Generalized Principal Component Analysis-Based Subspace Decomposition of Fault Deviations and Its Application to Fault Reconstruction

Abstract

In the present work, based on the generalized principal component analysis, we propose a new approach to decompose the subspace of fault deviations, which is used for reconstruction-based fault diagnosis through principal component analysis (PCA) monitoring system. The proposed method is advanced since it lightens the computational burden by eliminating the irrelavant information and simplifying the fault subspace. The fault effects are extracted through analyzing the generalized principal components of the normal operating data and the fault data. The significant fault deviations that cause the alarming monitoring statistic are calculated. This is achieved by designing a two-part feature decomposition procedure. In the first part, the normal operating subspace is extracted through analyzing the generalized principal components of both the historical normal data and fault data. The fault-free part of the data is eliminated by projecting the data into the normal operating subspace. In the second part, principal component analysis is performed on the remaining part of the data, where the largest fault deviation directions are decomposed in order. By the two-part decomposition, an integrated fault subspace for all monitoring statistic indices is obtained, which separates the measurement data into two different parts for fault reconstruction. One part is related to the normal operating subspace, which is deemed to follow normal rules, and thus insignificant to remove alarming monitoring statistics. The other is related to the fault subspace, which contributes to the outof-control signals. Theoretical support is constructed and the related statistical characteristics are analyzed. Its feasibility and performance are illustrated with the data from the Tennessee Eastman (TE) benchmark process.