Non-stationary Signal Analysis: Detrending and Anomaly Detection

Abstract

Smoothing signals, finding a trend component, and detecting anomalies in time series are key tasks in fields such as sensor data processing, healthcare, and cyber security. These challenges become particularly complex when working with data characterized by nonlinear trends, noise, and sudden changes. The situation is further complicated by the limited availability of annotated real-world datasets, which hinders the development and evaluation of supervised models. In this paper, we focus on methods for smoothing time series, identifying underlying trends, and isolating anomalies. We propose an approach based on graph neural networks, designed to detect trends in nonstationary time series with abrupt steps. Our methodology is demonstrated in the context of tram traffic detection, utilizing the signal data measured on the bridge by optical fiber sensors. Due to the absence of annotated real-world data, we evaluated our method using the Reverse Quality Estimator based on the annotated synthetic data and unannotated real data. The performance of our approach is then compared with state-of-the-art unsupervised methods.