Deep Learning of Partially Labeled Data for Quality Prediction Based on Stacked Target-Related Laplacian Autoencoder

Partially labeled data, which is common in industrial processes due to the low sampling rate of quality variables, remains an important challenge in soft sensor applications. In order to exploit the information from partially labeled data, a target-related Laplacian autoencoder (TLapAE) is proposed in this work. In TLapAE, a novel target-related Laplacian regularizer is developed, which aims to extract structure-preserving and quality-related features by preserving the feature-target mapping according to the local geometrical structure of the data. In addition, stacked TLapAE (STLapAE) is further constructed to extract deep feature representations of the data by hierarchically stacking TLapAE blocks. For model training, backward propagation equations are derived based on matrix calculus techniques to update the model parameters of the proposed TLapAE. The effectiveness of the proposed STLapAE is evaluated using the butane content prediction case in a debutanizer column, the silicon content prediction case in a blast furnace (BF) ironmaking process, and the ethane concentration prediction case in an ethylene fractionator. The results show that the proposed TLapAE model has significantly improved prediction accuracy compared to soft sensors using only labeled data and other partially labeled data modeling methods.