Topological Data Analysis for Real-Time Extraction of Time Series Features

Abstract

Real-time state estimation is critical in rapidly assessing structural health to empower real-time feedback mitigation strategies. Of interest to this paper is the state estimation of high-rate system dynamics. High-rate systems are defined as dynamic systems experiencing high-rate (< 100 ms) and high-amplitude (acceleration > 100 gn) events. Examples include hypersonic vehicles and active impact mitigation strategies. The advanced operation of these mechanisms can only be achieved through control and feedback systems capable of operating in the sub-millisecond range, thus necessitating tight performance constraints. Additionally, high-rate system dynamics are highly nonlinear and non-stationary, for which traditional real-time inference methods cannot provide accurate predictions. Topological data analysis (TDA) is gaining popularity for classifying complex time series. Its integration with architected machine learning algorithms shows promise in advancing the predictive capabilities for high-rate systems. This paper investigates the use of TDA features in conducting state estimation. Some TDA features are explored on a physical perspective, and their applicability to the high-rate state estimation problem is assessed. A promising TDA feature is selected, namely the maximum persistence of Hð, and applied to laboratory datasets extracted from the dynamic reproduction of projectiles in ballistic environments for advanced research (DROPBEAR) testbed. The task consists of detecting the location of a fast-moving boundary condition on a cantilever beam. Results demonstrate that the feature can be used to detect the location of the moving boundary condition online. A discussion on real-time location of a fast-moving boundary condition on a cantilever beam and the applicability to high-rate systems is provided.