Online Monitoring of Time-varying Process Using Probabilistic Principal Component Analysis

Abstract

This paper develops a moving window probabilistic PCA(MW PPCA) online process monitoring method for moni-toring time-varying industrial process. First, PPCA model and the method of iteratively solving the parameters of PPCA model by variational inference are introduced. On the basis of the PPCA model, three monitoring statistic, ${T}^{2}, SPE$ and $Var$, are in-troduced also. In order to solve the time-varying trend, this paper further utilizes a sequential update procedure for PPCA model which is based on a moving window, and uses the streaming variational inference method to recursively update the parameters of PPCA model in each window. Then, the non central chi square distribution approximation is used to solve the control limits of the three statistics under the confidence limits in order to adapt to the process changes more effectively, so as to update the control limits. Finally, the effectiveness of the distillation process is verified.