摘要
针对传统的PCA建模要求数据噪声服从正态分布,然而在实际的工业过程中建模数据经常含有离群点问题,提出了一种基于鲁棒主元分析的故障检测方法.该方法使用加权方差-协方差矩阵来代替传统PCA的协方差矩阵建立鲁棒PCA模型,计算此模型的SPE(Q)和T2统计量并监控这2个统计量是否超过了各自的控制限来检测是否存在故障.用Matlab进行了与传统PCA的对比仿真,结果表明,当离群点存在时传统的PCA方法很难检测出故障,而鲁棒PCA可以消除离群点的影响准确地检测出故障.鲁棒PCA比传统PCA方法分析过程数据更为准确,并能克服大多数鲁棒方法需要进行迭代的问题,能有效地检测过程故障.
In the classical principal component analysis ( PCA) case,the models require the noisy data to be of normal distributions. However,the model data in process monitoring often contain outliers. A robust principal component analysis method is proposed to analyze this problem. A very simple estimate derived from a one-step weighted variance-covariance estimate is used. It supersedes the covariance of the classical principal component analysis to develop a robust PCA model. Then the squared prediction error ( SPE) and T2 statistics based on this model are used for fault detection. One advantage of the proposed method is that it does not need iteration unlike a majority of robust methods. The comparison simulations in Matlab are conducted. It is shown that the proposed robust PCA method can remove the influence of outliers,analyze the process data more accurately and detect process faults more effectively than traditional PCA method.
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2010年第S1期140-143,共4页
Journal of Southeast University：Natural Science Edition
基金
江苏省高等学校自然科学基础研究面上资助项目(09KJB510005
08KJD510016)
关键词
主元分析
鲁棒性
离群点
故障检测
principal component analysis
robustness
outliers
fault detection
