Experimental and computational data and field data obtained from measurements are often sparse and noisy. Consequently, interpolating unknown functions under these restrictions to provide accurate predictions is very challenging. This study compares machine-learning methods and cubic splines on the sparsity of training data they can handle, especially when training samples are noisy. We compare deviation from a true function f using the mean square error, signal-to-noise ratio and the Pearson R2 coefficient. We show that, given very sparse data, cubic splines constitute a more precise interpolation method than deep neural networks and multivariate adaptive regression splines. In contrast, machine-learning models are robust to noise and can outperform splines after a training data threshold is met. Our study aims to provide a general framework for interpolating one-dimensional signals, often the result of complex scientific simulations or laboratory experiments.

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Machine-Learning Methods on Noisy and Sparse Data

The dynamic response of a thin buckled panel in a supersonic wind-tunnel experiment is investigated. Measured time histories of the panel displacement and velocity show co-existing, nonlinear responses with features of periodic and chaotic oscillations. Fully coupled computational analyses are conducted in order to study and interpret the aeroelastic phenomena observed during the experiments. A computationally efficient modeling framework is formulated with a nonlinear structural reduced-order model and enriched piston theory aerodynamics for the mean flow. The simulations predict the onset of the chaotic motions observed in the experiments, albeit with an approximately 21% increase in the oscillation amplitude. A linearized equation governing the distance between neighboring solutions is derived and used to compute the largest Lyapunov exponent in order to prove the existence of chaos. A modified Riks analysis highlights the co-existence of multiple equilibrium positions which predisposes the nonlinear system to chaos. The system’s sensitivity to cavity pressure, temperature differential, and initial conditions is also investigated. Variation of the cavity pressure and temperature differential yields additional regions of dynamic activity that were not explored during the experiments.

Investigation of aeroelastic instabilities for a thin panel in turbulent flow

Dynamic interaction between shock wave turbulent boundary layer and flexible panel

The U.S. Air Force Research Laboratory Structural Sciences Center recently started an experimental campaign in the Arnold Engineering Development Center von Karman Facility Tunnel C to investigate ...

Supersonic Aerothermoelastic Experiments of Aerospace Structures

Advances in measuring and understanding separated, nominally two-dimensional (2D) shock-wave/turbulent-boundary-layer interactions (STBLI) have triggered recent campaigns focused on three-dimensional (3D) STBLI, which display far greater configuration diversity. Nonetheless, unifying properties emerge for semi-infinite interactions, taking the form of conical asymptotic behavior where shock-generator specifics become insignificant. The contrast between 2D and 3D separation is substantial; the skewed vortical structure of 3D STBLI reflects the essentially 2D influence of the boundary layer on the 3D character of the swept shock. As with 2D STBLI, conical interactions engender prominent spectral content below that of the turbulent boundary layer. However, the uniform separation length scale, which is crucial to normalizing the lowest-frequency dynamics in 2D STBLI, is absent. Comparatively, the spectra of 3D STBLI are more representative of the mid-frequency, convective, shear-layer dynamics in 2D, while phenomena associated with 2D separation-shock breathing are muted. Asymptotic behavior breaks down in many regions important to 3D-STBLI dynamics, occurring in a configuration-dependent manner. Aspects of inceptive regions near shock generators and symmetry planes are reviewed. Focused efforts toward 3D modal and nonmodal analyses, moving-shock/boundary-layer interactions, fluid/structure interactions, and flow control are suggested as directions for future work. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 55 is January 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Dynamics of Three-Dimensional Shock-Wave/Boundary-Layer Interactions

An experimental methodology was designed to study the effects of turbulent flow and shock/boundary-layer interaction (SBLI) on the postflutter response of a thin, buckled panel. The approach combin...

David A. Ehrhardt

Papers

Experiments on a Thin Panel Excited by Turbulent Flow and Shock/Boundary-Layer Interactions

Investigation of aeroelastic instabilities for a thin panel in turbulent flow

Supersonic Aerothermoelastic Experiments of Aerospace Structures

Evaluation of reduced-order aeroelastic simulations for shock-dominated flows