No abstract

In this article, an analytical method is used to obtain multiple model (MM) forms strictly equivalent to a given nonlinear model. The proposed method induces no information loss, contrary to existing order reduction methods. Several MMs formally equivalent to the initial model may be obtained, due to the intermediate quasi-LPV forms. Thus some criteria are given, using the linear matrix inequality (LMI) formulation, in order to chose the most suitable MM for analysis or control purpose. This method is applied to an activated sludge reactor model.

No abstract

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 is 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 an accurate estimate of the covariance matrix of the data so that a PCA model might be developed that could then be used for fault detection and isolation. A very simple estimate derived from a one-step weighted variance-covariance estimate is used (Ruiz-Gazen, 1996). This is a "local" matrix of variance 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 be considered. Then, this procedure for outliers detection and isolation is successfully applied to an example with multiple faults.