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 out-of-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.
Highlights
In modern industrial processes, fault detection and diagnosis [1]–[11] have become one of the most critical areas of research in process control over the past decades, and an essential element in the operation of modern engineering systems to avoid serious consequences and reduce the maintenance costs
In the fault data set, those fault deviations that can cause alarming monitoring statistics are separated from the others, which is implemented in two steps
The generalized principal components (GPCs) are referred as the generalized eigenvectors corresponding to the r largest generalized eigenvalues of the autocorrelation matrix pencil composed of two data vectors, where r referred as the number of the GPCs
Summary
Fault detection and diagnosis [1]–[11] have become one of the most critical areas of research in process control over the past decades, and an essential element in the operation of modern engineering systems to avoid serious consequences and reduce the maintenance costs. The conventional reconstruction methods are based on PCA These algorithms extract the general fault information from the input data and may not be able to discriminate fault patterns well from normal conditions. In the fault data set, those fault deviations that can cause alarming monitoring statistics are separated from the others, which is implemented in two steps. SUBSPACE EXTRACTION APPROACH OF RESPON-SIBLE FAULT DEVIATIONS The proposed method is presented to develop a unified fault reconstruction model for any monitoring statistics. This method is applied for the decomposition of the responsible fault effects in two parts, which are introduced in 3.1 and 3.2. VOLUME 8, 2020 the preprocessed x can cover the fault deviation information relative to the normal center
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