On the use of reconstruction-based contribution for fault diagnosis

• Revelation of the invalidation cases of three fault detection indices based RBC.
• Geometric illustrations of the invalidation cases are presented.
• Three methods including the proposed CSC are introduced for effective diagnosis.
• The effect of the window width in CSC on its diagnosis performance is analyzed.

In the multivariate statistical process monitoring (MSPM) area, principal component analysis (PCA) and reconstruction-based contribution (RBC) are two commonly used techniques for fault detection and fault diagnosis problems, respectively. This paper starts with a review of the two methods. It is then pointed out that, when the dimensionality of the principal component subspace or the residual subspace in the PCA model is equal to 1, several fault detection indices based RBC will be invalid for fault diagnosis. Corresponding geometric interpretations of the invalidation cases are illustrated intuitively according to the definition of RBC. In order to perform effective fault diagnosis in such invalidation cases, three methods including the available combined index based RBC, the derived Mahalanobis distance based RBC, and the proposed chi-square contribution (CSC) are introduced. The CSC is constructed by employing a moving window and the effect of the window width on its diagnosis performance is investigated. The failure cases of the RBC, the effectiveness of the proposed CSC, as well as the comparison of these three methods for fault diagnosis are demonstrated by case studies on two numerical examples and a simulated three-tank system.