Construction of Predictive Uncertainty Quantification Framework to the Extrapolation of TPS Arc-Jet Experiment Data to Flight Conditions

The increased interest in space exploration and study of nearby non-stellar objects necessitates further development of modeling capabilities for accurate prediction of physical phenomena encountered. Among those, understanding of material response behavior and accurate uncertainty quantification for determined predictions in hypersonic entry scenarios is critical for proper sizing of TPS materials in vehicle heat shield designs. Studies concerning these articles are conducted in plasma wind tunnel facilities that enable a multitude of diagnostic techniques to be utilized where obtained data are used in validation and calibration of existing numerical tools among others. However, these facilities are not able to fully recreate encountered flight environments and predictions made with tools calibrated with corresponding data extrapolate beyond the achievable ground testing envelope. Objectives of this effort were to increase the confidence with which results of computational tools calibrated with data obtained at plasma wind tunnel facilities can be extrapolated to in-flight performance. This was addressed with development and formulation of a non-deterministic framework that considers model inadequacy and shortcomings of ground testing strategies through application of physics and probability based stochastic model(s). Anticipated statistical treatments necessitated development of the in-house Stochastic Modeling and Uncertainty Quantification (SMUQ) toolbox. Written following an object-oriented design, a number of statistical methodologies spanning fields of sensitivity analysis, surrogate modeling, non-deterministic calibration, and uncertainty quantification were included as part of the framework and validated against results from existing applications. The implemented routines take advantage of a multitude of optimizations and boast highly configurable input parametrization to ensure, together with streamlined pairing with external computational models, high versatility and applicability in a wide range of scientific fields and audience. The SMUQ toolbox was utilized in all applications of statistical methodologies performed as part of this work. In addition to plasma wind tunnel facility and Mars Science Laboratory (MSL) flight-oriented studies, the toolbox was also employed in research concerning re-entry of the Orion vehicle as well as more nuanced applications in the fields of aerodynamics and non-equilibrium chemistry. A large body of preliminary investigations was performed to meet the objectives of the research training plan over the course of the fellowship. Some of these included studies concerning effects of uncertainty models utilized as part of Bayesian inference exercises where it was found that inclusion of correlation effects in model error across the response domain can have significant impacts on calibration results. Effects of common simplification approaches like dimension reduction, grid discretization level, and absence of input correlation were also investigated through application of a series of sensitivity treatments with 3-D monolithic, recessing 1-D, and 1-D TC1-driver scenarios for the MSL heatshield. Of the myriad of obtained conclusions, it was found that reduction from 3-D to 1-D scenarios near the stagnation region did not appreciably alter dependence of the model output to input variation. These effects were even less prominent in the case of coarse grids where non-negligible deviation in quantity of interest predictions between simulations using different grid densities was observed. Limitations of state-of-the-art approaches in straight forward propagation of results obtained from non-deterministic calibration exercises with HyMETS ground facility measurements were also explored. It was found that given limited related body of work in the charring ablator field, without ad-hoc approaches model inadequacy could not be applied in extrapolation scenarios and limited uncertainty that could be accounted for did not adequately capture uncertainty quantified with available flight data. More importantly, based on calibrated predictions with ground facility data, quantified uncertainty bounds did not reliably encapsulate captured flight measurements. The non-deterministic framework addresses prediction of uncertainty due to model inadequacy as well as applicability of ground facility testing strategies to flight environments through a novel combination approach. A Gaussian process formulation is first utilized to approximate uncertainty due to model inadequacy beyond the calibration scenario. It is established that additional model and environmental quantities can be used in its formulation in addition to corresponding hyperparameters that are calibrated simultaneously with material response framework parameters. It was also found that there exists a conflict in how ground facility and flight data inform input quantities during a calibration exercise due to differences in obtained environments. A prior-posterior mixture is utilized in a following treatment to resolve discrepancy in obtained information where posterior obtained with plasma wind tunnel data is weighed against prior knowledge based on the applicability of the ground scenario to the extrapolated environment. Predictions concerning most likely outcomes as well as associated uncertainty are shown to be much more closely representative of uncertainty obtainable computationally once flight data are available. In addition to more adequate uncertainty bounds, predictions are also biased based on relevance of calibration data given the physical knowledge implemented in the computational model. The general structure and formulation of the framework allows for further development of the model inadequacy emulator once more data are available. While the present work was concerned with material response aspect of the hypersonic entry, contributing factors due to uncertainty in aerothermal environment solution process can also trivially be implemented in future efforts in a hierarchical procedure. The developed framework in sum yields significantly more accurate depictions of uncertainty in predictions for extrapolation scenarios with respect to material response of charring ablator TPS materials. Improved uncertainty quantification capabilities reliant on thorough probabilistic treatments can subsequently be leveraged in material sizing procedures for more optimal designs.