Gaussian mixture model sample selection strategy–based active semi-supervised soft sensor for industrial processes

Soft sensors have become reliable tools for estimating difficult-to-measure target variables in modern industrial processes. In order to make full use of labeled and unlabeled samples, an active semi-supervised soft sensor modeling method is proposed, which combines active learning and semi-supervised learning to maximize model performance and minimize the laboratory analysis cost of expanding the labeled sample data set. First, manifold regularization is introduced into the deep extreme learning machine (DELM) algorithm to form a semi-supervised DELM that improves the performance of a model trained with unlabeled samples. Then, considering non-Gaussian processes and the error information between the predicted and true values, an active sample selection strategy based on error Gaussian mixture model is developed. Using this strategy, the most uncertain and representative unlabeled samples are selected for labeling, and thereby expanding the labeled sample data set. Finally, the effectiveness of the proposed method is verified using industrial debutanizer process data.