A Robust Topological Framework for Detecting Regime Changes in Multi-Trial Experiments with Application to Predictive Maintenance

We present a general and flexible framework for detecting regime changes in complex, non-stationary data across multi-trial experiments. Traditional change point detection methods focus on identifying abrupt changes within a single time series (single trial), targeting shifts in statistical properties such as the mean, variance, and spectrum over time within that sole trial. In contrast, our approach considers changes occurring across trials, accommodating changes that may arise within individual trials due to experimental inconsistencies, such as varying delays or event duration. By leveraging diverse metrics to analyze time-frequency characteristics specifically topological changes in the spectrum and spectrograms, our approach offers a comprehensive framework for detecting such variations. Our approach can handle different scenarios with various statistical assumptions, including varying levels of stationarity within and across trials, making our framework highly adaptable. We validate our approach through simulations using time-varying autoregressive processes that exhibit different regime changes. Our results demonstrate the effectiveness of detecting changes across trials under diverse conditions. Furthermore, we illustrate the effectiveness of our method by applying it to predictive maintenance using the NASA bearing dataset. By analyzing the time-frequency characteristics of vibration signals recorded by accelerometers, our approach accurately identifies bearing failures, showcasing its strong potential for early fault detection in mechanical systems.