Forecasting Error Pattern-Based Anomaly Detection in Multivariate Time Series

The advent of Industry 4.0, partly characterized by the development of cyber-physical systems (CPSs), naturally entails the need for reliable security schemes. In particular, accurate detection of anomalies is of paramount importance, as even a small number of anomalous instances can trigger a catastrophic failure, often leading to a cascading one, throughout the CPS due to its interconnectivity. In this work, we aim to contribute to the body of literature on the application of anomaly detection techniques in CPSs. We propose novel Functional Data Analysis (FDA) and Autoencoder-based approaches for anomaly detection in the Secure Water Treatment (SWaT) dataset, which realistically represents a scaled-down industrial water treatment plant. We demonstrate that our methods can capture the underlying forecasting error patterns of the SWaT dataset generated by Mixture Density Networks (MDNs). We evaluate our detection performances using the F₁ score and show that our methods empirically outperform the baseline approaches—cumulative sum (CUSUM) and static thresholding. We also provide a comparative analysis of our methods to discuss their abilities as well as limitations.