Interval-valued statistical approaches for process monitoring

Abstract

Various data-driven approaches, such as Principal Component Analysis (PCA), are widely employed for process monitoring in industrial applications, particularly for detecting abnormal events. PCA-based Fault Detection and Isolation is a well-established strategy, praised for its robust performance. However, its reliability diminishes in uncertain systems where model uncertainties signi?cantly impact e ectiveness. To address this challenge, process modeling is conducted using PCA for interval-valued data, incorporating uncertainties directly into the modeling phase. Four of the most prominent methods for interval-valued PCA are detailed, alongside an extension of conventional PCAbased statistical process monitoring to handle interval-valued data. Over the past decade, this approach has garnered substantial research attention, leading to the development of multiple interval-valued PCA models. This thesis proposes a novel approach called Interval-Valued Principal Component Analysis (IV-PCA), designed to handle uncertainties by de?ning a safe interval for data ?uctuations. The developed technique is applied to the cement rotary kiln process and the Tennessee Eastman Process, where its performance is compared against conventional PCA and four leading Interval-Valued Data PCA (IVD-PCA) methods. Through tests involving actual involuntary system faults and various sensor faults, the IV-PCA demonstrates superior performance in accurately and quickly detecting distinct faults, even in stochastic environments with unknown and uncontrolled uncertainties. The results show signi?cant reductions in false alarms and missed detections compared to the best outcomes of the studied methods