Abstract:Anomaly detection plays a critical role in identifying abnormal patterns in multivariate time series (MTS) data is critical and holds significant value for contemporary industrial applications. However, existing methods generally overlook frequency-domain information, which limits their detection capability to simple amplitude anomalies and prevents effective identification of complex structural anomalies hidden in periodic patterns. To address this limitation, this study proposes an unsupervised anomaly detection model, termed the time-frequency autoencoder network (TF-AENET). The proposed model integrates time-domain and frequency-domain information through a dual-branch autoencoder architecture. In the time-domain branch, causal convolutions are employed to construct a temporal convolutional network (TCN) for extracting multi-scale temporal features. Furthermore, a linear multi-head attention mechanism is introduced to replace the traditional Transformer attention module, where kernel approximation and recursive cumulative updates are utilized to reduce computational complexity while strictly satisfying temporal causality constraints. In the frequency-domain branch, a fast Fourier transform combined with a multi-layer perceptron (MLP) is employed to analyze signal periodicity, vibration patterns, and global spectral distributions. To evaluate the effectiveness and superior performance of TF-AENET in anomaly detection, comprehensive comparisons with seven baseline models are conducted on four public benchmark datasets. Experimental results demonstrate that TF-AENET achieves an average F1-score of 93.19% on four public datasets, improving over the best baseline model by 5.30%, verifying the effectiveness and superiority of the time-frequency fusion architecture for multivariate time series anomaly detection.