Semi-supervised ensemble support vector regression based soft sensor for key quality variable estimation of nonlinear industrial processes with limited labeled data

Soft sensor technique has become a promising solution to enable real-time estimations of difficult-to-measure quality variables in industrial processes. However, traditional soft sensor models cannot always function well due to two challenging issues. First, labeled data are usually expensive to obtain in many real-world applications, thus leading to unsatisfactory performance for traditional supervised soft sensors. Meanwhile, the information behind abundant unlabeled data is not fully exploited. Second, it is very common for soft sensors to encounter the modeling uncertainty resulting from the diversity of training data, model hyperparameters, and optimization parameters. Therefore, a new soft sensor method called semi-supervised ensemble support vector regression (SSESVR) is proposed by combining semi-supervised learning with ensemble learning. The SSESVR method first formulates the estimation of pseudo-labels as a multi-learner pseudo-labeling optimization problem and then solve it through evolutionary approach, thus extending the labeled training set using satisfactory pseudo-labeled data. Further, by considering multimodal perturbation mechanism, a two-level ensemble architecture is employed to enable efficient cooperation of semi-supervised and ensemble learning framework. Two case studies are conducted to verify the effectiveness and superiority of the proposed SSESVR approach.