Kernel methods for advanced statistical process control

Abstract

This thesis investigated development and application of Kernel methods to enhance Statistical Process Control procedures. The first part of this thesis discussed the development of a control chart based on adaptive Kernel Principal Components Analysis (KPCA) to monitor non-stationary nonlinear process behaviour. Moreover, in order to have a fast adaptive KPCA model, we proposed an updating method that provides a reduced computation cost for large-scale KPCA model and a good tracking of the original matrix with a small reconstruction error. Analysis and comparison with other Principal Components Analysis control charts showed that the proposed procedure provides overall competitive detection results. The second part of this thesis investigated monitoring of nonlinear autocorrelated processes based on Support Vector Regression (SVR). The advantage of this procedure is that it allows modelling and control of nonlinear processes without the need to find analytical solutions to describe phenomena of interest. Results showed that the used control charts can effectively monitor the process behaviour while guarantying an acceptable robustness. The third part of this dissertation dealt with development of local Support Vector Domain Description (SVDD) based control chart to monitor complex and multimodal processes without specifying a probability distribution. This procedure allows simplifying and reducing the complexity of the problem which can help selecting SVDD parameters. Analysis of the proposed control chart using simulated and real case studies showed that this procedure allows better detection results while guaranteeing a reduced false alarm rate.