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

Researchers from the field of machine learning have introduced PhaseNet++, a novel anomaly detection model for Industrial Control Systems (ICS) that exploits phase information from sensor signals. Traditional methods analyze raw time-domain amplitudes using graph neural networks or Transformers, but they discard the phase spectrum from time-frequency transformations. PhaseNet++ argues that phase coherence across sensors provides a complementary detection signal, especially for detecting subtle cyber-physical attacks.

The model operates on Short-Time Fourier Transform (STFT) of sliding windows, retaining both magnitude and phase. A Phase Coherence Index (PCI), inspired by the Phase Locking Value from neuroscience, constructs a continuous adjacency matrix representing pairwise phase consistency across frequency bins. This guides a graph attention network and a Transformer encoder that capture system-wide dependencies. A dual-head decoder reconstructs magnitude and phase using circular and coherence-aware loss functions. On the SWaT benchmark (Secure Water Treatment), PhaseNet++ achieves an F1-score of 90.98%, ROC-AUC of 95.66%, and average precision of 91.51%. The phase-aware module adds only 264,816 parameters, demonstrating that incorporating phase information is computationally lightweight. While its absolute F1-score ranks second among recent methods under different protocols, the work establishes the first systematic study of phase-domain anomaly detection for ICS, opening a new direction for securing critical infrastructure.