27 Evaluating Initial Model for Dynamic Model Updating: Criteria and Application 285 updating. In addition, modal frequencies of the fifth and the sixth mode which are not used in the updating are also accurate. This shows the updated model is not only able to reproduce but also able to predict. From the sixth column of Table 27.7, it could be seen that real values for all the three parameters are found by updating. Every result shows that the initial model is successfully updated. The conclusion could be drawn that the Criterion 2 is effective in judging the updatability of initial models. 27.5 Conclusions Each initial finite element model must be evaluated to determine whether it is updatable or not before updating. However, initial model evaluation is an issue that has been neglected over the years. This paper presents a study on the criteria of initial model evaluation for effective dynamic model updating. Two evaluation criteria are proposed as follows, Criterion 1: If any of the experimental modal frequency i.e. f e j , is not contained in the corresponding range, the initial model is not updatable with the given definition domain of structural parameters. Criterion 2: If each of the experimental modal frequency i.e. f e j , is contained in the corresponding range, the initial model is updatable with the given definition domain of structural parameters. To demonstrate the effectiveness of the criteria, two initial models are constructed for a beam with one including erroneous boundary condition and the other with correct boundary condition. Results verify that the criteria are able to distinguish the model updatability. Though practical problem may be different from the simulation case on the aspect that the real experimental modal frequencies are always noise-contaminated, it’s most likely that the identification error of modal frequencies will be small under most circumstance. Otherwise, it could not be taken as reference in the model updating. Therefore, the identification error won’t be an issue in the application of the proposed evaluation criteria. The proposed criteria are able to qualitatively tell whether the initial model is updatable. But, quantitative evaluation still needs to be studied. Acknowledgements The authors of the paper would like to express appreciation of the support from National Natural Science Foundation of China (10902024), Jiangsu Natural Science Foundation (BK2010397), and Ministry of Education Program for New Century Excellent Talents in University (NCET-11-0086)and Foundation for Distinguished Young Teacher of Southeast University. References 1. 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 2. Friswell MI, Mottershead JE (1995) Finite element model updating in structural dynamics. Kluwer Academic Publishers, Dordrecht 3. Li Z, Sun Z, Guo L (2007) Concurrent multi-scale modeling of structures and damage analyses. J Southeast Univ 37(2):251–260 (in Chinese) 4. Hemez FM, Doebling SW (2001) Review and assessment of model updating for non-linear, transient dynamics. Mech Syst Signal Process 15(1):45–74 5. Goge D, Fullekurg U (2005) Advanced test strategy for identification and characterization of nonlinearities of aerospace structures. AIAA J 43(5):974–986 6. Khodaparast HH, Mottershead JE (2008) Perturbation methods for the estimation of parameter variability in stochastic model updating. Mech Syst Signal Process 22(8):1751–1773 7. Schlune H, Plos M, Gylltoft K (2009) Improved bridge evaluation through finite element model updating using static and dynamic measurements. Eng Struct 31(7):1477–1485 8. Celic D, Boltezar M (2008) Identification of the dynamic properties of joints using frequency-response functions. J Sound Vib 317(1–2):158–174 9. Goge D (2003) Automatic updating of large aircraft models using experimental data from ground vibration testing. Aerosp Sci Technol 7(1):33–45 10. Cottin N, Reetz J (2006) Accuracy of multi-parameter eigenvalues used for dynamic model updating with measured natural frequencies only. Mech Syst Signal Process 20(1):65–77 11. Titurus B, Friswell MI (2008) Regularization in model updating. Int J Numer Methods Eng 75(4):440–478 12. Fei Q, Youlin X, Ng C et al (2007) Structural health monitoring oriented finite element model of Tsing Ma Bridge tower. Int J Struct Stab Dyn 7(4):647–668 13. Allemang RJ (1982) A correlation coefficient for modal vector analysis. Proceedings of the 1st international modal analysis conference, Orlando, Florida 14. Ewins DJ (2000) Model validation: correlation for model updating. Sadhana 25(3):221–234 15. Fei Q (2012) Criteria of evaluating initial model for effective dynamic model updating. J Vibroeng 14(3):1362–1369 16. Link M, Friswell MI (2003) Generation of validated structural dynamic models results of a benchmark study utilizing the GARTEUR SMAG19 test-bed. Mech Syst Signal Process 17(1):9–20
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