Abstract
The term “model updating” describes the process of adjusting the parameters of a finite element model in order that its predictions, in terms of eigenvalues and eigenvectors, are in agreement with measurements obtained by modal testing. The sensitivity method described in this chapter has been implemented numerous times in commercial codes and applied successfully in industry. It has become a mature technology in regular use in the automotive and aerospace industries worldwide. However, there are various subtleties surrounding the application of model updating that are discussed here for the benefit of potential users. Firstly there must be an awareness of the frequency range in which the updated model is to be applied. The available data is generally insufficient to define the system parameters without the use of additional information provided by regularization. And the choice of parameters is of critical importance: it is not only a matter of choosing sensitive parameters; they should also be chosen as part of an engineering understanding of the dynamics of the system. Careful choice of parameters, together with regularization, will lead to validated models that predict the behavior of the system beyond the scope of the original test data.
Similar content being viewed by others
Abbreviations
- f :
-
Vector of forces
- x :
-
Displacement vector
- z :
-
Vector of outputs
- C :
-
Damping matrix
- G :
-
Matrix of sensitivities
- H :
-
Matrix of frequency response functions
- K :
-
Stiffness matrix
- M :
-
Mass matrix
- P :
-
Matrix of stiffness-matrix eigenvalues
- W :
-
Weighting matrix
- λ :
-
Eigenvalue
- θ :
-
Vector of parameters
- φ :
-
Eigenvector
- Ψ :
-
Matrix of stiffness-matrix eigenvectors
- Cov(•, •):
-
Covariance matrix
- \( \left(\overline{\bullet}\right) \) :
-
Mean
References
Adhikari S, Friswell MI (2010) Distributed parameter model updating using the Karhunen-Loève expansion. Mech Syst Signal Process 24:326–339
Ahmadian H, Gladwell GML, Ismail F (1997) Parameter selection strategies in finite element model updating. ASME J Vib Acoust 119:37–45
Ahmadian H, Mottershead JE, Friswell MI (1998) Regularisation methods for finite element model updating. Mech Syst Signal Process 12(1):47–64
Ahmadian H, Mottershead JE, Friswell MI (2002) Physical realisation of generic element parameters in model updating. Trans Am Soc Mech Eng J Vib Acoust 124(4):628–632
Au SK (2012) Connecting Bayesian and frequentist quantification of parameter uncertainty in system identification. Mech Syst Signal Process 29:328–342
Balmes E (1997) Garteur Group on Ground Vibration Testing – results from the tests of a single structure by 12 laboratories in Europe. Proceedings of the International Modal Analysis Conference IMAC XV, Orlando, pp 1346–1352
Batou A (2015) Model updating in structural dynamics – uncertainties on the position and orientation of sensors and actuators. J Sound Vib 354:47–64
Beck JL, Katafygiotis L (1998) Updating models and their uncertainties. I: Bayesian statistical framework. J Eng Mech 124(4):445–461
Behmanesh I, Moaveni B, Lombaert G, Papadimitriou C (2015) Hierarchical Bayesian model updating for structural identification. Mech Syst Signal Process 64–65:360–376
Carvalho J, Datta BN, Gupta A, Lagadapati M (2007) A direct method for model updating with incomplete measured data and without spurious modes. Mech Syst Signal Process 21:2715–2731
Collins JD, Hart GC, Hasselman TK, Kennedy B (1974) Statistical identification of structures. AIAA J 12(2):185–190
D’Ambrogio W, Fregolent A (2000) The use of antiresonances for robust model updating. J Sound Vib 236:227–243
Datta BN, Deng S, Sokolov VO, Sarkissian DR (2009) An optimization technique for damped model updating with measured data satisfying quadratic orthogonality constraints. Mech Syst Signal Process 23:1759–1772
Degener M (1997) Ground vibration results from the tests of an aircraft model performed as part of an European round robin exercise. Proceedings of the CEAS international forum on aeroelasticity and structural dynamics, Rome
Degener M, Hermes H (1996) Ground vibration test and finite element analysis of the GARTEUR SM-AG19 testbed. Deutsche Forschungsanstalt für Luft- und Raumfahrt e V Institut für Aeroelastik, IB 232-96 J 08
Fang SE, Ren WX, Perera R (2012) A stochastic model updating method for parameter variability quantification based on response surface models and Monte-Carlo simulation. Mech Syst Signal Process 33:83–96
Fang SE, Zhang QH, Ren WX (2015) An interval model updating strategy using interval response surface models. Mech Syst Signal Process 60–61:909–927
Fox R, Kapoor M (1968) Rate of change of eigenvalues and eigenvectors. AIAA J 6:2426–2429
