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Uncertainty quantification has proven to be an indispensable study for enhancing reliability and robustness of engineering systems in the early design phase. Single and multi-fidelity surrogate modelling methods have been used to replace the expensive high fidelity analyses which must be repeated many times for uncertainty quantification. However, since the number of analyses required to build an accurate surrogate model increases exponentially with the number of random input variables, most surrogate modelling methods suffer from the curse of dimensionality. As an alternative approach, the Low-Rank Approximation method can be applied to high-dimensional uncertainty quantification studies with a low computational cost, where the number of coefficients for building the surrogate model increases only linearly with the number of random input variables. In this study, the Low-Rank Approximation method is implemented for multi-fidelity applications with additive and multiplicative correction approaches to make the high-dimensional uncertainty quantification analysis more efficient and accurate. The developed uncertainty quantification methodology is tested on supersonic aircraft design problems and its predictions are compared with the results of single- and multi-fidelity Polynomial Chaos Expansion and Monte Carlo methods. For the same computational cost, the Low-Rank Approximation method outperformed both in surrogate modeling and uncertainty quantification cases for all the benchmarks and real-world engineering problems addressed in the present study.

To advance a supersonic aircraft design process, an uncertainty quantification study is conducted for sonic boom prediction while considering uncertainties associated with flight and atmospheric conditions. The uncertainty quantification process is implemented within a multidisciplinary analyses framework and assisted with a multifidelity surrogate model based approach. The sonic boom prediction framework requires input from the flowfield pressure distribution solution to generate the near-field pressure signature of the aircraft, which is then propagated throughout the atmosphere to the ground by using aeroacoustic methods. The open-source SU2 suite is employed as a high-fidelity flow solver tool to obtain the aerodynamic solution, while in-house postprocessing scripts are developed to generate the required near-field pressure signature. For low-fidelity flow analysis, A502 PAN AIR, a higher-order panel code which solves flows around slender bodies in low angles of attack for subsonic and supersonic regimes, is used. For nonlinear aeroacoustic propagation, NASA Langley Research Center’s code sBOOM exploits the near-field pressure signature for both high-fidelity and low-fidelity sonic boom calculations. Efficient uncertainty quantification tools are developed in house by implementing multifidelity polynomial chaos expansion and multifidelity Monte Carlo methods. Several flight and atmospheric parameters are selected to include randomness where these uncertainties are propagated into the sonic boom loudness prediction of the JAXA wing-body model, which is a low boom aircraft. Finally, an overall assessment of the multifidelity uncertainty quantification methods is presented in terms of efficiency and numerical accuracy.

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