Probabilistic Nonlinear Soft Sensor Modeling Based on Generative Topographic Mapping Regression

Projection regression is an important tool for process soft sensing in order to eliminate redundant information and obtain proper data features. As most industrial process is intrinsically nonlinear and process variables are collected in random noise environment, it is significant to adopt probabilistic nonlinear latent variable model to carry out dimension reduction for feature extraction before regression modeling. Generative topographic mapping (GTM) is such a probabilistic nonlinear model. However, GTM is an unsupervised method, in which the extracted features may include irrelevant ones with the output information. Thus, it may result in inaccuracy of soft sensor performance. To deal with this problem, a generative topographic mapping regression is developed based on supervised GTM in this paper, which incorporates the output information to guide feature extraction and projection regression. By utilizing the output to jointly generate the latent variables, output-related features can be extracted for output prediction. The effectiveness and flexibility of the proposed method are validated on a numerical example and an industrial process.