Extracting latent dynamics from process data for quality prediction and performance assessment via slow feature regression

Latent variable (LV) models such as partial least squares (PLS) have been widely used to derive low-dimensional subspaces and build regression models in process control problems, especially in quality prediction tasks. However, they are based on the assumption that industrial processes operate at steady states, thereby ignoring process dynamics. In this article, slow feature regression (SFR), a novel linear regression model with LV subspaces, is proposed, which consists of two steps. In the first step, slow features as LVs are extracted via slow feature analysis (SFA), a rising machine learning methodology. Different from classical LV models, SFA assumes LVs have slowly varying dynamics, which can be derived by analyzing the temporal structure within abundant process data. Owing to evident dynamics in industrial processes, slowness can be considered as a valid prior knowledge to utilize. In the second step, the slowest features are selected as a reasonable description of processes to further predict the product quality, which is also likely to be slowly varying. In addition to the Hotelling´s T² statistic, a novel S² index is proposed to evaluate the dynamic variations within processes and assess the real-time performance of the prediction model. The effectiveness of the SFR-based approach is demonstrated through an application in the Tennessee Eastman process.