基于近似偏最小一乘的闭环系统辨识新方法
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摘要
本文基于近似最小一乘准则和主成分分析,针对反馈通道模型阶次低于前向通道模型阶次且反馈通道不存在噪声的闭环系统,进行了近似偏最小一乘递推辨识算法的推导.为解决最小一乘准则函数不可微的问题,本文算法用确定性可导函数近似代替残差绝对值.近似偏最小一乘辨识算法可以克服基于最小二乘准则的辨识算法在受到满足(SαS)分布的尖峰噪声干扰时残差平方项过大的缺点,具有目标函数可导,计算简单的优点.同时,通过主成分分析去除数据向量各元素之间的线性相关,可以得出模型参数的唯一解.仿真实验表明,本文算法可以对反馈通道模型阶次低于前向通道模型阶次的闭环系统进行直接辨识,抑制了尖峰噪声对辨识结果的影响,具有优良的稳健性,可以更好地应用于闭环系统辨识.
Based on approximate least absolute deviation criterion and principal component analysis, a recursive partial approximate least absolute deviation(PALAD) identification algorithm is deduced for closed-loop system whose model order of feedback channel is lower than that of the forward channel and there is no noise in the feedback channel. To solve the non-differentiable problem of the least absolute deviation, a deterministic derivable function is established to approximate the absolute value under certain situations in this paper. The proposed method can overcome the disadvantage of large square residual of least square criterion when the identification data is disturbed by the impulse noise which obeys symmetrical alpha stable distribution(SαS). By adopting principal component analysis to eliminate the linear correlation among the elements of data vector, the unique solution of model parameters can be easily acquired by the proposed method.The simulation experiments show that the proposed method can be directly used to identify closed-loop system whose model order of feedback channel is lower than that of the forward channel. Moreover, the proposed algorithm can restrain the impact of impulse noise effectively, has strong robustness and can be better applied to closed-loop identification..
Based on approximate least absolute deviation criterion and principal component analysis, a recursive partial approximate least absolute deviation(PALAD) identification algorithm is deduced for closed-loop system whose model order of feedback channel is lower than that of the forward channel and there is no noise in the feedback channel. To solve the non-differentiable problem of the least absolute deviation, a deterministic derivable function is established to approximate the absolute value under certain situations in this paper. The proposed method can overcome the disadvantage of large square residual of least square criterion when the identification data is disturbed by the impulse noise which obeys symmetrical alpha stable distribution(SαS). By adopting principal component analysis to eliminate the linear correlation among the elements of data vector, the unique solution of model parameters can be easily acquired by the proposed method.The simulation experiments show that the proposed method can be directly used to identify closed-loop system whose model order of feedback channel is lower than that of the forward channel. Moreover, the proposed algorithm can restrain the impact of impulse noise effectively, has strong robustness and can be better applied to closed-loop identification..
引文
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[17]ANTOINE N,ALI C?.PLS,balanced,and canonical variate realization techniques for identifying VARMA models in state space[J].Chemometrics and Intelligent Laboratory Systems,1997,38(2):209–221.
[18]LAUR′I D,SALCEDO J,GARC′IA-NIETO S,et al.A PLS approach to identifying predictive ARX models[C]//The 18th IEEE International Conference on Control Applications Part of 2009 IEEE multiconference on Systems and Control.New York:IEEE,2009:1460–1465.
[19]XU B C,LIU X L.Research on identification algorithm based on the approximate least absolute deviation criteria[J].International Journal of Automation and Computing,2012,9(5):501–505.
[20]XU Baochang,ZHANG Yingdan.Multi-innovation identification algorithm based on approximate least absolute deviation[J].Control Engineering of China,2015,22(1):60–65.(徐宝昌,张瀛丹.基于近似最小一乘准则的多新息辨识算法[J].控制工程,2015,22(1):60–65.)
[21]XIANG Wei,CHEN Zonghai.New identification method of nonlinear systems based on hammerstein models[J].Control Theory&Applications,2007,24(1):143–147.(向微,陈宗海.基于Hammerstein模型描述的非线性系统辨识新方法[J].控制理论与应用,2007,24(1):143–147.)
[22]DONG Jian,XIE Kaigui.Research of the non-linear regress models based on the least absolute criteria[J].Journal of Chongqing Normal University(Natural Science Edition),2001,18(4):71–74.(董建,谢开贵.基于最小一乘准则的非线性回归模型研究[J].重庆师范学院学报(自然科学版),2001,18(4):71–74.)
[23]DONG Qi.Relaxation algorithm based on“least absolute deviation”criterion[J].Predictive Method Research,1990,9(2):16–18.(董祺.“残差绝对值和最小”准则的松弛算法[J].预测方法研究,1990,9(2):16–18.)
[24]WANG Guizeng,YE Hao.Principal Component Analysis and Partial Least Squares Method[M].Beijing:Tsinghua University Press,2012:41–59.(王桂增,叶昊.主元分析与偏最小二乘法[M].北京:清华大学出版社,2012:41–59.)
[25]QIN S J.Recursive PLS algorithms for adaptive data modeling[J].Computers&Chemical Engineering,1998,22(4/5):503–514.
[26]COATES M J,KURUOGLU E E.Time-frequency based detection in impulsive noise environments using alpha-stable noise model[J].Digital Signal Processing,2002,82(3):1917–1925.
[27]GUO Ying.The study on novel time delay estimation methods based on stable distribution[D].Dalian:Dalian University of Technology,2009.(郭莹.稳定分布环境下的时延估计新方法研究[D].大连:大连理工大学,2009.)
