Student’s-<i>t</i> Mixture Regression-Based Robust Soft Sensor Development for Multimode Industrial Processes

Abstract

Because of multiple manufacturing phases or operating conditions, a great many industrial processes work with multiple modes. In addition, it is inevitable that some measurements of industrial variables obtained through hardware sensors are incorrectly observed, recorded or imported into databases, resulting in the dataset available for statistic analysis being contaminated by outliers. Unfortunately, these outliers are difficult to recognize and remove completely. These process characteristics and dataset imperfections impose challenges on developing high-accuracy soft sensors. To resolve this problem, the Student’s-t mixture regression (SMR) is proposed to develop a robust soft sensor for multimode industrial processes. In the SMR, for each mixing component, the Student’s-t distribution is used instead of the Gaussian distribution to model secondary variables, and the functional relationship between secondary and primary variables is explicitly considered. Based on the model structure of the SMR, a computationally efficient parameter-learning algorithm is also developed for SMR. Results conducted on two cases including a numerical example and a real-life industrial process demonstrate the effectiveness and feasibility of the proposed approach.

Keywords

• robust soft sensor
• multimode process
• Student’s-<i>t</i> mixture regression
• Gaussian mixture model
• expectation maximization