A Novel Fault Detection Method Using Betti Curve

Power equipment malfunctions pose a threat to the safe operation of the entire power grid, making the rapid and accurate identification of power equipment faults a key focus of research in the electric power field. Existing methods based on artificial intelligence and expert systems face issues such as strong dependence on sample data and difficulties in acquiring expert knowledge. In response, this paper proposes a device fault detection method based on TDA, leveraging TDA's capability in feature recognition. First, the time-series data is mapped to a high-dimensional space, allowing the application of topological methods for analysis. Betti curves are used to analyze the topological structure of the time series, revealing its topological features at different scales. Then, in addition to the topological features, statistical features of the time series are incorporated to enhance the expressive power of the features. Finally, these topological and statistical features are integrated into a feature space, and a machine learning classifier is used for fault type recognition and classification. The method has shown promising results in experiments.