Deconstructing Principal Component Analysis Using a Data Reconciliation Perspective

TL;DR

This paper reveals the fundamental connection between data reconciliation and PCA, proposing a unified framework that enhances their combined application for improved data processing in process industries.

Contribution

It introduces a unified framework linking PCA and data reconciliation, enabling their collaborative use with partial measurements and process knowledge.

Findings

Unified framework for PCA and DR

Enhanced data processing with partial measurements

Improved denoising and consistency in measurements

Abstract

Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from erroneous measurements. PCA is primarily used as a method for reducing the dimensionality of high dimensional data and as a preprocessing technique for denoising measurements. These techniques have been developed and deployed independently of each other. The primary purpose of this article is to elucidate the close relationship between these two seemingly disparate techniques. This leads to a unified framework for applying PCA and DR. Further, we show how the two techniques can be deployed together in a collaborative and consistent manner to process data. The framework has been extended to deal with partially measured systems and to incorporate partial knowledge available about the process model.