Fault detection and isolation with robust principal component analysis
Résumé
Principal component analysis (PCA) is a powerful fault detection and isolation method. However, the classical PCA which is based on the estimation of the sample mean and covariance matrix of the data is very sensitive to outliers in the training data set. Usually robust principal component analysis was applied to remove the effect of outliers on the PCA model. In this paper, a fast two-step algorithm is proposed. First, the objective was to find a robust PCA model that could be used for fault detection and isolation. Hence a scale-M estimator is used to determine a robust model. This estimator is computed using an iterative re-weighted least squares (IRWLS) procedure. To initialize this algorithm a very simple estimate derived from a one-step weighted variance-covariance estimate is used. Second, structured residuals are used for multiple fault detection and isolation. These structured residuals are based on the reconstruction principle and the existence condition of such residuals is used to determine the detectable faults and the isolable faults. The proposed scheme avoids the combinatorial explosion of faulty scenarios related to multiple faults to consider. Then, this procedure for outliers detection and isolation is successfully applied to an example with multiple faults.