Time Series Anomaly Detection Using Learning Entropy on Water Networks

Abstract

The detection of anomalies in time series is a well-developed field; however, identifying very small incipient anomalies in nonlinear and nonpolynomial contexts remains challenging. This article proposes a novel approach to detect such anomalies in time series heavily affected by noise and pronounced trends. Our method utilizes a novel Hilbert–Huang transform (HHT) approach [also known as empirical mode decomposition (EMD)] to eliminate nonlinear and nonpolynomial trends. Anomalies are then optimally identified using a novel approximate individual sample learning entropy (AISLE)-based method applied to a simple long short-term memory (LSTM) neural network. The combination of the prediction error from the simple LSTM network with the corresponding learning entropy (LE) allows us to highlight very small incipient anomalies without the need for complex neural networks. Results are far superior to those obtainable by observing prediction error alone. In particular, in the detection of leaks in water distribution networks (WDNs), the signal-to-noise ratio (SNR) increases from approximately 30 using prediction error alone to an impressive 121 when incorporating LE. Benchmarks performed on a publicly available synthetic dataset of urban Hanoi’s WDN demonstrate the method’s effectiveness, achieving an overall Accuracy of 94.20%, a Precision of 100.00%, and a Recall of 92.37%.