Soft Sensor Development for Multimode Processes Based on Semisupervised Gaussian Mixture Models

Abstract

The Gaussian mixture models (GMM) is an effective tool for modeling processes with multiple operating modes that widely exist in industrial process systems. Traditional supervised version of GMM, namely the Gaussian mixture regression (GMR), for developing soft sensors merely relies on the labeled samples. However, labeled samples in the soft sensor application are usually very infrequent due to economical or technical limitations, which may lead the GMR to unreliable parameter estimation and finally poor performance for predicting the primary variable. To tackle this problem, a semisupervised GMM for regression purpose is proposed, where both labeled and unlabeled samples take effect, and the Gaussian parameters and regression coefficients are learned simultaneously based on the expectation-maximization algorithm. Two case studies are carried out using simulated dataset and real-life dataset collected from a primary reformer in an ammonia synthesis process, which demonstrates the effectiveness of the proposed method.