Semisupervised Robust Modeling of Multimode Industrial Processes for Quality Variable Prediction Based on Student's t Mixture Model

Gaussian mixture model (GMM) has been widely used for soft sensor modeling of multimode industrial processes. However, it has been recognized that the performance of GMM deteriorates with the presence of outliers, which commonly exist in industrial datasets. In addition, samples with known labels in soft sensor applications are often rare because of expensive sampling equipment or time-consuming laboratory analysis. Shortage of labeled samples could lead GMM-based models to low prediction accuracy. To tackle such problems, a semisupervised robust soft sensor modeling method called semisupervised Student's t mixture model (SsSMM) is proposed. Like the GMM, the SsSMM employs finite mixture models to learn data distributions; nevertheless, with the virtual of the long tail property of Student's t distribution, the SsSMM possesses stronger robustness against outliers compared with the GMM. Moreover, the semisupervised model structure of SsSMM enables exploiting unlabeled samples of the SsSMM, such that the issues caused by insufficient labeled samples can be tackled. To identify model parameters of the SsSMM, we also develop an expectation-maximization-based training algorithm. Experimental results on numerical and industrial examples demonstrate that the proposed method is effective in: first, modeling multimode characteristics; second, exploiting unlabeled samples for performance improvement; third, dealing with distinct outliers (in synthetic dataset) and indistinctive outliers (in industrial dataset).