Semisupervised learning for probabilistic partial least squares regression model and soft sensor application

Due to long sampling time and large measurement delay, variables such as melt index, concentrations of key components in the stream, and product quality variables are difficult to measure online. At the same time, routinely recorded variables such as flow, temperature and press are much easier to measure. As a result, only a small portion of data has values for all variables, while other large parts of data only have values for those routinely recorded variables. Focused on regression modeling between those two types of process variables with imbalanced sampling values, this paper develops a semisupervised form of the Probabilistic Partial Least Squares (PPLS) model. In this model, both labeled data samples (with values for both two types of variables) and unlabeled data samples (with values only for routinely recorded variables) can be effectively used. For parameter learning of the semisupervised PPLS model, an efficient Expectation-Maximization algorithm is designed. An industrial case study is provided as an example for soft sensor application, which is constructed based on the new developed model.