Robust and sparse canonical correlation analysis for fault detection and diagnosis using training data with outliers

A well-known shortcoming of the traditional canonical correlation analysis (CCA) is the lack of robustness against outliers. This shortcoming hinders the application of CCA in the case where the training data contain outliers. To overcome this shortcoming, this paper proposes robust CCA (RCCA) methods for the analysis of multivariate data with outliers. The robustness is achieved by the use of weighted covariance matrices in which the detrimental effect of outliers is reduced by adding small weight coefficients on them. The RCCA is then extended to the robust sparse CCA (RSCCA) by imposing the l1-norm constraints on canonical projection vectors to obtain the sparsity property. Based on the RCCA and RSCCA, a robust data-driven fault detection and diagnosis (FDD) method is proposed for industrial processes. A residual generation model is built using projection vectors of the RCCA or RSCCA. The robust squared Mahalanobis distance of the residual is used for fault detection. A contribution-based fault diagnosis method is developed to identify the faulty variables that may cause the fault. The performance and advantages of the proposed methods are illustrated with two case studies. The results of two case studies prove that the RCCA and RSCCA methods have high robustness against outliers, and the robust FDD method is able to yield reliable results even if using the low-quality training data with outliers.