09:40
Reduced-order modelling
Chair: Lorenz Tichy
09:40
30 mins
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Machine learning-based parametric model order reduction for the gust load analysis
Sangmin Lee, SiHun Lee, Younggeun Park, Seung-Hoon Kang, Kijoo Jang, Haeseong Cho, SangJoon Shin
Abstract: Gust load analysis plays an important role in the design process of an aircraft. The medium fidelity aeroelastic analysis such as that by doublet-lattice method (DLM) offer an efficient way of computing aerodynamic loads regarding the gust. Although DLM offers efficient aeroelastic analysis, significant amount of the computational time will still be required when multi-parametric study is required. As a substitute, parametric model order reduction (pMOR) will be considered to alleviate the computational time along with sufficient accuracy. Here, to approximate the nonlinear full order model (FOM) successfully with a slowly decaying Kolmogorov n-width problem, nonlinear pMOR method is considered. More specifically, nonlinear pMOR method adopting generative machine learning methods, variational autoencoder (VAE) will be considered.
In this research, results by nonlinear pMOR with multiple parameters will be presented for the prediction of the gust response. The nonlinear pMOR and prediction will be attempted by LSH-VAE [2]. LSH-VAE is capable of accurate pMOR even when dealing with a large FOM dataset with an aid of the deep hierarchical structure. The deep hierarchical structure, composed of the bidirectional encoder-decoder group, will be adopted to mitigate the loss of long-range correlation. The loss function of LSH-VAE consists of a hybrod weighted least squares and Kullback-Leibler divergence loss to improve performance. Subsequently, in the reduced-dimensional latent space, the target latent variable will be acquired by conducting spherically linear interpolation. The decoder network will be used to generate the interpolated object from the interpolated latent vector.
The current scheme will be applied for a high altitude long endurance aircraft under a discrete gust. To perform pMOR, the gust amplitude and duration will be considered as the parameters. The FOM will be obtained using a DLM-based analysis, ZAERO, for 10 baseline parameters selected by Latin hypercube sampling. For the accuracy evaluation, an unanalyzed parameter will be selected. Interpolated structural responses such as the wing tip displacement and internal stresses will be compared to the results by the unanalyzed parameter. Then, the computational efficiency will be evaluated. Finally, the structural response that satisfies certain range of the flight condition will be sought by using LSH-VAE.
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10:10
30 mins
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Model order reduction for nonlinear aeroelastic dynamical system using automatic differentiation
Declan Clifford, Andrea Da Ronch
Abstract: One means towards reducing the emissions outputs of the aviation industry is by increasing wing aspect ratio, thus increasing aerodynamic efficiency. This however results in highly flexible lifting surfaces. As part of the aircraft design process, it is necessary to understand the dynamics of these highly flexible lifting surfaces to gust excitation. This may be as part of verifying structural limits are not exceeded – via a worst-case gust search, or, to design control laws for gust alleviation. Performing either of these tasks via direct time integration of the full-order model (FOM) may prove to be computationally intractable. Use of explicit integration schemes with the high-dimensional, nonlinear FOM requires the resolution of impractically small steps-sizes, whilst use of implicit schemes comes with additional computational complexities for nonlinear systems. Thus, there exists the motivation for nonlinear Model Order Reduction (MOR) to reduce system size and computational complexity, while retaining the critical dynamical properties of the system.
In Ref. [1] a MOR algorithm for application to flexible aircraft control design was formulated. The approach is based on the eigenspectrum of the FOM Jacobian matrix, projecting a Taylor Series expansion of the original system onto a representative basis of eigenvectors, thus reducing the state-space dimension, and retaining only critical frequency content. In the work of Ref. [1], reduced order nonlinear terms were approximated via Finite Differencing (FD). This method was further developed in Ref. [2], introducing Automatic Differentiation (AD) to overcome round-off and/or truncation errors associated with approximating the reduced order nonlinear terms via FD.
This work builds on the method of Ref. [2], presenting a framework to build nonlinear aeroelastic ROM systems using source-transformation AD. Within this work, a study is performed to determine the significance of retaining specific aeroelastic modes in the construction of the nonlinear ROM system. Aeroelastic mode-tracking Ref. [3] is used to assist in determining the physical phenomenon these modes represent by solving eigenvalue problems over varying parameter ranges. This permits mode identification specifically as structural mode shapes, aerodynamic mode shapes or gust-related mode shapes.
[1] A. Da Ronch, K. J. Badcock, Y Wang, A. Wynn, and R. Palacios, “Nonlinear Model
Reduction for Flexible Aircraft Control Design,” in: AIAA Flight Mechanics Conference, 2012.
[2] D. Massegur, D. Clifford, A. Da Ronch, and S. Symon, “Comparing Reduced
Order Models for Nonlinear Dynamical Systems,” in: 33rd Congress of the International Council of the Aeronautical Sciences, September 2022.
[3] X. Hang, Q. Fei, W. Su, “On Tracking Aeroelastic Modes in Stability Analysis Using Left and Right Eigenvectors”, AIAA Journal, 2019
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