Deep Spatial–Temporal Slow Feature Transfer Network for Multimode Chemical Process Soft Sensing on Imbalanced Data

For soft sensor modeling of multimode chemical processes, a common method is to build an individual model corresponding to each mode. However, certain individual mode models may not be reliable due to the imbalanced data across different modes. The soft sensor built for one mode with sufficient data exhibits suboptimal performance for other modes with insufficient data. To address this issue, a deep transfer learning method is introduced for soft sensor and a deep transfer spatial–temporal slow feature regression framework (STSFE) is proposed. In the framework, a Siamese network is employed for slow feature extraction. In addition, the encoder–decoder structure is embedded for input reconstruction verifying the effectiveness of slow features. However, the Siamese network fails to consider correlation of variables in quality prediction. To address this limitation, the Siamese network is designed with an embedded spatial–temporal attention mechanism to construct the STSFE model, and the spatial–temporal slow features are augmented with the historical quality variable for current quality prediction. The STSFE model is initially trained for the mode with sufficient data (source domain), and then transfer learning is employed to facilitate knowledge transfer from the source domain to the target domain (the mode with insufficient data) by reusing the lower level extraction part of STSFE. The effectiveness of the proposed method is validated through a benchmark sewage treatment case and a real chemical process.