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浙江大学学报(工学版)
J4  2009, Vol. 43 Issue (5): 827-831    DOI: 10.3785/j.issn.1008-973X.2009.05.008
自动化技术、计算机技术     
基于秩-1矩阵摄动的递归主元分析算法
刘世成,王海清,李平
（浙江大学 工业控制技术国家重点实验室,工业控制研究所,浙江 杭州 310027）
Recursive PCA algorithm based on rank-one matrix perturbation
LIU Shi-cheng, WANG Hai-qing, LI Pin
(State Key Laboratory of Industrial Control Technology, Institute of Industrial Process Control, Zhejiang University, Hangzhou 310027, China)
 全文: PDF 
摘要：

针对传统主元分析（PCA）算法仅适用于定常系统监测的不足,提出了一种基于秩-1矩阵摄动的递归主元分析（RPCA）算法以适应实际工业过程的时变特性.RPCA算法首先对初始化样本协方差矩阵进行特征值分解,得到特征向量矩阵与特征值矩阵；然后在各时刻采用秩-1矩阵摄动算法对这两个矩阵递归更新并对其各向量与各元素排序,同时以累计方差百分比（CPV）为标准选取主元数目,从而显著降低了运算复杂度,节省了存储量.青霉素间歇发酵过程在线监测的仿真结果表明,RPCA算法大大降低了系统的误警率,并及时监测出过程中存在的故障.
关键词： 主元分析;  秩-1矩阵;  矩阵摄动;  递归主元分析;  在线监测;  累计方差百分比    
Abstract:

As traditional PCA-based methods are limited to the application in time-invariant systems, a recursive PCA (RPCA) algorithm based on rank-one matrix perturbation was  proposed to fit with the time-variant characteristics of  practical industrial processes. Firstly the covariance matrix of initial samples was decomposed to an eigenvector  matrix and a diagonal eigenvalue matrix. Then the eigenvector and eigenvalue matrices were updated with every new data sample, and the number of the selected components was  determined according to the cumulative percent variance (CPV) criterion simultaneously. Thus the computational complexity was greatly reduced and the memory saved. The proposed  method was applied to on-line monitoring a fed-batch penicillin fermentation process and compared with the conventional PCA monitoring methods. The results clearly illustrated  the superiority of the proposed method, with fewer false alarms within normal batch processes and small fault detection delay when faults  existed．
Key words: principal component analysis (PCA)    rank-one matrix    matrix perturbation    recursive principal component analysis (RPCA)    on-line monitoring    cumulative percent     variance (CPV)
出版日期: 2009-06-01
:  TP206.3  
基金资助:

国家自然科学基金资助项目（20776128）;教育部留学回国人员科研启动基金资助项目.
通讯作者: 王海清，男，副教授.     E-mail: hqwang@iipc.zju.edu.cn
作者简介: 刘世成（1978-），男，山东淄博人，博士生，从事统计质量控制、过程建模与监测等研究.
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引用本文:

刘世成, 王海清, 李平. 基于秩-1矩阵摄动的递归主元分析算法[J]. J4, 2009, 43(5): 827-831.

LIU Shi-Cheng, WANG Hai-Qing, LI Beng. Recursive PCA algorithm based on rank-one matrix perturbation. J4, 2009, 43(5): 827-831.

链接本文:

http://www.zjujournals.com/xueshu/eng/CN/10.3785/j.issn.1008-973X.2009.05.008    或    http://www.zjujournals.com/xueshu/eng/CN/Y2009/V43/I5/827

［1］ NOMIKOS P, MACGREGOR J F. Multivariate SPC charts for monitoring batch processes ［J］. Technometrics, 1995, 37(1): 4159．
［2］ WANG Hai-qing, SONG Zhi-huan, LI Ping. Fault detection behavior and performance analysis of PCA-based monitoring methods ［J］. Industrial & Engineering Chemistry  Research, 2002, 41(10): 24552464．
［3］ KUNG S Y, DIAMANTARAS K I, TAUR J S. Adaptive principal component extraction (APEX) and applications ［J］. IEEE Transactions on Signal Processing, 1994, 42(5): 12021217．
［4］ ERDOGMUS D, RAO Y N, HILD II K E, et al. Simultaneous principal component extraction with application to adaptive blind multiuser detection ［J］. EURASIP Journal on  Applied Signal Processing, 2002， 12(6): 14731484．
［5］ LI W, YUE H H, VALLE-CERVANTES S, et al. Recursive PCA for adaptive process monitoring ［J］. Journal of Process Control, 2000, 10(5): 471486．
［6］ PEDDANENI H, ERDOGMUS D, RAO Y N, et al. Recursive principal components analysis using eigenvector matrix perturbation ［C］∥Proceedings of the 14th IEEE Signal  Processing Society Workshop. Sao Luis: IEEE, 2004: 8392．
［7］ CHOI S W, MARTIN E B, MORRIS A J, et al. Adaptive multivariate statistical process control for monitoring time-varying processes ［J］. Industrial & Engineering Chemistry  Research, 2006, 45(9): 31083118．
［8］ BIROL G, CINAR A. A modular simulation package for fed-batch fermentation: penicillin production ［J］. Computers & Chemical Engineering, 2002, 26(11): 15531565．
［9］ 刘世成,王海清,李平. 基于多向核主元分析的青霉素生产过程在线监测［J］. 浙江大学学报：工学版, 2007, 41(2): 202207．
LIU Shi-cheng, WANG Hai-qing, LI Ping. On-line monitoring of penicillin production process based on multiway kernel principal component analysis ［J］. Journal of Zhejiang 
University: Engineering Science, 2007, 41(2): 202207．
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