Multivariate Statistical Process Monitoring Using Kernel Principal Component Analysis

Résumé: Fault detection and diagnosis field (FDD) plays an important role in industrial processes. It assures the safe operation of the process and reduces its maintenance costs. The implementation of mechanisms for early detection and diagnosis of faults is called process monitoring. Due to the size and complexity of industrial processes, multivariate statistical methods are finding wide application in process monitoring. Some popular methods are principal component analysis (PCA) for linear processes, and kernel principal component analysis (KPCA) for nonlinear processes. The main challenge in the KPCA based fault detection and diagnosis method is the high computation time and memory storage space whenever the size of the training data increases. The developed kernel matrix size depends on the number of training observations. So, it requires O(n 2 ) storage space for its build and for which O(n ) computation time for its eigendecomposition procedures. In this dissertation, three new methods have been proposed to address the computation drawbacks of KPCA. The first method aims to eliminate the redundant observations among the training dataset based on the Euclidean distances between observations such that any two observations with zero Euclidean distance are considered similar and one of them can be removed. The second method removes the correlated observations and keeps only the representative non-correlated observations to build a reduced training dataset. The third method reduces the training dataset by eliminating the dependent observation guarding only the independent observations. The reduced training datasets are used to build KPCA algorithm to compute the fault indices thresholds in order to fire the alarms when the index violated its threshold. The proposed methods are applied to two case study industrial processes: Ain El Kebira rotary kiln process and Tennessee Eastman process. The obtained results are compared to the ordinary KPCA and different Reduced KPCA (RKPCA) methods; in terms of false alarm rate (FAR), missed detection rate (MDR), and detection time delay (DTD); to evaluate the efficiency of these proposed methods. The proposed RKPCA techniques are able to enhance the time and space computation of KPCA and contribute better monitoring performance

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