Exponential discriminant analysis for fault diagnosis

Fisher discriminant analysis (FDA), as a dimensionality reduction technique, is widely used for fault diagnosis. It, however, suffers from under-sampled or small sample size (SSS) problem, that is, it cannot be directly applied in the case of small training data set in higher dimensional processes. Many modified approaches have been proposed to address this problem but a comprehensive solution to this problem is still missing. In this paper, we propose application of exponential discriminant analysis (EDA) for fault detection and isolation. The proposed technique not only overcomes the small sample size problem but also has an increased discriminant power. Compared with FDA, EDA is equivalent to performing an exponential transformation to distance between samples. Thus, the between-class distance is enlarged, whereas the within-class distance is shortened. Therefore, margin between different classes is enlarged, thereby improving fault isolation capability. Tennessee Eastman process is used as benchmark to present a comparison of FDA and EDA. Furthermore, EDA is applied for monitoring of Coupled Liquid Tanks System.

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