Concurrent PLS-based process monitoring with incomplete input and quality measurements

• The CPLS-based method provided a complete monitoring strategy for input and quality variables, however, no literature considered the influence of missing measurement in this method.
• We derive the conditional distribution of scores and residuals given the observable measurement, and employ this probabilistic measurement to construct monitoring statistics.
• We perform probabilistic analysis on monitoring statistics in the presence of missing measurement, and then derive the uncertain ranges of monitoring statistics caused by missing data.
• The proposed method is illustrated by its application in Tennessee-Eastman process.

The process monitoring based on concurrent partial least square (CPLS) performs well on the monitoring of input and quality variables through five monitoring statistics. However, in practice, the case of missing variable is very common and the incomplete measurements will make it difficult to implement this monitoring method. Considering the presence of missing measurements occurring in both input and quality variables, this paper analyzes the influence of missing measurements on monitoring performance based on the assumption that input and quality variables satisfy multivariate Gaussian distribution under normal operation. The proposed method estimates the conditional distributions of missing variables, scores and residuals given the observable variables, and denotes monitoring statistics with these conditional distributions. Then, the probabilistic uncertain ranges of monitoring statistics are derived by calculating the general quadratic formulations of Gaussian-distributed missing variables. To determine the process operation in the presence of missing variables, the proposed method employs these uncertain ranges as monitoring statistics. Simulation examples illustrate feasibility of this proposed method and demonstrate its effectiveness.