Process-Aware Frequency-Enhanced Conditional VAE With Graph Neural Networks for Anomaly Detection of Industrial Multivariate Time Series

Abstract

This article presents a novel anomaly detection method for industrial multivariate time series (IMTS) based on a process-aware frequency-enhanced conditional variational autoencoder (FCVAE) and graph neural networks (GNN). The proposed FCVAE-GNN method consists of three main stages: frequency-enhanced representation learning, process-aware relational modeling, and anomaly scoring. In the first stage, global and local frequency features are extracted through fast Fourier transform (FFT)-based analysis and target attention mechanisms, which are then incorporated into a conditional variational autoencoders (VAEs) to learn frequency-enhanced latent representations. In the second stage, sensors are grouped according to production process stages, and intraprocess bidirectional gated recurrent unit (GRU) networks capture sequential dependencies among sensors; the learned embeddings guide adaptive graph structure learning, and graph attention mechanisms aggregate neighbor information for multistep prediction. In the third stage, reconstruction and prediction errors are fused through a weighted harmonic mean to compute robust anomaly scores. The proposed method has three main advantages: 1) the frequency-enhanced modules effectively process nonstationary industrial time series by extracting both global spectral patterns and local time-varying frequency characteristics; 2) the process-aware sensor embedding leverages domain knowledge to guide graph structure learning, constructing sensor correlation graphs that conform to physical process flows; and 3) the joint optimization of reconstruction and prediction tasks enables the model to learn representations that capture both data distribution patterns and temporal dynamics, improving detection coverage for various anomaly types. Comprehensive experiments on the proprietary cigarette-production dataset cigarette industrial process time-series data (CIG) and two public benchmarks [pooled server metrics (PSM) and mars science laboratory (MSL)] compared FCVAE-GNN against seven representative baselines. On the public PSM benchmark, FCVAE-GNN achieves the best F1 score of 0.6104 and AUC-ROC of 0.8040, and across the three datasets, it attains the highest mean AUC-ROC of 0.6932, demonstrating consistent cross-dataset stability suitable for industrial deployment.