Linear latent variable regression (LVR)-based process monitoring

Fast-paced developments in data acquisition, instrumentation technology and the era of the Internet-of-Things have resulted in large amounts of data produced by modern industrial processes. The ability to extract useful information from these multivariate datasets has vital benefits that could be utilized in process monitoring. In the absence of a physics-based process model, data-driven approaches such as latent variable modeling have proved to be practical for process monitoring over the past four decades. The aim of this chapter is to review and show the challenges in multivariate process monitoring based on linear models. Specifically, after presenting the limitations of the full-rank regression model, we provide a brief overview of linear latent variable models such as principal component analysis, principal component regression, and partial least squares regression. To deal with dynamic systems, we present dynamic extensions of these methods that capture both static and dynamic features in multivariate processes. We then provide a brief overview of univariate monitoring schemes, such as exponentially-weighted moving average and cumulative sum and generalized likelihood ratio monitoring schemes and their multivariate counterparts. To apply such tools to multivariate data, we employ appropriate multivariate dimension-reduction techniques according to the features of a process, and we use monitoring schemes to monitor more informative variables in a lower dimension. Next, we aim to identify which process variables contribute to abnormal change; conventional contribution plots and radial visualization tool are briefed. Lastly, the effectiveness of the presented inferential modeling techniques is assessed using simulated data. We also present a study on monitoring influent measurements at a water resource recovery facility. Finally, we discuss limitations of the presented monitoring approaches and give some possible directions to rectify these limitations.