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

机译：故障检测评估信息理论框架和最佳维度减少方法的设计

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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.
机译：基于数据的故障检测是一种不断增长的区域，具有在制造业中最常用的各种维数减少技术。这些方法之间的评估通常基于给定特定数据集的误报率和故障检测率比较。本文旨在提出对不同故障检测方法评估的普遍标准。为此，提出了一种信息 - 理论框架，其将故障检测问题置于信息的视图中。然后根据提取的特征空间中包含的信息来建立故障检测评估的基础。开发的理论表明，相互信息不仅仅是一种可能在某些问题中可能有用的另一种性能指标，而是通用指示器关于故障检测方法如何执行的情况 - 通过维度减少技术在提取的特征中保留的信息越大，故障检测性能越好。该框架用于推导出最佳的ISO-information变换矩阵，用于对故障检测的维度减少方法，这在应用主成分分析和随机偏压的振荡过程中的应用中说明了。

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