanDJ (1987) Correcting finite element models with measured modal results using eigenstructure assignment methods. Proceedings of the 4th IMAC Conference, Union College, Schenectady, NY, 1987, pp. 583–587.
32.
MinasCInmanDJ (1990) Matching finite element models to modal data. Transactions of the ASME, Journal of Vibration and Acoustics112: 84–92. https://doi.org/10.1115/1.2930103
33.
RenWChenH (2010) Finite element model updating in structural dynamics by using the response surface method. Engineering Structures32: 2455–2465. https://doi.org/10.1016/j.engstruct.2010.04.019
34.
SehgalSKumarH (2016) Structural dynamic model updating techniques: a state of the art review. Archives of Computational Methods in Engineering23: 515–533. https://doi.org/10.1007/s11831-015-9150-3
35.
SunLLiYZhangW (2020) Experimental study on continuous bridge-deflection estimation through inclination and strain. Journal of Bridge Engineering25: 04020020. https://doi.org/10.1061/(asce)be.1943-5592.0001543
36.
SundarVSManoharCS (2013) Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation. International Journal of Non-Linear Mechanics52: 32–40. https://doi.org/10.1016/j.ijnonlinmec.2013.02.002
37.
WahlbergBLjungL (1992) Hard frequency-domain model error bounds from least-squares like identification techniques. IEEE Transactions on Automatic Control37: 900–912. https://doi.org/10.1109/9.148343
XieH (1999) Sensitivity Analysis of Eigenvalue Problem. PhD Thesis. Nanjing University of Aeronautics and Astronautics, CN (in Chinese).
40.
XuJYuanY (2022) A direct method for updating mass and stiffness matrices with submatrix constraints. Linear and Multilinear Algebra70: 4266–4281. https://doi.org/10.1080/03081087.2021.1874263
41.
YeXChenB (2019) Model updating and variability analysis of modal parameters for super high-rise structure. Concurrency and Computation Practice & Experience31: 1–11. https://doi.org/10.1002/cpe.4712
42.
YinTJiangQHYuenKV (2017) Vibration-based damage detection for structural connections using incomplete modal data by Bayesian approach and model reduction technique. Engineering Structures132: 260–277. https://doi.org/10.1016/j.engstruct.2016.11.035
43.
YuanY (2008) A model updating method for undamped structural systems. Journal of Computational and Applied Mathematics219: 294–301. https://doi.org/10.1016/j.cam.2007.07.025
44.
YuanYDaiH (2008) The nearness problems for symmetric matrix with a submatrix constraint. Journal of Computational and Applied Mathematics213: 224–231. https://doi.org/10.1016/j.cam.2007.01.033
45.
YuanYLiuH (2011) An iterative method for solving finite element model updating problems. Applied Mathematical Modelling35: 848–858. https://doi.org/10.1016/j.apm.2010.07.040
YuanYLiuH (2014) An iterative updating method for damped structural systems using symmetric eigenstructure assignment. Journal of Computational and Applied Mathematics256: 268–277. https://doi.org/10.1016/j.cam.2013.07.047
48.
YuanYZhaoWLiuH (2016) Analytical dynamic model modification using acceleration and displacement feedback. Applied Mathematical Modelling40: 9584–9593. https://doi.org/10.1016/j.apm.2016.06.014
49.
ZengMYuanY (2023) Sparse structure preserving finite element model updating problem for gyroscopic systems. Mechanical Systems and Signal Processing203: 110734. https://doi.org/10.1016/j.ymssp.2023.110734
50.
ZhangHYuanY (2020) Model updating for undamped gyroscopic systems with connectivity constraints. Mathematical and Computer Modelling of Dynamical Systems26: 434–452. https://doi.org/10.1080/13873954.2020.1787459
51.
ZhengZCRenGXWilliamsFW (1997) The eigenvalue problem for damped gyroscopic systems. International Journal of Mechanical Sciences39: 741–750. https://doi.org/10.1016/s0020-7403(96)00072-0
52.
ZimmermanDCWidengrenM (1990) Correcting finite element models using a symmetric eigenstructure assignment technique. American Institute of Aeronautics and Astronautics (AIAA) Journal28: 1670–1676. https://doi.org/10.2514/3.25267
