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

2026-05-05 · Source: cs.LG updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Cybersecurity & Data Privacy, Internet of Things (IoT) & Connected Devices · Depth: Expert, extended

Summary

PhaseNet++ is a novel frequency-domain autoencoder designed for multivariate time series anomaly detection in industrial control systems (ICS). Unlike traditional methods that focus on time-domain amplitude, PhaseNet++ explicitly utilizes the Fourier phase spectrum, which encodes critical timing and synchronization relationships between physically coupled sensors. The model processes Short-Time Fourier Transform (STFT) of sensor windows, retaining both magnitude and phase spectra. It introduces a Phase Coherence Index (PCI), inspired by neuroscience's Phase Locking Value, to create a continuous adjacency matrix that guides a graph attention network. A sensor-token Transformer encoder captures system-wide structure, and a dual-head decoder reconstructs magnitude and phase using circular and coherence-aware objectives. Evaluated on the Secure Water Treatment (SWaT) benchmark, PhaseNet++ achieved an F1-score of 90.98%, ROC-AUC of 95.66%, and average precision of 91.51%, with its phase-aware modules adding only 5.0% (264,816 parameters) to the total 5.29M parameters.

Key takeaway

For research scientists developing anomaly detection systems for critical infrastructure, PhaseNet++ demonstrates that incorporating frequency-domain phase information significantly enhances detection capabilities, especially against stealthy attacks that preserve amplitude but disrupt timing. You should consider integrating phase-aware features and coherence-based graph structures into your models, potentially fusing them with existing amplitude-aware methods to achieve more robust and comprehensive anomaly detection.

Key insights

Phase information, often discarded, offers a complementary and powerful modality for ICS anomaly detection.

Principles

• Phase spectrum encodes critical timing relationships.
• Phase coherence can define graph structure for sensor networks.
• Circular loss functions are essential for angular phase data.

Method

PhaseNet++ transforms sensor windows via STFT, computes a Phase Coherence Index (PCI) for graph adjacency, and reconstructs magnitude and phase using a dual-head decoder with circular and coherence losses.

In practice

• Use STFT to extract both magnitude and phase spectra.
• Employ Phase Locking Value (PLV) for inter-sensor synchrony.
• Apply circular loss for accurate phase reconstruction.

Topics

• Industrial Control Systems
• Frequency-Domain Anomaly Detection
• Phase Coherence Index
• Graph Attention Networks
• Transformer Architecture

Code references

• raviteja-bommireddy/PhaseNet

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.