Recursive transformed component statistical analysis for incipient fault detection
Recursive transformed component statistical analysis for incipient fault detection
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用于早期故障检测的递归变换组件统计分析
DOI：
10.1016/j.automatica.2017.02.028
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发表时间：
2017-06-01
期刊：
影响因子：
6.4
通讯作者：
Zhou, Donghua
中科院分区：
文献类型：
--
作者：
Shang, Jun;Chen, Maoyin;Zhou, Donghua
本文提出了一种新的数据驱动过程监测方法——递归变换成分统计分析（RTCSA），用于早期故障检测。RTCSA在没有空间划分的情况下，对滑动窗口中的数据进行递归处理，通过秩一修正得到正交变换分量（TCs）。tc的统计信息可以揭示一些重要的过程特征，这意味着可以通过监控tc的统计信息来检测故障。通过二阶统计量，检测指标简化为样本协方差矩阵的有序特征值的相对变化。从统计意义上分析了故障可检测性，进而分析了随机矩阵的特征值，包括一类实不相关Wishart矩阵的任意第lth大特征值的概率分布函数的封闭表达式。这表明一个按比例排列的特征值对微小的变化是敏感的。检测指标的结构保证了RTCSA对早期故障的敏感性。与现有的多元统计过程监测方法（如主成分分析（PCA）及其变体）相比，通过数值算例和田纳西伊士曼过程（Tennessee Eastman process）说明了RTCSA具有优越的可检测性。(C) 2017 Elsevier Ltd.版权所有。
This paper presents a new data-driven process monitoring method called recursive transformed component statistical analysis (RTCSA) for the purpose of incipient fault detection. Without space partition, RTCSA processes data in sliding windows to obtain orthogonal transformed components (TCs) recursively using rank-one modification. The statistical information of TCs can reveal some important process features, implying that faults can be detected by monitoring the statistics of TCs. With second order statistics, the detection index reduces to relative changes of ordered eigenvalues of the sample covariance matrix. Fault detectability is analyzed in a statistical sense, leading to the analysis of the eigenvalues of stochastic matrices, including the closed-form expressions for the probability distribution function of the arbitrary lth largest eigenvalue of a class of real uncorrelated Wishart matrices. It indicates that a scaled ordered eigenvalue is sensitive to small changes. The structure of the detection index ensures that RTCSA is sensitive to incipient faults. Compared with existing multivariate statistical process monitoring approaches such as principal component analysis (PCA) and its variants, the superior detectability of RTCSA is illustrated by a numerical example and the Tennessee Eastman process. (C) 2017 Elsevier Ltd. All rights reserved.