SF-PFE: A slow feature extraction method based on the fusion of fast and slow pathways for parallel linear and nonlinear process monitoring

In modern industrial processes, the behaviour of process variables often involves both linear and nonlinear dependencies, as well as distinct characteristics between high-frequency and low-frequency transformations. To address these complexities and improve the accuracy of process monitoring and fault detection, this research proposes a novel model called SF-PFE, designed for parallel feature extraction and monitoring. This model combines a linear mapping module with a transformation gate to simultaneously capture both linear and nonlinear features. Inspired by the SlowFast framework, it divides time-series data into two pathways: a slow pathway for low-frequency data and a fast pathway for high-frequency data. The extracted features are then integrated using methods such as feature concatenation and weighted summation, combining long-term and short-term data trends to enhance fault diagnosis. Furthermore, a slow feature constraint is employed to maintain variability while extracting speed-related features, offering better insight into dynamic process behaviours. Comprehensive experiments on the Tennessee Eastman process dataset show that SF-PFE significantly outperforms existing techniques in the literature.