Pseudo label estimation based on label distribution optimization for industrial semi-supervised soft sensor

In process industry, the lack of sufficient labeled data often leads to poor performance of traditional supervised soft sensors. Thus, a pseudo label estimation method based on label distribution optimization (PLELDO) is proposed. PLELDO first converts the pseudo label estimation into an explicit label distribution optimization problem, and then obtains high-confidence pseudo labels. Further, a semi-supervised ensemble soft sensor modeling framework namely EnPLELDO is developed. EnPLELDO first obtains sufficient good pseudo labeled data by repeating small-scale pseudo label estimation. Then, a set of diverse base models are constructed from the extended training sets. Finally, these enhanced base models are combined through stacking strategy. The application results from an industrial fed-batch fermentation process show that, compared with several state-of -the-art methods, PLELDO can obtain better pseudo label estimations and EnPLELDO can deliver more accurate predictions of key quality variables by leveraging the scarce labeled data and large-scale unlabeled data.