42 Robust Expansion of Experimental Mode Shapes Under Epistemic Uncertainties 427 in terms of error: in the above example, the robust design, the design 24, allows to reach around 10 % less of expansion error at O˛ D0:5. Though expansion errors are somewhat theoretical, output of the cost function can be, in future work, maximum response levels in operation at the frequency band of interest. The ECRE-based expansion yields the extended mode shape after the resolution of a simple linear system. The main drawbacks of this technique remains the CPU-time. In a future work, model responses approximation techniques such as metamodeling will be used in order to reduce the time of computation. References 1. Pascual R, Golinval JC, Razeto M (1998) On the reliability of error localization indicators. In: Proceedings of the ISMA23, Leuven, Belgium, 1998. 2. Corus M, Balmès E (2003) Improvement of a structural modification method using data expansion and model reduction techniques. In: Proceedings of IMAC XXI, Kissimee, Florida (USA), 2003. 3. Pascual RJ (1999) Model based structural damage assessment using vibration measurements. PhD thesis, Université de Liège 4. Balmès E (2000) Review and evaluation of shape expansion methods. In: Proceedings of IMAC XVIII: A Conference on Structural Dynamics. vol 4062, San Antonio, Texas (USA), pp 555–561 5. Mottershead JE, Friswell MI (1993) Model updating in structural dynamics: a survey. J Sound Vib 167(2):347–375 6. Kidder R (1973) Reduction of structural frequency equations. AIAA J 11(6):892 7. Guyan RJ (1964) Reduction of stiffness and mass matrices. AIAA J 3:380 8. O’Callahan JC (1989) A procedure for an improved reduced system (IRS) model. In: Proceedings of IMAC VII, Las Vegas, Nevada (USA), pp 17–21 9. O’Callahan JC, Avitabile P, Riemer R (1989) System equivalent reduction expansion process (SEREP). In: Proceedings of IMAC VII, Las Vegas, Nevada (USA), pp 29–37 10. Balmès E (1999) Sensors, degrees of freedom and generalized mode expansion methods. In: Proceedings of IMAC XVII, Kissimee, Florida (USA), pp 628–634 11. Ladevèze P, Leguillon D (1983) Error estimate procedure in the finite element method and applications. SIAM J Numer Anal 20(3):485–509 12. Reynier M, Ladeveze P, Feuardent V (1998) Selective error location indicators for mass and stiffness updating. In: Tanaka M, Dulikravich GS (eds) Inverse problems in engineering mechanics, Elsevier Science Ltd, Oxford, pp 291–298 13. Ben-Haim Y, Hemez FM (2011) Robustness, fidelity and prediction-looseness of models. Proc R Soc A 468:227–244 14. Hemez F, Ben-Haim Y (2004) Info-gap robustness for the correlation of tests and simulations of a non-linear transient. Mech Syst Signal Pr 18:1443–1467 15. Pereiro D, Cogan S, Sadoulet-Reboul E, Martinez F (2013) Robust model calibration with load uncertainties. In: Topics in model validation and uncertainty quantification. Conference proceedings of the society for experimental mechanics series 41, vol 5. Springer, pp 89–97 16. Deraemaeker A, Ladevèze P, Leconte P (2002) Reduced bases for model updating in structural dynamics based on constitutive relation error. Comput Method Appl M 191:2427–2444 17. Feissel P, Allix O (2007) Modified constitutive relation error identification strategy for transient dynamics with corrupted data: the elastic case. Comput Method Appl M 196:1968–1983 18. Banerjee B, Walsh TF, Aquino W, Bonnet M (2013) Large scale parameter estimation problems in frequency-domain elastodynamics using an error in constitutive equation functional. Comput Method Appl M 253:60–72 19. Ben-Haim Y (2006) Information-gap theory: decisions under severe uncertainty, 2nd edn. Academic Press, London
RkJQdWJsaXNoZXIy MTMzNzEzMQ==