Nonlinear feature extraction for soft sensor modeling based on weighted probabilistic PCA

• A novel weighted probabilistic PCA is developed for nonlinear feature extraction.
• Different weights are assigned to training samples according to similarities.
• A novel weighted loglikelihood function is constructed to obtain model parameters.
• The developed method is tested through a numerical example and an industrial process.

As industrial process plants are often instrumented with a large number of sensors, it is important to carry out feature extraction before soft sensor modeling. Probabilistic principal component analysis (PPCA) has been identified as an effective method for dimensional reduction. However, PPCA is a linear method, which cannot deal with nonlinear data distribution. To cope with this problem and enhance the performance of soft sensor model, a new nonlinear dimensional reduction method, weighted probabilistic principal component analysis (WPPCA), is proposed in this paper. By assigning different weights for training samples according to their similarities to the testing sample, nonlinear features can be extracted properly for regression modeling. For performance evaluation of the proposed method, detailed illustrations of a numerical example and an industrial process are provided.