Detecting anomalies in time series data via a deep learning algorithm combining wavelets, neural networks and Hilbert transform

The quest for more efficient real-time detection of anomalies in time series data is critically important in numerous applications and systems ranging from intelligent transportation, structural health monitoring, heart disease, and earthquake prediction. Although the range of application is wide, anomaly detection algorithms are usually domain specific and build on experts’ knowledge. Here a new signal processing algorithm –inspired by the deep learning paradigm – is presented that combines wavelets, neural networks, and Hilbert transform performs robustly and is transferable. The proposed neural network structure facilitates learning short and long-term pattern interdependencies; a task usually hard to accomplish using standard neural network training algorithms. The paper provides guidelines for selecting the neural network's buffer size, training algorithm, and anomaly detection features. The algorithm learns online the system’s normal behavior and does not require the existence of anomalous data, for assessing its statistical significance. This is essential for applications that require customization. The anomalies are detected by analyzing hierarchically the instantaneous frequency and amplitude of the residual signal. Its applicability is demonstrated through detection of anomalies in the Seismic Electric Signal activity, that is potentially important for earthquake prediction; and automated detection of road anomalies (e.g. potholes, bumps, etc.) using smartphone sensors. The evaluation of the anomaly detection algorithm is based on the statistical significance of the Receiver Operating Characteristic curve. Finally, we propose strategies for decision-making that may increase the efficiency of the application of the algorithm, and expedite evaluation of real-time data.