Process Modeling and Monitoring With Incomplete Data Based on Robust Probabilistic Partial Least Square Method

In real industrial processes, both outliers and missing data are very common. Owing to the assumption that the data sampled from a normal process follow the Gaussian distribution, the regular datadriven process monitoring methods, such as the probabilistic partial least square (PPLS) method and the probabilistic principal component analysis method, are sensitive to outliers. By introducing heavy-tailed t distribution instead of Gaussian distribution to capture the distribution of normal data, the robust data-driven method can significantly reduce the influence of outliers on the development of the model. To reduce the influence of missing data, this paper proposes a process modeling and monitoring method with incomplete data based on the robust PPLS method. In the proposed method, to use more useful information in modeling, incomplete data along with complete data are employed in the parameter estimation using the maximum likelihood method; according to the robust PPLS model and the Bayes' rule, the distributions of latent variables and missing data are derived, and subsequently, the expectation-maximization algorithm is used to achieve the parameter estimation. In addition, based on the conditional distribution of missing data, two monitoring indices are developed to evaluate the deviation of latent variables and residuals. A simulation case illustrates the application of the proposed method, and the results of application demonstrate its efficacy.