PhaseNet++: Phase-Aware Frequency-Domain Anomaly Detection for Industrial Control Systems via Phase Coherence Graphs

• URL: http://arxiv.org/abs/2605.00929v1
• Date: Thu, 30 Apr 2026 19:59:30 GMT
• Title: PhaseNet++: Phase-Aware Frequency-Domain Anomaly Detection for Industrial Control Systems via Phase Coherence Graphs
• Abstract summary: We present PhaseNet++, a frequency-domain autoencoder that operates on the Short-Time Fourier Transform (STFT) of sliding sensor windows.<n>A Phase Coherence Index ( PCI) summarizes pairwise phase consistency across frequency bins into a continuous adjacency matrix.<n>A sensor-token Transformer encoder captures system-wide structure, and a dual-head decoder reconstructs magnitude and phase jointly.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multivariate time series anomaly detection in ICS has attracted growing attention due to the increasing threat of cyber-physical attacks on critical infrastructure. State-of-the-art methods model inter-sensor relationships from raw time-domain amplitude values, using graph neural networks, Transformers. However, these methods discard the phase spectrum produced by time frequency transformations, We argue that phase information constitutes a complementary and previously overlooked detection modality for ICS anomaly detection. We present PhaseNet++, a frequency-domain autoencoder that operates on the Short-Time Fourier Transform (STFT) of sliding sensor windows, retaining both magnitude and phase spectra. A Phase Coherence Index (PCI), inspired by the Phase Locking Value from neuroscience, summarizes pairwise phase consistency across frequency bins into a continuous adjacency matrix. This matrix guides a graph attention network that propagates information preferentially among phase-synchronized sensors. A sensor-token Transformer encoder captures system-wide structure, and a dual-head decoder reconstructs magnitude and phase jointly via circular and coherence-aware objectives. Evaluated on the Secure Water Treatment (SWaT) benchmark, PhaseNet++ achieves an F1-score of 90.98%, ROC-AUC of 95.66%, and average precision of 91.51%. Ablation studies show that the phase-aware front-end and PCI graph module together add only 264,816 parameters, demonstrating that the phase inductive bias is lightweight. While the absolute F1-score is second best than that of all recent raw-value methods evaluated under different protocols, we position this work as the first systematic study of phase-domain anomaly detection for ICS.

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