Bayesian Inferencing on an Aircraft T-Tail Using Probabilistic Surrogates and Uncertainty Quantification

Uncertainty quantification is a notion that has received much interest over the past decade. It involves the extraction of statistical information from a problem with inherent variability. This variability may stem from a lack of knowledge or through observational uncertainty. Traditionally, uncertainty quantification has been a challenging pursuit owing to the lack of efficient methods available. The archetypal uncertainty quantification method is Monte Carlo theory, however, this method possesses a slow convergence rate and is therefore a computational burden in some scenarios. In contrast to Monte Carlo theory, polynomial chaos theory is an alternative approach that offers the ability to estimate statistical moments efficiently. Because polynomial chaos theory behaves like a surrogate model, it is possible to query this inexpensively for information, which allows it to be useful for Bayesian inferencing. This paper builds upon previous work, because a polynomial chaos model is demonstrated to not only be useful for uncertainty quantification applications by finding inexpensive point estimates for statistical moments, but is also able to form a component of the Bayesian likelihood function. It is thus the aim of this paper to demonstrate and combine the aforementioned notions of uncertainty quantification and Bayesian inferencing on an in-house physical T-tail structure, which is reflective of a realistic scenario. The vibrational modes of the T-tail structure will provide a basis on which the results of the uncertainty quantification analysis may be compared and on which a subsequent Bayesian inferencing procedure may be carried out to infer the correct dimensions, based on comparing the model predictions with real-life vibrational data.