Interval-based principal component analysis for reliable fault detection under data uncertainty

Principal Component Analysis (PCA) has gained widespread use in industrial process monitoring due to its ability to model high-dimensional data and detect abnormal events. Traditional PCA techniques, however, assume that sensor measurements are accurate and precise. In real-world applications, measurements are often uncertain affected by noise, degradation, or computational errors making it more appropriate to represent them as intervals rather than single values. To address this limitation, several interval-based PCA approaches have been developed, such as the Center Method (C-PCA) and the Vertex Method (V-PCA), among others. These methods adapt PCA to handle interval-valued data by transforming them into a form suitable for conventional PCA modeling. Despite these advancements, key challenges remain, particularly in the reliable estimation of interval eigenvalues and eigenvectors, and in the effective detection of faults when working with uncertain data. This paper proposes a fault detection methodology tailored to interval-valued process data. It begins by modeling such data using an interval-based PCA approach, and then focuses on fault detection through interval residual analysis. A key contribution is the introduction of a global detection indicator, designed to overcome the ambiguity often encountered in residual-based decision-making. The effectiveness of the proposed method is demonstrated through its application to a simulated Continuous Stirred Tank Reactor (CSTR) process. Results show that incorporating data uncertainty into the detection framework enhances fault diagnosis reliability and reduces the likelihood of false alarms. • Interval-based PCA methods (C-PCA and V-PCA) handle uncertainty in process data. • A global detection indicator is introduced to reduce ambiguity in decisions. • A novel fault detection method targets interval data via interval residual analysis. • Data uncertainty is integrated into the framework to improve diagnostic reliability. • The method reduces false alarm and missed detection rates in a simulated CSTR.