Pseudo-labeling optimization based ensemble semi-supervised soft sensor in the process industry

Nowadays, soft sensor techniques have become promising solutions for enabling real-time estimation of difficult-to-measure quality variables in industrial processes. However, labeled data are often scarce in many real-world applications, which poses a significant challenge when building accurate soft sensor models. Therefore, this paper proposes a novel semi-supervised soft sensor meth-od, referred to as ensemble semi-supervised negative correlation learning extreme learning machine (EnSSNCLELM), for industrial processes with limited labeled data. First, an improved supervised regression algorithm called NCLELM is developed, by integrating the philosophy of negative correlation learning into extreme learning machine (ELM). Then, with NCLELM as the base learning technique, a multi-learner pseudo-labeling optimization approach is proposed, by converting the estimation of pseudo labels as an explicit optimization problem, in order to obtain high-confidence pseudo-labeled data. Furthermore, a set of diverse semi-supervised NCLELM models (SSNCLELM) are developed from different enlarged labeled sets, which are obtained by combining the labeled and pseudo-labeled training data. Finally, those SSNCLELM models whose prediction accuracies were not worse than their supervised counterparts were combined using a stacking strategy. The proposed method can not only exploit both labeled and unlabeled data, but also combine the merits of semi-supervised and ensemble learning paradigms, thereby providing superior predictions over traditional supervised and semi-supervised soft sensor methods. The effectiveness and superiority of the proposed method were demonstrated through two chemical applications.