Detecting anomalies in manufacturing processes is crucial for ensuringsafety. However, noise significantly undermines the reliability of data-drivenanomaly detection models. To address this challenge, we propose a slowfeature-constrained decomposition autoencoder (SFC-DAE) for anomaly detec-tion in noisy scenarios. Considering that the process can exhibit both long-termtrends and periodic properties, the process data is decomposed into trends andcycles. The repetitive information is mitigated by slicing and randomly mask-ing certain trends and cycles. Dependencies among slices are constructed toextract intrinsic information, while high-frequency noise is reduced using a slowfeature-constrained loss. Anomalies are detected and localized through a recon-struction error strategy. The effectiveness of SFC-DAE is demonstrated usingdata from a sugar factory and a secure water treatment system.