Semi-supervised Robust Probabilistic Partial Least Squares Model and Its Applications to Multi-rate Process Monitoring

We present a semi-supervised robust probabilistic partial least squares (semi-supervised RPPLS) method, which can handle data with unequal sample sizes of input variables and output variables. The model should be developed based on complete data samples. However, the dataset is divided into two parts. The first part that contains samples of both the process variables and corresponding quality variables is denoted as the labeled dataset. The other part that consists of the process variable samples only is called the unlabeled dataset. We employ the unlabeled dataset together with the labeled dataset to develop a valid statistical model. Furthermore, on the basis of the semi-supervised RPPLS model, three monitoring indices, namely, GT², SPEx, and SPEy, are proposed to evaluate the process state and the model changes. A comparison indicates that the proposed method is more effective than the downsampling RPPLS method in the monitoring of the Tennessee Eastman process.