基于秩_1矩阵摄动的递归主元分析算法.pdf

43 5 浙 江 大 学 学 报( ) V ol 43 N o 5 2009 5 J ournal of Zhejiang U niver sity ( Eng ineering Science) M ay 2009 DOI: 10 3785/ j issn 100 8973X 2009 05 00 8 1 刘世成, 王海清, 李 平 ( , , 3 10027) : ( PCA) , 1 ( RPCA) RPCA , ; 1 , ( CPV) , , , RPCA , : ; 1 ; ; ; ; : T P20 6 3; T Q 465 1 : A : 100 897 3X ( 2009) 050 82705 Recursive PCA algorithm based on rankone matrix perturbation L IU Sh icheng, W A N G H aiqing, L I Ping ( State Key Laboratory of Industrial Control Technology , I nstitute of Industrial Process Control, Zhej iang University , H angzhou 3 10027, China) Abstract: A s t radit ional PCAbased m et hods are lim it ed t o t he applicatio n in t imeinvariant syst em s, a re cur sive P CA ( RPCA ) algorit hm based on r ankone mat rix p ert urb at ion w as propo sed t o f it w ith t he tim e variant ch ar act eristics of pract ical indu st rial proces ses First ly t he cov ar iance mat rix of init ial sam ples w as decom po sed to an eigenvect or m atrix and a diag onal eigenvalue m at rix T hen t he eigenvect or and eigenv al u e m at rices w ere updat ed w it h every new data sam ple, and t he number of t he select ed component s w as de t ermined acco rding to t he cum ulat ive percent variance ( CP V ) cr it erion simult aneou sly T hu s the co mput a t ional complex it y w as great ly reduced and t he memory saved T he proposed met ho d w as applied t o online monit oring a f edb at ch penicillin f erment at ion proces s and comp ared w ith t he convent ional P CA monito ring methods T he results clearly illu st rat ed t he sup eriorit y of t he proposed method , w it h f ew er f alse alarms w