Input-dependence effects in dynamics model calibration

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Abstract This paper investigates the use of non-linear structural dynamics computational models with multiple levels of fidelity for the calibration of input-dependent model parameters. Non-linear behavior complicates the calibration of model parameters that are input-dependent (i.e., functions of temperature, loading, etc.). Different types of models may also be available for the estimation of unmeasured system properties, with different levels of physics fidelity, mesh resolution and boundary condition assumptions. To infer these system properties, Bayesian calibration can be used to combine information from multiple sources (such as experimental data and prior knowledge) and comprehensively quantify the uncertainty in the model parameters. Estimating the posterior distributions is done using Markov Chain Monte Carlo sampling, which requires a large number of computations, thus making the use of a high-fidelity model for calibration prohibitively expensive. On the other hand, use of a low-fidelity model could lead to significant error in calibration and prediction. Therefore, this paper pursues a multi-fidelity approach for input-dependent model parameter calibration with a surrogate of the low-fidelity model corrected using higher fidelity simulation data. The effects of non-linear behavior and input-dependence of model parameters and measurements are systematically organized and distinguished using a Bayesian network. The methodology is illustrated with a curved panel, subjected to acoustic and thermal loading, where the damping properties of the panel could be functions of the acoustic loading and temperature magnitudes. Two models (a frequency response analysis and a full time history analysis) are combined to estimate the damping characteristics of the panel. The effect of the temperature on the performance of the strain gages and therefore on the calibration results is also studied.