Structural damage detection using nonlinear parameter identification with Tikhonov regularization

Structural Control and Health Monitoring

Volumn 14, Issue 3, 2007, Pages 406-427

  Weber, Benedikt ^a   Paultre, Patrick ^a   Proulx, Jean ^a  

^a UNIVERSITÉ DE SHERBROOKE   (Canada)

Author keywords

Damage detection; Generalized cross validation; Model updating; Parameter identification; Tikhonov regularization

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; IDENTIFICATION (CONTROL SYSTEMS); PROBLEM SOLVING; RANDOM ERRORS; STIFFNESS;

GENERALIZED CROSS-VALIDATION; MODEL UPDATING; TIKHONOV REGULARIZATION;

DAMAGE DETECTION;

EID: 34247514923     PISSN: 15452255     EISSN: 15452263     Source Type: Journal    
DOI: 10.1002/stc.164     Document Type: Article

References (32)

1. Doebling SW, Farrar CR, Prime MB, Shevitz DW. Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review. Los Alamos National Laboratory Report LA-13070-MS, 1996.
2. Sohn H, Farrar CR, Hemez FM, Shunk DD, Stinemates DW, Nadler BR. A review of structural health monitoring literature: 1996-2001. Los Alamos National Laboratory Report LA-13976-MS, 2003.
3. Frisweel MI, Penny JET. Is damage location using vibrations measurements practical? EUROMECH 365 International Workshop: DAMAS 97, Structural Damage Assessment using Advanced Signal Processing Procedures, Sheffield, U.K., June/July 1997.
4. Gladwell GML, Ahmadian H. Generic element matrices suitable for finite element model updating. Mechanical Systems and Signal Processing 1995; 9(6):601-614.
5. Peeters B, Maeck J, De Roeck G. Vibration-based damage detection in civil engineering: excitation sources and temperature effects. Smart Materials and Structures 2001; 10:518-527.
6. Hansen PC. Rank-deficient and discrete ill-posed problems. SIAM Monographs on Mathematical Modeling and Computation, 1998.
7. Vogel CR. Computational Methods for Inverse Problems. SIAM, Frontiers in Applied Mathematics. SIAM: Philadelphia, PA, 2002.
8. Eykhoff P. System Identification: Parameter and State Estimation. Wiley: New York, 1974.
9. Natke HG, Cempel C. Model-Aided Diagnosis of Mechanical Systems: Fundamentals, Detection, Localization, Assessment. Springer: Berlin, 1997.
10. Vogel CR. An overview of numerical methods for nonlinear ill-posed problems. In Inverse and Ill-Posed Problems, Engl HW, Groetsch CW (eds). Academic Press: New York, 1987; 231-245.
11. Engl HW, Hanke M, Neubauer A. Regularization of Inverse Problems. Kluwer: Dordrecht, 1996.
12. Fritzen CP, Bohle K. Identification of damage in large scale structures by means of measured FRFs - procedure and application to the 140-highway-bridge. Key Engineering Materials, vols. 167-168. Trans Tech Publications: Switzerland, 1999; 310-319.
13. Fritzen CP, Bohle K. Application of model-based damage identification to a seismically loaded structure. Smart Materials and Structures 2001; 10:452-458.
14. Görl E, Link M. Damage identification using changes of eigenfrequencies and mode shapes. Mechanical Systems and Signal Processing 2003; 17(1):103-110.
15. Link M. Updating of analytical models - basic procedures and extensions. In Modal Analysis and Testing, Silva JMM, Maia NMM (eds). Kluwer Academic Publishers: Dordrecht, 1999; 281-304.
16. Prells U. A regularization method for the linear error localization of models of elastomechanical systems. Inverse Problems in Engineering 1996; 3:197-217.
17. Hemez FM, Farhat C. Bypassing the numerical difficulties associated with updating simultaneously mass and stiffness matrices. AIAA Journal 1995; 33(3):539-546.
18. Ahmadian H, Mottershead JE, Friswell MI. Regularization methods for finite element model updating. Mechanical Systems and Signal Processing 1998; 12(1):47-64.
19. Friswell MI, Mottershead JE, Ahmadian H. Finite element model updating using experimental test data: parametrization and regularization. Philosophical Transactions: Mathematical, Physical and Engineering Sciences 2001; 359(1778):169-186.
20. Collins JD, Hart GC, Hasselman TK, Kennedy B. Statistical identification of structures. AIAA Journal 1974; 12(2):185-190.
21. Kosmatka JB, Ricles JM. Damage detection in structures by modal vibration characterisation. Journal of Structural Engineering 1999; 125(12):1384-1392.
22. Hassiotis S, Jeong GD. Identification of stiffness reductions using natural frequencies. Journal of Engineering Mechanics 1995; 121(10):1106-1113.
23. Ren WX, De Roeck G. Structural damage identification using modal data. I: simulation verification. Journal of Structural Engineering 2002; 128(1):87-95.
24. Teughels A, De Roeck G. Structural damage identification of the highway bridge Z24 by FE model updating. Journal of Sound and Vibration 2004; 278(3):589-610.
25. Baruch M. Optimization procedure to correct stiffness and flexibility matrices using vibration tests. AIAA Journal 1978; 16(11):1208- 1210.
26. Kabe AM. Stiffness matrix adjustment using mode data. AIAA Journal 1985; 23(9):1431-1436.
27. Nelson RB. Simplified calculation of eigenvector derivatives. AIAA Journal 1976; 14(9):1201-1205.
28. Golub GH, Van Loan CF. Matrix Computations (3rd edn). Johns Hopkins University Press: Baltimore, MD, 1996.
29. 1-regularization functions for the SI of structures. In Proceedings of the First European Workshop in Structural Health Monitoring 2002, Balageas DL (ed.). DEStech Publications: 2002; 790-797.
30. Golub HG, Heath M, Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 1979; 21(2):215- 223.
31. Moré JJ. The Levenberg-Marquardt algorithm: implementation and theory. In Numerical Analysis, Watson GA (ed.). Lecture Notes in Mathematics, vol. 630. Springer: Berlin, 1977; 105-116.
32. O'Sullivan F, Wahba G. A cross validated Bayesian retrieval algorithm for nonlinear remote sensing experiments. Journal of Computational Physics 1985; 59:441-455.