Ph.D. Defense

Bilal Mufti 

(Advisor: Prof. Dimitri N. Mavris)

"Reduced-Order Modeling Techniques for Aircraft Design in High-Dimensional Spaces"

Friday, November 22 

11:15 a.m.

Collaborative Design Environment (CoVE),

Weber Space Science and Technology Building (SST II)

and

Teams Meeting

Abstract

Future aircraft designs are expected to meet rigorous performance demands, including enhanced fuel efficiency and high-speed capabilities, all while adhering to stringent environmental regulations that call for reduced noise levels and lower emissions. The design of these aircraft necessitates the early use of high-fidelity simulation tools during the conceptual design phase, where these simulations are applied in various areas, including multidisciplinary analysis, design optimization, uncertainty quantification, and design space exploration. However, the high computational cost associated with these tools renders them impractical for such applications. Surrogate models offer a computationally economical alternative, replacing these intensive simulations with efficient mathematical models. While data-fit surrogate models predict scalar outputs, Reduced-Order Models (ROMs) extend this capability to predict field solutions, capturing the underlying physics crucial for early-stage aircraft design.

To enable the exploration of revolutionary aircraft designs and capture subtle design nuances, it is crucial to develop these ROMs over high-dimensional design spaces. However, constructing such ROMs presents challenges due to (1) large input dimensionality, leading to the curse of dimensionality, (2) the high computational cost of training, and (3) the prediction of nonlinearities, such as shock waves within flow fields. This dissertation's primary objective is to develop or enhance methods to address these three challenges, structured into three research areas.

For the first research area, we address the challenge of high input dimensionality by introducing a model-based active subspace method for supervised input dimensionality reduction. This method leverages direct function evaluations to identify the active subspace, enhancing computational efficiency. Notably, it circumvents the need for gradient information and the complex formulations often associated with active subspace methods, making it well-suited for the construction of ROMs over high-dimensional design spaces.

To address the second research challenge concerning the high computational cost, we develop a multi-fidelity reduced-order modeling approach that combines Procrustes manifold alignment with dimensionality reduction techniques. This method applies dimensionality reduction to both input and output spaces within a multi-fidelity framework, facilitating a cost-effective construction of ROMs in high-dimensional design spaces. Procrustes alignment ensures consistent integration of various field data types, enhancing model flexibility and efficiency, while the dimensionality reduction techniques mitigate potential issues related to high dimensionality.

In the third research area, we tackle the challenge of predicting nonlinearities by proposing a nonlinear ROMs framework based on deep learning and manifold learning, specifically designed to handle flow fields with complex variations, such as shock waves in transonic and supersonic regimes. This framework combines convolutional neural networks (CNNs) for extracting nonlinear shape modes and manifold learning for field prediction, accurately capturing and reconstructing shock-related features. The resulting method enhances predictive accuracy for applications where nonlinear behavior is critical, allowing for precise characterization of shock phenomena.

This dissertation provides methods that span different points on the cost-versus-accuracy spectrum, enabling aircraft designers to make informed choices based on their requirements for prediction accuracy and computational budgets. While these methods are developed for aircraft design applications, they can also be considered machine learning and deep learning techniques applicable to a wide range of engineering design problems. In summary, this thesis introduces three methods: (1) a computationally efficient model-based active subspace approach for supervised input dimension reduction, (2) a multi-fidelity framework for high-dimensional ROMs construction, and (3) a nonlinear ROMs framework utilizing deep learning and manifold learning to predict complex field solutions.

Committee

• Prof. Dimitri N. Mavris – School of Aerospace Engineering (advisor)
• Prof. Lakshmi Sankar– School of Aerospace Engineering
• Prof. Graeme J. Kennedy – School of Aerospace Engineering
• Dr. Christian Perron – School of Aerospace Engineering
• Dr. Ryan Jacobs – GE Aerospace Research