Co-training partial least squares model for semi-supervised soft sensor development

• A semi-supervised style algorithm called co-training partial least squares algorithm has been developed.
• Both labeled and unlabeled data samples are incorporated for modeling in the new semi-supervised model.
• The linear regression function is employed for the designing of the soft sensor.
• The superiority of the developed method is evaluated through two examples.

Typically, the easy-to-measure variables are used to predict the hard-to-measure ones in soft sensor modeling. In practice, however, the easy-to-measure variables are redundant while the other ones are quite rare, which are often obtained from offline lab analyses. In this paper, the semi-supervised learning method is introduced for soft sensor modeling. Particularly, the co-training strategy is combined with the conventionally used partial least squares model (PLS). A co-training styled algorithm called co-training PLS is proposed for the development of a semi-supervised soft sensor. By splitting the whole process variables into two different parts, two diverse PLS regression models can be developed. Through an iterative learning procedure, the final new labeled data sets can be determined, based on which two new regressors are constructed for soft sensing. Two examples are provided for performance evaluation of the proposed method, with detailed comparative studies to the traditional PLS and co-training kNN model based soft sensors.