Iterated Robust kernel Fuzzy Principal Component Analysis and application to fault detection

Abstract

In this paper, we propose an Iterated Robust kernel Fuzzy Principal Component Analysis (IRkFPCA), which is the method that attempts to combine the advantages of the state of art methods and use a more accurate multi-objective function for jointly reducing the modeling errors, optimizing the robustness to outliers and improving the time complexity since it does not require the storage and inversion of the covariance matrix to obtain a memory-efficient approximation of kernel PCA. This proposed technique computes iteratively the principal components, which are used for modeling and fault detection. The detection stage is related to the evaluation of residuals, also known as detection indices, which are signals that reveal the fault presence. Those indices are obtained from the analysis of the difference between the process measurements and their estimations using the IRkFPCA technique. The performance of the proposed method is illustrated and compared to Iterated kernel Principal Component Analysis (IkPCA) and Iterated Principal Component Analysis (IPCA) methods through two simulated examples, one using synthetic data and the other using simulated continuously stirred tank reactor (CSTR) data. The results of the comparative studies reveal that the developed IRkFPCA method provides a better performance in terms of modeling and fault detection accuracies than the Iterated Robust Fuzzy Principal Component Analysis (IRFPCA) and Iterated kernel Principal Component Analysis (IkPCA) methods; while both methods provide improved accuracy over the Iterated Principal Component Analysis (IPCA) method.