Friswell MI (1989) The adjustment of structural parameters using a minimum variance estimator. Mech Syst Signal Process 3(2):143–155
Friswell MI, Mottershead JE (1995) Finite element model updating in structural dynamics. Kluwer Academic Publishers, Dordrecht
Friswell MI, Mottershead JE, Ahmadian H (1998) Combining subset selection and parameter constraints in model updating. Trans Am Soc Mech Eng J Vib Acoust 120(4):854–859
Friswell MI, Mottershead JE, Ahmadian H (2001) Finite element model updating using experimental test data: parameterisation and regularisation. R Soc Philos Trans Math Phys Eng Sci 359:169–186
Gladwell GML, Ahmadian H (1995) Generic element matrices suitable for finite element model updating. Mech Syst Signal Process 9(6):601–614
Goller B, Pradlwarter HJ, Schuëller GI (2009) Robust model updating with insufficient data. Comput Methods Appl Mech Eng 198:3096–3104
Goller B, Broggi M, Calvi A, Schuëller GI (2011) A stochastic model updating technique for complex aerospace structures. Finite Elem Anal Des 47:739–752
Goulet J-A, Michel C, Smith IFC (2013) Hybrid probabilities and error domain structural identification using ambient vibration monitoring. Mech Syst Signal Process 37:199–212
Govers Y, Link M (2010) Stochastic model updating – covariance matrix adjustment from uncertain experimental modal data. Mech Syst Signal Process 24(3):696–706
Govers Y, Link M (2012) Using stochastic experimental modal data for identifying stochastic finite element parameters of the AIRMOD benchmark structure. Proceedings of the international conference on noise and vibration engineering, USD2012, Leuven, Belgium, pp 4697–4715
Hansen PC (1994) Regularisation tools: a MATLAB package for analysis and solution of discrete ill-posed problems. Numer Algorithms 6:1–35
Hua XG, Ni YQ, Chen ZQ, Ko JM (2008) An improved perturbation method for stochastic finite element model updating. Int J Numer Methods Eng 73:1845–1864
Hua XG, Ni YQ, Ko JM (2009) Adaptive regularisation parameter optimization in output-error-based finite element model updating. Mech Syst Signal Process 23:563–579
Hua XG, Wen Q, Ni YQ, Chen ZQ (2017) Assessment of stochastically updated finite element models using reliability indicator. Mech Syst Signal Process 82:217–229
Jacquelin E, Adhikari S, Friswell MI (2012) A second-moment approach for direct probabilistic model updating in structural dynamics. Mech Syst Signal Process 29:262–283
Katafygiotis L, Beck JL (1998) Updating models and their uncertainties. II: model identifiability. J Eng Mech 124(4):463–467
Kenigsbuch R, Halevi Y (1998) Model updating in structural dynamics: a generalised reference basis approach. Mech Syst Signal Process 12(1):75–90
Khodaparast HH, Mottershead JE, Friswell MI (2008) Perturbation methods for the estimation of parameter variability in stochastic model updating. Mech Syst Signal Process 22(8):1751–1773
Khodaparast HH, Mottershead JE, Badcock KJ (2011) Interval model updating with irreducible uncertainty using the Kriging predictor. Mech Syst Signal Process 25(4):1204–1226
Kuo Y-C, Datta BN (2012) Quadratic model updating with no spillover and incomplete measured data: existence and computation of solution. Linear Algebra Appl 436:2480–2493
Lallement G, Piranda J (1990) Localisation methods for parameter updating of finite element models in elastodynamics. IMAC IIX, Orlando, pp 579–585
Link M (1999) Updating of analytical models – basic procedures and extensions. In: Silva JMM, Maia NMM (eds) Modal analysis and testing. Kluwer Academic Publishers, Dordrecht, pp 281–304
Link M, Friswell MI (2003) Working group 1: generation of validated structural dynamic models- results of a benchmark study Utilising the GARTEUR SM-AG19 test-bed. In: Golinval J-C, Link M (eds) COST action F3 “structural dynamics” (1997–2001)- an European co-operation in the field of science and technology. Mechanical Systems & Signal Processing, vol 17, no (1), pp 9–20
Mao X, Dai H (2012) Finite element model updating with positive definiteness and no spillover. Mech Syst Signal Process 28:387–398
Mares C, Mottershead JE, Friswell MI (2006) Stochastic model updating: part 1- theory and simulated examples. Mech Syst Signal Process 20(7):1674–1695
Mottershead JE, Foster CD (1991) On the treatment of ill-conditioning in spatial parameter estimation from measured vibration data. Mech Syst Signal Process 5(2):139–154
Mottershead JE, Friswell MI (1993) Model updating in structural dynamics: a survey. J Sound Vib 167(2):347–375
Mottershead JE, Friswell MI, Ng GHT, Brandon JA (1996) Geometric parameters for finite element model updating of joints and constraints. Mech Syst Signal Process 10(2):171–182
