Stochastic finite element model calibration based on frequency responses and bootstrap sampling

Abstract

A new stochastic finite element model calibration framework for estimation of the uncertainty in model parameters and predictions from the measured frequency responses is proposed in this paper. It combines the principles of bootstrapping with the technique of FE model calibration with damping equalization. The challenge for the calibration problem is to find an initial estimate of the parameters that is reasonably close to the global minimum of the deviation between model predictions and measurement data. The idea of model calibration with damping equalization is to formulate the calibration metric as the deviation between the logarithm of the frequency responses of FE model and a test data model found from measurement where the same level of modal damping is imposed on all modes. This formulation gives a smooth metric with a large radius of convergence to the global minimum. In this study, practical suggestions are made to improve the performance of this calibration procedure in dealing with noisy measurements. A dedicated frequency sampling strategy is suggested for measurement of frequency responses in order to improve the estimate of a test data model. The deviation metric at each frequency line is weighted using the signal-to-noise ratio of the measured frequency responses. The solution to the improved calibration procedure with damping equalization is viewed as a starting value for the optimization procedure used for uncertainty quantification. The experimental data is then resampled using the bootstrapping approach and the FE model calibration problem, initiating from the estimated starting value, is solved on each individual resampled dataset to produce uncertainty bounds on the model parameters and predictions. The proposed stochastic model calibration framework is demonstrated on a six degree-of-freedom spring-mass system prior to being applied to a general purpose satellite structure.