Adversarial smoothing tri-regression for robust semi-supervised industrial soft sensor

Abstract

In industrial processes, soft sensor techniques are used to predict the hard-to-measure quality variables under the classic supervised learning paradigm. However, the data challenges, i.e., the widespread noises and inadequate labeled samples, usually make the data-driven sensors weak for application. In this paper, a simple but effective regularization method termed as adversarial smoothing regularization (ASR) is proposed, which measures the local smoothness of prediction around each input sample. By minimizing the divergence between the predictions for noisy and clean inputs, the proposed ASR regulates the learning model to be robust against local perturbation in a semi-supervised manner. Theoretical analysis explains the smoothing capability of ASR, and shows that it is helpful for the improvement of generalization performance. We also design a tri-regression framework to further use the information of unlabeled samples with pseudo labels and present the adversarial smoothing tri-regression (ASTR) model for soft sensor. Based on two industrial processes, comprehensive soft sensor experiments and noise tests are performed to show the robust semi-supervised learning capability of the proposed ASR and ASTR.