The impact of missing measurements on PCA and PLS prediction and monitoring applications

Abstract

A significant issue in the practical application of PCA and PLS models for inferential sensors and process monitoring is the presence of sets of measurements (objects) that are incomplete. Since the missing measurements in the incomplete objects are usually correlated with some of the available measurements, an opportunity exists to use these objects if efficient algorithms and tools exist and if their performance and limitations are defined. This paper analyses the uncertainties in the predictions, latent variables, Hotelling T 2 and residual squared prediction error (SPE) that arise from the missing measurements. Intervals for these values are developed which give an indication of the degree of uncertainty introduced by the missing measurements. These intervals can be used to assess whether or not the inferential models or the process monitoring scheme perform well in the presence of missing measurements. They can also be used to determine which measurements to recover to get the greatest uncertainty reduction. The results are illustrated by application to industrial data from a Kamyr digester.