Mixture robust semi-supervised probabilistic principal component regression with missing input data

Industrial processes often operate in multiple operating modes. In most cases, the outputs are measured at a slower rate than the inputs due to various reasons, such as the unavailability of real-time sensors. In some cases, measurements of inputs are also not available and/or there are outliers in the measurements due to sensor failures. Furthermore, there can exist different properties of outliers in different variables. Not all of the aforementioned challenges have been considered or considered simultaneously while modeling a probabilistic principal component regression model in the existing literature. In the current paper, a mixture robust semisupervised probabilistic principal component regression model with missing input data is developed, which can handle all the aforementioned challenges effectively when utilized for online predictions of process variables. The proposed approach is solved using the Expectation-Maximization algorithm, and the performance is demonstrated by a numerical example. An experimental case study of the hybrid tanks system is also utilized to demonstrate the practical applicability of the proposed method.