An Information-Theoretic Framework for Fault Detection Evaluation and Design of Optimal Dimensionality Reduction Methods

Data-based fault detection is a growing area with various dimensionality reduction techniques being most commonly used in the manufacturing industries. The evaluation among these methods is generally based on false alarm rate and fault detection rate comparisons given a specific dataset This article aims to propose a universal criterion for the evaluation of different fault detection approaches. To this end, an information-theoretic framework is presented that imbeds the fault detection problem into an information point of view. The basis for fault detection evaluation is then established in terms of the information contained in the extracted feature space. The developed theory shows that mutual information is not merely another performance index which may be useful in some problem, but rather a universal indicator about how well fault detection methods can perform the larger the information preserved in the extracted features by a dimensionality reduction technique, the better the fault detection performance. The framework is used to derive an optimal iso-information transformation matrix for dimensionality reduction methods for fault detection, which is demonstrated in the application of principal component analysis and canonical variate analysis to an oscillatory process with random bias. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.