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

ABSTRACT We present a general and adaptable framework for detecting regime changes in complex, non‐stationary data across multi‐trial experiments. While traditional change point detection methods focus on identifying abrupt changes within a single time series (single trial), our approach identifies changes that occur across trials, accommodating variations due to experimental inconsistencies, such as differing event timings or durations. By utilizing diverse metrics, including topological analysis of time‐frequency characteristics in the spectrum and spectrograms, our method provides a robust framework for detecting cross‐trial changes. This flexibility allows it to address a range of scenarios with varying statistical assumptions, including different levels of stationarity within and across trials. We validate our approach through simulations using time‐varying autoregressive processes exhibiting various regime changes. Our results highlight the method's effectiveness in detecting cross‐trial changes under varied conditions. Furthermore, we showcase its potential for practical applications by analyzing vibration signals from the NASA bearing dataset. Through time‐frequency analysis, our framework accurately identifies bearing failures, demonstrating its strong capability for early fault detection in predictive maintenance of mechanical systems.