Please wait a minute...
浙江大学学报(工学版)  2018, Vol. 52 Issue (9): 1694-1701    DOI: 10.3785/j.issn.1008-973X.2018.09.009
吴平, 陈亮, 周伟, 郭玲玲
浙江理工大学 机械与自动控制学院, 浙江 杭州 310018
Online subspace identification based on principal component analysis and noise estimation
WU Ping, CHEN Liang, ZHOU Wei, GUO Ling-ling
Faculty of Mechanical Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China
 全文: PDF(1556 KB)   HTML

提出一种在线子空间辨识方法,该方法主要采用Hessenberg QR分解和特征值分解,通过对噪声项进行估计,并结合主成分分析提取子空间矩阵,获得系统的状态空间方程.引入遗忘因子机制,实现对时变系统的辨识.为了验证所提方法的适用性和有效性,分别采用数值模型和工业污水处理过程进行仿真验证.仿真结果表明,相比于其他子空间辨识方法,所提方法在辨识线性时不变系统时,能够获取很好的辨识精度;在辨识线性时变系统时,能够快速跟踪系统变化,并能够获取较好的辨识精度。


An online subspace identification algorithm was proposed. The underlying principles of the proposed online subspace identification method use Hessenberg QR algorithm QR factorization and eigenvalue decomposition to estimate the noise term, and then extract the subspace matrices by using principal component analysis. The state space model can be derived from the estimated subspace matrices. An exponential weight forgetting mechanism was introduced to capture the characteristics of the time-varying processes. In order to demonstrate the capability and efficiency of the proposed method, a numerical example and an industrial wastewater treatment process are used to verify the performance. The results of numerical and industrial benchmark simulations show that, compared with other subspace identification methods, the proposed method can derive good identification accuracy in the linear time invariant system, and can derive good performance in terms of system tracking and identification accuracy in the linear time variant system.

收稿日期: 2017-06-25 出版日期: 2018-09-20
CLC:  TP13  


作者简介: 吴平(1982-),男,博士,从事过程辨识建模、过程监测研究
E-mail Alert


吴平, 陈亮, 周伟, 郭玲玲. 基于主成分分析和噪声估计的在线子空间辨识[J]. 浙江大学学报(工学版), 2018, 52(9): 1694-1701.

WU Ping, CHEN Liang, ZHOU Wei, GUO Ling-ling. Online subspace identification based on principal component analysis and noise estimation. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2018, 52(9): 1694-1701.


