Investigation of Fast Topological Data Analysis Feature Extraction for High-Rate Dynamic Prediction

Real-time estimation of high-rate dynamic systems is crucial for advanced monitoring in digital avionics. For high-speed aerospace systems, there is a need for real-time estimation that can leverage advances in machine learning (ML) methods such as topological data analysis (TDA). While TDA effectively classifies complex, non-stationary systems for dynamics forecasting, its computational demands limit its application in realtime scenarios. This study advances FastTDA, a computationefficient alternative that fits an ellipse to a point cloud, relating the minor axis to H1 persistence without requiring persistence diagrams. We evaluate both TDA and FastTDA methods for onestep ahead prediction across synthetic time series with varying noise levels from the Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research (DROPBEAR) testbed, a validated platform for high-rate structural dynamics. FastTDA provides features that serve as inputs to recurrent neural networks (RNN) trained to predict system states such as dominant frequency (synthetic case) and cart location (laboratory case). Results show that FastTDA generally outperforms traditional TDA in real-time responsiveness and dynamic forecasting performance, regardless of the level of environmental noise. The dynamics under study are relatively linear and can largely be characterized by a dominating single harmonic response. These findings demonstrate the practical potential of FastTDA-enabled ML pipelines for aerospace structural analysis with embedded sensors, enabling real-time dynamic state monitoring.