Data-driven sensor delay estimation in industrial processes using multivariate projection methods

A key step in preparing industrial data for multivariate statistical modelling of (batch-)continuous processes is the estimation of sensor delays along the production line, to use as a correction for understanding relationships between them. Without such a correction, the measurements collected from the sensors do not all relate to the same portion of material travelling through the plant, which is where from a physical point of view the correlations are expected to arise from. Most methods to do these corrections currently reported in literature are limited in that they optimize only correlations bivariately between the different sensors, despite the eventual goal of being understood as a multivariate process model. This work proposes several methods for multivariate sensor delay estimation, based on multivariate projection methods, and critically investigates these using simulated and empirical process data from two industrial facilities. The objective is to provide more clarity on if, how, and why taking into account these multivariate correlations using such projection methods is beneficial. One of the proposed methods, named PLS-SEQ, was shown to outperform bivariate sensor delay estimation, which is regarded as benchmark method in this work, for all datasets. The average reduction in delay estimation error achieved by using PLS-SEQ is between 6% and 64%. The other newly proposed multivariate projection-based methods did not show such unanimous improvement in accuracy, but helped identifying the presence of sensor clusters in industrial data as a novel key challenge for sensor delay estimation. The presented results illustrate that projection-based multivariate methods, in particular the newly proposed method PLS-SEQ, show promising potential for sensor delay estimation, outperforming the bivariate sensor delay estimation methods used as benchmark. Ultimately, using these methods can improve the predictive and descriptive quality of statistical models for key industrial processes.