Uncertainty quantification in high-dimensional supersonic flows using nonlinear reduced order modeling
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Iyengar, Nikhil
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Abstract
The development of commercial supersonic aircraft is dependent on the mitigation of sonic boom loudness to acceptable levels. Since uncertainties in the atmosphere and flight conditions can drastically impact the loudness of an aircraft, there is a need to rigorously quantify the uncertainty in aircraft performance to avoid certification delays. The calculation of sonic booms requires the precise near-field pressure distribution around the aircraft, which is obtained using computational fluid dynamics (CFD) simulations. These simulations can pose intractable computational costs in multi-query problems, such as uncertainty quantification (UQ). This thesis presents a non-intrusive, parametric reduced order modeling (ROM) method to perform UQ in high-dimensional, computationally expensive full-order models (FOM). The central idea is to identify a low-dimensional latent space that effectively captures the dynamics of the FOM. Unlike classical methods for dimensionality reduction (DR) that approximate models using flat surfaces, this study explores nonlinear DR to identify the low-dimensional manifold on which the data exists. Compared to linear methods, the proposed global manifold learning-based approaches can better predict shocks, maintain accuracy throughout the field, and consistently capture statistical moments. Once a suitable DR method is identified, the focus shifts to accurately performing UQ in nonlinear latent spaces. Here, the Polynomial Chaos-Kriging (PCK) method, which attempts to combine the properties of a global predictive model with the local predictive accuracy of an interpolation-based technique, is utilized. In particular, the PCK model is combined with both linear DR and manifold learning approaches and evaluated on several CFD test problems with stochastic inputs. It is observed that the manifold learning-based PCK method significantly reduces modeling errors near nonlinear structures compared to classical approaches, even in sparse datasets. Equally important, the addition of Kriging to polynomial chaos expansions substantially improves the predictive capacity of the ROM, irrespective of the dimensionality reduction method. Lastly, by leveraging this reduced order model, two procedures are designed to efficiently propagate the impact of atmospheric and flight uncertainties on the sonic boom pressure signatures of a low-boom supersonic aircraft. It is shown that these ROMs yield pressure signatures at the ground that both qualitatively match the shape and perceived loudness with low error. Thus, this study not only provides novel insight for the ROM and UQ fields based on findings from real-world engineering data sets, but also contributes to the development of methods for the robust design of supersonic aircraft.
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Date
2024-01-17
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Dissertation