Stochastic Finite Element Model Updating by Bootstrapping
This paper presents a new stochastic finite element model calibration framework for estimation of the uncertainty in model parameters, which combines the principles of bootstrapping with the technique of FE model calibration with damping equalization. The bootstrapping allows to quantify the uncertainty bounds on the model parameters by constructing a number of resamples, with replacement, of the experimental data and solving the FE model calibration problem on the resampled datasets. To a great extent, the success of the calibration problem depends on the starting value for the parameters. The formulation of FE model calibration with damping equalization gives a smooth metric with a large radius of convergence to the global minimum and its solution can be viewed as the initial estimate for the model parameters. In this study, practical suggestions are made to improve the performance of this algorithm in dealing with noisy measurements. The performance of the proposed stochastic calibration algorithm is illustrated using simulated data for a six degree-of-freedom mass-spring model.
KeywordsStochastic FE model calibration Frequency response Experiment design 0.632 Bootstrap Uncertainty quantification
The authors would like to express their gratitude to Prof. Tomas McKelvey for the discussions.
- 1.Jiang, D., Zhang, P., Fei, Q., Wu, S.: Comparative study of model updating methods using frequency response function data. J. Vibroeng. 16(5), 2305–2318 (2014)Google Scholar
- 5.Balmès, E.: A finite element updating procedure using frequency response functions—applications to the MIT/SERC interferometer testbed. In: Proceedings of the IMAC XI, Kissimmee, FL (1993)Google Scholar
- 10.Khorsand Vakilzadeh, M., Yaghoubi, V., Mckelvey, T., Abrahamsson, J.S.T., Ljung, L.: Experiment design for improved frequency domain subspace system identification of continuous-time systems. In: Proceedings of the 17th IFAC Symposium on System Identification, Beijing (2015)Google Scholar
- 12.Sipple, J.D., Sanayei, M.: Full-scale bridge finite-element model calibration using measured frequency-response functions. J. Bridge Eng. 20, 04014103, (2014)Google Scholar
- 13.Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer, New York (2009)Google Scholar
- 14.Abrahamsson, T.J.S., Bartholdsson, F., Hallqvist, M., Olsson, K.H.A., Olsson, M., Sällström, Å.: Calibration and validation of a car subframe finite element model using frequency responses. In: Proceedings of the 33rd IMAC, Orlando, FL (2015)Google Scholar
- 20.Kozak, M.T., Cömert, M.D., Özgüven, H.N.: A model updating routine based on the minimization of a new frequency response based index for error localization. In: Proceedings of the 25th International Modal Analysis Conference, pp. 84–95. Orlando, FL (2007)Google Scholar