WWTP diagnosis based on 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 variance-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. Hence a scale-M estimator is computed using an iterative re-weighted least squares (IRWLS) procedure. This algorithm is initialized from a nearly robust variance-covariance estimate which tends to emphasize the contribution of close observations in comparison with distant observations (outliers). 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 is successfully applied for sensor fault detection and isolation of the hydraulic part of an activated sludge wastewater treatment plant (WWTP).