Mottershead JE, Mares C, Friswell MI, James S (2000) Selection and updating of parameters for an aluminium space-frame model. Mech Syst Signal Process 14(6):923–944
Mottershead JE, Mares C, James S, Friswell MI (2006) Stochastic model updating: part 2- application to a set of physical structures. Mech Syst Signal Process 20(8):2171–2185
Mottershead JE, Link M, Friswell MI (2011) The sensitivity method in finite element model updating: a tutorial. Mech Syst Signal Process 25(7):2275–2296
Mthembu L, Marwala T, Friswell MI, Adhikari S (2011) Model selection in finite element model updating using the Bayesian evidence statistic. Mech Syst Signal Process 25:2399–2412
Natke HG (1991) On regularization methods applied to the error localization of mathematical models. Proc Int Modal Analysis Conf IMAC IX, Florence, pp 70–73
Natke HG (2004) Einführung in Theorie und Praxis der Zeitreihen und Modalanalyse. Vieweg Verlag, Braunschweig/Wiesbaden
Natke HG, Lallement G, Cottin N (1995) Properties of various residuals within updating of mathematical models. Inverse Prob Eng 1:329–348
Patelli E, Govers Y, Broggi M, Martins Gomes H, Link M, Mottershead JE (2017) Sensitivity or Bayesian model updating: a comparison of techniques using the DLR AIRMOD test data. Arch Appl Mech 87(5):905–925
Prells U (1996) A regularisation method for the linear error localisation of models of elastomechanical systems. Inverse Prob Eng 3:197–217
Schedlinski C (2012) Finite element model validation of a large spinning facility. Proceedings, ISMA 2012, Leuven
Schedlinski C (2018) ICS.sysval product description. http://www.ics-engineering.com
Schedlinski C, Staples B (2004) Computational model updating of axisymmetric systems. Proceedings of the noise and vibration engineering conference, ISMA 2004, Leuven
Schedlinski C, et al (2004) Experimental modal analysis and computational model updating of a body in white. Proceedings of the noise and vibration engineering conference, ISMA 2004, Leuven
Schedlinski C, et al (2008) Computational model updating of structural damping and acoustic absorption for coupled fluid-structure-analyses of passenger cars. Proceedings of the Noise and Vibration Engineering Conference, ISMA 2008, Leuven
Silva T, Maia NMM, Link M, Mottershead JE (2016) Parameter selection and covariance updating. Mech Syst Signal Process 70–71:269–283
Simoen E, De Roeck G, Lombaert G (2015) Dealing with uncertainty in model updating for damage assessment: a review. Mech Syst Signal Process 56–57:123–149
Smith SW (1998) Iterative matrix approximation for model updating. Mech Syst Signal Process 12(1):187–202
Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. Wiley, New York
Titurus B, Friswell MI (2008) Regularization in model updating. Int J Numer Methods Eng 75(4):440–478
Wang X, Hill TL, Neild SA, Shaw AD, Khodaparast HH, Friswell MI (2018) Model updating strategy for structures with localized nonlinearities using frequency response measurements. Mech Syst Signal Process 100:940–961
Webber B, Paultre P, Proulx J (2009) Consistent regularisation of nonlinear model updating for damage identification. Mech Syst Signal Process 23:1965–1985
Xie D (2011) A numerical method of structure-preserving model updating problem and its perturbation theory. Appl Math Comput 217:6364–6371
Yuan Y (2009) A symmetric inverse eigenvalue problem in structural dynamic model updating. Appl Math Comput 213:516–521
Yuen K-V (2010) Bayesian methods for structural dynamics and civil engineering. Wiley, Singapore
Yuen K-V (2012) Updating large models for mechanical systems using incomplete modal measurement. Mech Syst Signal Process 28:297–308
Zhang EL, Feissel P, Antoni J (2011) A comprehensive Bayesian approach for model updating and quantification of modelling errors. Probab Eng Mech 26:550–560
Acknowledgments
The content and images presented for the automotive example problem are published with the kind permission of the Volkswagen AG, Germany.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 The Society for Experimental Mechanics
About this entry
Cite this entry
Mottershead, J.E., Link, M., Friswell, M.I., Schedlinski, C. (2020). Model Updating. In: Allemang, R., Avitabile, P. (eds) Handbook of Experimental Structural Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6503-8_18-1
Download citation
DOI: https://doi.org/10.1007/978-1-4939-6503-8_18-1
Received:
Accepted:
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-6503-8
Online ISBN: 978-1-4939-6503-8
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering
Publish with us
Chapter history
-
Latest
Model Updating- Published:
- 02 September 2021
DOI: https://doi.org/10.1007/978-1-4939-6503-8_18-2
-
Original
Model Updating- Published:
- 22 January 2021
DOI: https://doi.org/10.1007/978-1-4939-6503-8_18-1