TDA-Informed Feedforward Recurrent Neural Networks for High-Rate State Estimation Application

Abstract

Real-time state estimation is essential for conducting efficient structural health assessment and enabling feedback control strategies in high-rate systems. High-rate systems are dynamic systems that experience extreme acceleration (> 100 gn where gn is the gravitational constant near the earth’s surface) within very short periods (< 1 millisecond), commonly observed in applications such as hypersonic systems and impact mitigation mechanisms. These engineering systems require control and feedback methodologies capable of operating within the sub-millisecond ranges, posing significant challenges for traditional prediction methods due to the underlying nonlinear and nonstationary behavior. This paper introduces and investigates a deep learning algorithm that combines topological data analysis (TDA) features with machine learning to enhance state estimation of high-rate systems. The algorithm consists of an ensemble of recurrent neural networks (RNNs) constructed with a parallel arrangement of long short-term memory cells. The ensemble incorporates predictions from multiple RNNs trained on varying window sizes and delays, allowing the system to capture both shortand long-term data dependencies. A Feedforward Neural Network is employed to predict and analyze the contribution of each RNN’s output to an overall state estimation using TDA-derived features such as the maximum persistence of the first dimensional persistence homology group, H1. The proposed approach is validated using data from the dynamic reproduction of projectiles in ballistic environments for advanced research (DROPBEAR) testbed. Results demonstrate the promise of the algorithm at predicting time series and system states over longer prediction horizons.