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This chapter presents the technique route of model updating in the presence of imprecise probabilities. The emphasis is put on the inevitable uncertainties, in both numerical simulations and experimental measurements, leading the updating methodology to be significantly extended from deterministic sense to stochastic sense. This extension requires that the model parameters are not regarded as unknown-but-fixed values, but random variables with uncertain distributions, i.e. the imprecise probabilities. The final objective of stochastic model updating is no longer a single model prediction with maximal fidelity to a single experiment, but rather the calibrated distribution coefficients allowing the model predictions to fit with the experimental measurements in a probabilistic point of view. The involvement of uncertainty within a Bayesian updating framework is achieved by developing a novel uncertainty quantification metric, i.e. the Bhattacharyya distance, instead of the typical Euclidian distance. The overall approach is demonstrated by solving the model updating sub-problem of the NASA uncertainty quantification challenge. The demonstration provides a clear comparison between performances of the Euclidian distance and the Bhattacharyya distance, and thus promotes a better understanding of the principle of stochastic model updating, as no longer to determine the unknown-but-fixed parameters, but rather to reduce the uncertainty bounds of the model prediction and meanwhile to guarantee the existing experimental data to be still enveloped within the updated uncertainty space.

Overview of Stochastic Model Updating in Aerospace Application Under Uncertainty Treatment