Enhanced diagnostics using orthogonal de-noising based nonlinear discriminant analysis and its application to multivariate data

Many multivariate statistical techniques have been developed to solve fault diagnosis problems for productivity and quality improvement. Recently, nonlinear kernel techniques (e.g. support vector machines) have been successfully applied to a number of applications such as bio-informatics, face recognition, handwritten digit recognition, etc. The basis of these techniques is to map input data into a nonlinear space; these mapped data are then analysed. Using the kernel trick on these methods makes it possible to develop powerful kernel-based nonlinear techniques and to extract information from the mapped data. This paper proposes a new diagnosis method based on kernel Fisher discriminant analysis (KFDA), a nonlinear kernel technique. It utilizes KFDA to extract nonlinear patterns of data effectively. In addition, an orthogonal de-noising technique, called orthogonal signal correction, is incorporated into the proposed framework and used as a pre-processing step. This de-noising is executed before KFDA modeling in order to remove unwanted variation of data. A case study on two processes has been conducted. The proposed method produced reliable diagnosis results and the use of KFDA modeling combined with the orthogonal de-noising technique was able to improve the classification performance.