Probabilistic machine learning pipeline using topological descriptors for real-time state estimation of high-rate dynamic systems

Abstract

High-rate systems are structures that undergo rapid changes, exhibiting dynamics that evolve over short durations, often less than 100 ms. In this study, we propose a probabilistic machine learning pipeline for estimating the state of a high-rate system. Our approach begins with the extraction of features using topological data analysis (TDA) that capture the underlying structure of datasets. We examine the design of probabilistic models for structural state estimation, emphasizing the importance of prediction intervals. Our method validation involves two datasets: a toy example of linear chirp signals and an experimental dataset from the Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research (DROPBEAR) testbed. We use metrics such as mean absolute error (MAE) and time response assurance criterion (TRAC), along with uncertainty metrics such as negative log-likelihood (NLL), calibration curves, and expected calibration error (ECE), to evaluate model performance. The results indicate that the RNN–NNE model achieves the lowest MAE of 5.705 mm, the highest TRAC, and the lowest ECE of 7.335%, highlighting its superior predictive accuracy and robustness in handling uncertainty.