Incipient Fault Detection and Diagnosis Based on Kullback-Leibler Divergence Using Principal Component Analysis: Part I
Résumé
Detection of faults under the Principal Component Analysis (PCA) framework can be made into either the principal or the residual subspace. Because of the large amount of variabilities naturally present in the principal subspace, there are usually ambiguities to detect small variations caused by incipient faults with the use of the first principal components. Distance-based detection and diagnosis methodology is usually used and the Hotelling's T2 is the most common statistical distance defined in the principal subspace. However, because the T2 often fails in detecting small shifts, the residual subspace has become the privileged space for fault detection with the SPE criterion. Therefore, there is a challenge to detect incipient faults within the principal subspace. We propose a fault detection approach based on a probability distribution measure. Residuals are generated by comparing the probability density of each of the latent scores to a reference one, using the Kullback-Leibler Divergence. From simulations it is shown that the proposed criterion successfully detects incipient faults which are undetectable by the distance discriminants. Also, it allows to isolate the fault and gives insights to the severity level of the detected abnormality thanks to its global character. A theoretical analysis is conducted to support the approach and the simulation results.