[1] HUANG B, KADALI R. Dynamic modeling, predictive control and performance monitoring:a data-driven subspace approach[M]. London: Springer Verlag, 2008:2-3.
[2] 齐晓慧, 王俭臣. 固定翼飞机动力学模型的子空间辨识方法[J]. 上海交通大学学报, 2016, 50(4):613-618 QI Xiao-hui, WANG Jian-chen. Subspace model identification method for flight dynamics of fixed-wing airplane[J]. Journal of Shanghai Jiaotong University, 2016, 50(4):613-618
[3] JUILLET F, SCHMID P J, HUERRE P. Control of amplifier flows using subspace identification techniques[J]. Journal of Fluid Mechanics, 2013, 725(5):522-565.
[4] 孙磊, 金晓明. 基于子空间辨识的模型预测控制策略及其应用[J]. 控制理论与应用, 2009, 26(3):313-315 SUN Lei, JIN Xiao-ming. Model-predictive-control based on subspace identification and its application[J]. Control Theory & Applications, 2009, 26(3):313-315
[5] OLOFSSON K E J, SOPPELSA A, BOLZONELLA T, et al. Subspace identification analysis of RFX and 430 T2R reversed-field pinches[J]. Control Engineering Practice, 2013, 21(7):917-929.
[6] CORBETT B, MHASKAR P. Subspace identification for data-driven modeling and quality control of batch processes[J]. AIChE Journal, 2016, 62(5):1581-1601.
[7] AKHENAK A, DUVIELLA E, BAKO L, et al. Online fault diagnosis using recursive subspace identification:application to a dam-gallery open channel system[J]. Control Engineering Practice, 2013, 21(6):797-806.
[8] NEZAM S A, VENKATASUBRAMANIAN V. Electromechanical mode estimation using recursive adaptive stochastic subspace identification[J]. IEEE Transactions on Power Systems, 2013, 29(1):349-358.
[9] HOUTZAGER I, VAN WINGERDEN J, VERHAEGEN M. Recursive predictor-based subspace identification with application to the real-time closed-loop tracking of flutter[J]. IEEE Transactions on Control Systems Technology, 2012, 20(4):934-949.
[10] GILA P, SANTOS F, PALMA L, CARDOSO A. Recursive subspace system identification for parametric fault detection in nonlinear systems[J]. Applied Soft Computing, 2015, 37:444-455.
[11] VERHAEGEN M, DEPRETTERE E. A fast, recursive MIMO state space model identification algorithm[C]//Proceedings of the 1991 Conference on Decision and Control. Brighton:IEEE, 1991:1349-1354.
[12] LOVERA M, GUSTAFSSON T, VERHAEGEN M. Recursive subspace identification of linear and non-linear Wiener state-space models[J]. Automatica, 2000, 36(11):1639-1650.
[13] MERCÈRE G, BAKO L, LECOEUCHE S. Propagator based methods for recursive subspace model identification[J]. Signal Processing, 2008, 88(3):468-491.
[14] 杨华,李少远. 一种新的基于遗忘因子的递推子空间辨识算法[J]. 控制理论与应用, 2009, 26(1):69-72 YANG Hua, LI Shao-yuan. A novel recursive MOESP subspace identification algorithm based on forgetting factor[J]. Control Theory & Applications, 2009, 26(1):69-72
[15] KAMEYAMA K, OHSUMI A, MATSUURA Y, et al. Recursive 4SID-based identification algorithm with fixed input-output data size[J]. International Journal of Innovative Computing Information and Control, 2005, 1(1):17-33.
[16] 谢磊, 梁武星, 张泉灵, 等. 基于快速滑窗QR分解的自适应子空间辨识[J]. 化工学报, 2008, 59(6):1448-1453 XIE Lei, LIANG Wu-xing, ZHANG Quan-ling, et al. Adaptive subspace identification baised on fast foving window QR decomposition[J]. Journal of Chemical Industry and Engineering, 2008, 59(6):1448-1453
[17] ALENANY A, SHANG H. Recursive subspace identification with 0prior information using the constrained least squares approach[J]. Computers & Chemical Engineering, 2013, 54(54):174-180.
[18] YIN S, DING S X, HAGHANI A, et al. A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process[J]. Journal of Process Control, 2012, 22(9):1567-1581.
[19] DING S X, YIN S, PENG K X, et al. A novel scheme for key performance indicator prediction and diagnosis with application to an industrial hot strip mill[J]. IEEE Transactions on Industrial Informatics, 2013, 9(4):2239-2247.
[20] CHEN Z X, FANG H J, CHANG Y. Weighted data-driven fault detection and isolation:a subspace-based approach and algorithms[J]. IEEE Transactions on Industrial Electronics, 2016, 63(5):3290-3298.
[21] NAIK A S, YIN S, DING S X, ZHANG P. Recursive identification algorithms to design fault detection systems[J]. Journal of Process Control, 2010, 20(8):957-965.
[22] WU P, PAN H P, REN J, YANG C J. A new subspace identification approach based on principal component analysis and noise estimation[J]. Industrial & Engineering Chemistry Research, 2015, 54(8):5106-5114.
[23] OKU H. Recursive subspace model identification algorithms for slowly time-varying systems in closed loop[C]//2007 European Control Conference. Greece:IEEE, 2007:5715-5720.
[24] WANG J, QIN S J. A new subspace identification approach based on principal component analysis[J]. Journal of Process Control, 2002, 12(8):841-855.
[25] SOTOMAYOR O A Z, PARK S W, GARCIA C. Multivariable identification of an activated sludge process with subspace-based algorithms[J]. Control Engineering Practice, 2003, 11(8):961-969.

No related articles found!