Adaptive regularization parameter optimization in output-error-based finite element model updating

Mechanical Systems and Signal Processing

Volumn 23, Issue 3, 2009, Pages 563-579

  Hua, X G ^a,b   Ni, Y Q ^a   Ko, J M ^a  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b HUNAN UNIVERSITY   (China)

Author keywords

Adaptive regularization parameter optimization; Finite element (FE) model updating; Minimum product criterion (MPC); Tikhonov regularization

Indexed keywords

CABLE STAYED BRIDGES; MATHEMATICAL MODELS; MODAL ANALYSIS; MODEL PREDICTIVE CONTROL; NUMERICAL ANALYSIS; OPTIMIZATION; PARAMETER ESTIMATION; PREDICTIVE CONTROL SYSTEMS; STRUCTURAL OPTIMIZATION; TRUSSES;

ADAPTIVE REGULARIZATION PARAMETER OPTIMIZATION; ADAPTIVE STRATEGIES; COMPUTATIONALLY EFFICIENT; CONSTANT VALUES; CORRUPTED DATUMS; CURVE METHODS; FE MODEL UPDATING; FINITE ELEMENT (FE) MODEL UPDATING; FINITE ELEMENT MODEL UPDATING; FIXED STRATEGIES; GENERALIZED CROSS VALIDATIONS; ITERATION PROCESSES; ITERATION STEPS; MINIMUM PRODUCT CRITERION (MPC); MODAL DATUMS; NONLINEAR LEAST-SQUARES; NUMERICAL STUDIES; OPTIMAL REGULARIZATIONS; REGULARIZATION METHODS; REGULARIZATION PARAMETERS; SYSTEM OF EQUATIONS; TIKHONOV REGULARIZATION; TRUSS BRIDGES;

FINITE ELEMENT METHOD;

EID: 58049184152     PISSN: 08883270     EISSN: 10961216     Source Type: Journal    
DOI: 10.1016/j.ymssp.2008.05.002     Document Type: Article

References (33)

1. Aktan A.E., Farhey D.N., Helmicki A.J., Brown D.L., Hunt V.J., Lee K.L., and Levi A. Structural identification for condition assessment: experimental arts. Journal of Structural Engineering, ASCE 123 12 (1997) 1674-1684
2. Brownjohn J.M.W., Xia P.Q., Hao H., and Xia Y. Civil structure condition assessment by FE model updating: methodology and case studies. Finite Elements in Analysis and Design 27 10 (2001) 761-775
3. Teughels A., and De Roeck G. Structural damage identification of the highway bridge Z24 by model updating. Journal of Sound and Vibration 278 3 (2004) 589-610
4. Mottershead J.E., and Friswell M.I. Model updating in structural dynamics: a survey. Journal of Sound and Vibration 67 2 (1993) 347-375
5. Friswell M.I., and Mottershead J.E. Finite Element Model Updating in Structural Dynamics (1999), Kluwer Academic Publishers, London
6. Imregun M., and Visser W.J. A review of model updating techniques. Shock and Vibration Digest 23 1 (1991) 9-20
7. Link M. Updating of analytical models-review of numerical procedures and application aspects. In: Ewins D.J., and Inman D.J. (Eds). Structural Dynamics @2000: Current Status and Future Directions (2001), Research Studies Press, Hertfordshire 193-224
8. Maia N.M.M., and Silva J.M.M. Theoretical and Experimental Modal Analysis (1997), Research Studies Press, Somerset
9. Fiswell M.I., Mottershead J.E., and Ahmadian H. Finite-element model updating using experimental data: parameterization and regularization. Philosophical Transactions of the Royal Society of London, Series A-Mathematical Physical and Engineering Sciences 359 1778 (2001) 169-186
10. Natke H.G. On regularization method within system identification. In: Tanaka M., and Bui H.D. (Eds). Inverse Problems in Engineering Mechanics: IUTAM Symposium (1993), Springer, Berlin 3-20
11. Tikhonov A.N. Numerical Methods for the Solution of Ill-Posed Problems (1995), Kluwer Academic Publishers, Boston
12. Rothwell E., and Drachman B. A unified approach to solving ill-conditioned matrix problems. International Journal for Numerical Methods in Engineering 28 3 (1989) 609-620
13. Ojalve I.U., and Ting T. Interpretation and improved solution approach for ill-conditioned linear equations. AIAA Journal 28 11 (1990) 1976-1979
14. Mottershead J.E., and Foster C.D. On the treatment of ill-conditioning in spatial parameter estimation from measured vibration data. Mechanical Systems and Signal Processing 5 2 (1991) 139-154
15. Fregolent A., D'Ambrogio W., Salvini P., and Sestieri A. Regularization techniques for dynamic model updating using input residual. Inverse Problems in Engineering 2 4 (1996) 171-200
16. Ren W.X. A singular value decomposition based truncation algorithms in solving the structural damage equation. Acta Mechanica Solida Sinica 18 2 (2005) 181-188
17. D'Ambrogio W., and Fregolent A. On the use of consistent and significant information to reduce ill-conditioning in dynamic model updating. Mechanical Systems and Signal Processing 12 1 (1998) 203-222
18. Ahmadian H., Mottershead J.E., and Friswell M.I. Regularisation methods for finite element model updating. Mechanical Systems and Signal Processing 12 1 (1998) 47-64
19. Ziaei-Rad S., and Imregun M. On the use of regularisation techniques for finite element model updating. Inverse Problem in Engineering 7 5 (1999) 471-503
20. Mares C., Friswell M.I., and Mottershead J.E. Model updating using robust estimation. Mechanical Systems and Signal Processing 16 1 (2002) 169-183
21. B. Titurus, M.I. Friswell, Regularization in model updating, International Journal for Numerical Methods in Engineering, Available online December 2007, doi:10.1002/nme.2257.
22. X.G. Hua, Structural health monitoring and condition assessment of bridge structures, Ph.D. Thesis, Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong, 2006.
23. Xia Y., Hao H., Brownjohn J.M.W., and Xia P.Q. Damage identification of structures with uncertain frequency and modal shape data. Earthquake Engineering and Structural Dynamics 31 5 (2002) 1054-1066
24. Fox R.L., and Kapoor M.P. Rates of changes of eigenvalues and eigenvectors. AIAA Journal 6 12 (1968) 2426-2429
25. Hansen P.C. Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (1998), Society for Industrial and Applied Mathematics, Philadelphia
26. Hansen P.C. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review 34 4 (1992) 561-580
27. Hansen P.C., and O'Leary D.P. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM Journal on Scientific Computing 14 6 (1993) 1487-1503
28. Wahba G. Practical approximate solutions to linear operator equations when the data are noisy. SIAM Journal on Numerical Analysis 14 4 (1977) 651-667
29. Golub G.H., Heath M., and Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21 2 (1979) 215-223
30. Reginska T. A regularization parameter in discrete ill-posed problems. SIAM Journal on Scientific Computing 17 3 (1996) 740-749
31. Hansen P.C. The discrete Picard condition for discrete ill-posed problems. BIT Numerical Mathematics 30 11 (1990) 658-672
32. Friswell M.I. The adjustment of structural parameters using a minimum variance estimator. Mechanical Systems and Signal Processing 3 2 (1989) 143-155
33. Farquharson C.G., and Oldenburg D.W. A comparison of automatic techniques for estimating the regularization parameter in nonlinear inverse problems. Geophysical Journal International 156 3 (2004) 411-425