A cyclic perspective on transient gust encounters through the lens of persistent homology

TL;DR

This paper introduces a novel approach using persistent homology and autoencoders to characterize and reduce the complexity of flow dynamics during gust encounters, revealing a common circular structure in the flow's topology.

Contribution

It applies topological data analysis combined with neural networks to identify low-dimensional, interpretable representations of complex gust flow phenomena.

Findings

Flow dynamics can be represented as a simple circle in reduced space.

Persistent homology effectively captures topologically relevant features.

The method reconstructs original flow fields from low-dimensional embeddings.

Abstract

Large amplitude gust encounters exhibit a range of separated flow phenomena, making them difficult to characterize using the traditional tools of aerodynamics. In this work, we propose a dynamical systems approach to gust encounters, viewing the flow as a cycle (or a closed trajectory) in state space. We posit that the topology of this cycle, or its shape and structure, provides a compact description of the flow, and can be used to identify coordinates in which the dynamics evolve in a simple, intuitive way. To demonstrate this idea, we consider flowfield measurements of a transverse gust encounter. For each case in the dataset, we characterize the full-state dynamics of the flow using persistent homology, a tool that identifies holes in point cloud data, and transform the dynamics to a reduced-order space using a nonlinear autoencoder. Critically, we constrain the autoencoder such that it preserves topologically relevant features of the original dynamics, or those features identified by persistent homology. Using this approach, we are able to transform six separate gust encounters to a three-dimensional latent space, in which each gust encounter reduces to a simple circle, and from which the original flow can be reconstructed. This result shows that topology can guide the creation of low-dimensional state representations for strong transverse gust encounters, a crucial step toward the modeling and control of airfoil-gust interactions.