Inferential sensor design in the presence of missing data: a case study

Inferential sensors are an important part of modern control strategy to improve the quality of petrochemical products. The design of these models is based in the data collected from the process. Due to uncontrolled process upsets or technical problems in the data logging facilities, the data-sets are often incomplete. This paper address this problem and proposes a methodology to design the inferential sensors using partial least squares (PLS) in the presence of missing data. Our approach is based on the determination of the data covariance matrix in a pair-wise fashion followed by a correction to impose non-negative definiteness in order to use the maximum information present in the incomplete data-set. The methodology is tested on a simulation study with 3 different levels of missing data (5%, 20%, and 40%). Results show that it is possible to develop reliable PLS models for moderate levels (20%) of missing data. Based on our approach, the inferential models can be optimized (process variable selection) using the standard chemometric methods and their confidence intervals (CI) estimated based on the available data.