Real-time state estimation using recurrent neural network and topological data analysis

Abstract

High-rate systems are defined as physical systems that undergo large perturbations, often exceeding 100 g’s, over very short durations, often less than 100 milliseconds. Examples include blast mitigation mechanisms and advanced weaponry. The use of control feedback to empower high-rate systems requires the capability to estimate system states of interest in the realm of microseconds. However, due to the dynamics of these high-rate systems being highly nonlinear and nonstationary, it is challenging to predict their behavior using conventional state estimation methods. To address this issue, we conduct a study that explores the integration of topological data analysis (TDA) and recurrent neural network (RNN) to improve predictive capabilities for high-rate systems. Here, TDA features are used as the input to a machine learning algorithm to determine the state of a high-rate system. We conduct practical evaluations using laboratory datasets from experiments in the dynamic reproduction of projectiles in ballistic environments for advanced research (DROPBEAR), focusing on localizing fast-changing boundary conditions on a cantilever beam. The study demonstrates the ability of the method to classify and predict a system’s fundamental frequencies. This approach helps understand the structure of the underlying high-rate dynamics, leading to improved accuracy and precision in state estimation and prediction.