Mixture modeling for industrial soft sensor application based on semi-supervised probabilistic PLS

Due to the difficulty in measuring key performance indices in the process, only a small portion of collected data may have values for both routinely recorded variables and key performance indices, while a large portion of data only has values for routinely recorded variables. In order to improve the performance of data-driven soft sensor modeling, the idea of semi-supervised learning is incorporated with the traditional partial least squares modeling method. Furthermore, the single semi-supervised model structure is extended to the mixture form, in order to handle more complex data characteristics. An efficient Expectation-Maximization algorithm is designed for model training. An industrial case study is presented for performance evaluation of the developed method, with a Bayesian inference approach developed for results integration of different local models.