• semisupervised learning;
  • Bayesian regularization;
  • soft sensor modeling;
  • probabilistic


Most traditional soft sensors are built upon the labeled dataset that contains equal numbers of input and output data samples. However, the output variables that correspond to quality variables and other important controlled variables are always difficult to obtain in chemical processes. Therefore, we may only obtain the output data for a small portion of the whole dataset and have much more input data samples. In this article, a semisupervised method is proposed for soft sensor modeling, which can successfully incorporate the unlabeled data information. To determine the effective dimensionality of the latent space, the Bayesian regularization method is introduced into the semisupervised model structure. Two industrial application case studies are provided to evaluate the feasibility and efficiency of the newly developed probabilistic soft sensor. © 2010 American Institute of Chemical Engineers AIChE J, 2011