[28]CHEN Xiru,WU Yuehua.A problem about the relationship between the minimum Ll-norm estimate and linear programming[J].Journal of Nanjing Institute of Technology,1988,18(5):16–21.(陈希孺,吴月华.最小Ll模估计与线性规划的关系的一个问题[J].南京工业学院学报,1988,18(5):16–21.)
[2]LJUNG L.System Identification:Theory for The Users[M].Englewood Cliffs,NJ:Prentice-Hall Inc,1987:34–67.
[3]SODERSTROM T,STOICA P.System Identification[M].Hemel Hemptead,UK:Prentice-Hall,1989:13–49.
[4]GEVERS M,BOMBOIS X,HILDEBRAND R,et al.Optimal experiment design for open and closed-loop system identification[J].Communications in information and systems,2011,11(3):197–224.
[5]CHIUSO A,PICCI G.Consistency analysis of some closed-loop subspace identification methods[J].Automatica,2005,41(3):377–391.
[6]PIPEIKIS R.Closed-loop robust identification using the indirect approach[J].Information,2000,11(3):297–310.
[7]MEDIANU S,LUPU C,POPESCU D,et al.Optimal closed-loop identification solution using direct and indirect methods for a flexible transmission system[C]//The 2nd International Conference on Systems and Computer Science.New York:IEEE,2013:74–79.
[8]CALANCA A,L.CAPISANI M,FERRARA A,et al.MIMO closedloop identification of an industrial robot[J].IEEE Transactions on Control Systems Technology,2011,19(5):1214–1224.
[9]MO Jianlin,WANG Wei,XU Xiaoming,et al.Closed-loop problem in system identification[J].Control Theory&Applications,2002,19(1):9–14.(莫建林,王伟,许晓鸣,等.系统辨识中的闭环问题[J].控制理论与应用,2002,19(1):9–14.)
[10]FANG Chongzhi,XIAO Deyun.Process Identification[M].Beijing:Tsinghua University Press,1988:361–396.(方崇智,萧德云.过程辨识[M].北京:清华大学出版社,1988:361–396.)
[11]DING F,CHEN T.Identification of hammerstein nonlinear ARMAX systems[J].Automatica,2005,41(9):1479–1489.
[12]L¨U You,LIU Jizhen,YANG Tingting,et al.NOx emission characteristic modeling based on feature extraction using PLS and LS–SVM[J].Chinese Journal of Scientific Instrument,2013,34(11):2418–2424.(吕游,刘吉臻,杨婷婷,等.基于PLS特征提取和LS–SVM结合的NOx排放特性建模[J].仪器仪表学报,2013,34(11):2418–2424.)
[13]SUN Maojie,YANG Huizhong.Local weighted mixed kernel partial least squares algorithm and its applications to soft-sensing[J].Information and Control,2015,44(4):481–486.(孙茂伟,杨慧中.局部加权混合核偏最小二乘算法及其在软测量中的应用[J].信息与控制,2015,44(4):481–486.)
[14]WANG Wei,CHAI Tianyou,ZHAO Lijie.Dynamic partial least squares modeling with recurrent neural networks of stable learning[J].Control Theory&Applications,2012,29(3):337–341.(王巍,柴天佑,赵立杰.带有稳定学习的递归神经网络动态偏最小二乘建模[J].控制理论与应用,2012,29(3):337–341.)
[15]QIN S J.Statistical process monitoring:basics and beyond[J].Journal of Chemometrics,2003,17(8/9):480–502.
[16]YIN Li,LIU Qiang.Study on the identification of the milling force parameter model based on partial least square regression and application[J].Mechanical Science and Technology,2005,24(3):269–272.(尹力,刘强.基于偏最小二乘回归(PLSR)方法的铣削力模型系数辨识研究[J].机械科技与技术,2005,24(3):269–272.)
[17]ANTOINE N,ALI C?.PLS,balanced,and canonical variate realization techniques for identifying VARMA models in state space[J].Chemometrics and Intelligent Laboratory Systems,1997,38(2):209–221.
[18]LAUR′I D,SALCEDO J,GARC′IA-NIETO S,et al.A PLS approach to identifying predictive ARX models[C]//The 18th IEEE International Conference on Control Applications Part of 2009 IEEE multiconference on Systems and Control.New York:IEEE,2009:1460–1465.
[19]XU B C,LIU X L.Research on identification algorithm based on the approximate least absolute deviation criteria[J].International Journal of Automation and Computing,2012,9(5):501–505.
[20]XU Baochang,ZHANG Yingdan.Multi-innovation identification algorithm based on approximate least absolute deviation[J].Control Engineering of China,2015,22(1):60–65.(徐宝昌,张瀛丹.基于近似最小一乘准则的多新息辨识算法[J].控制工程,2015,22(1):60–65.)
[21]XIANG Wei,CHEN Zonghai.New identification method of nonlinear systems based on hammerstein models[J].Control Theory&Applications,2007,24(1):143–147.(向微,陈宗海.基于Hammerstein模型描述的非线性系统辨识新方法[J].控制理论与应用,2007,24(1):143–147.)
[22]DONG Jian,XIE Kaigui.Research of the non-linear regress models based on the least absolute criteria[J].Journal of Chongqing Normal University(Natural Science Edition),2001,18(4):71–74.(董建,谢开贵.基于最小一乘准则的非线性回归模型研究[J].重庆师范学院学报(自然科学版),2001,18(4):71–74.)
[23]DONG Qi.Relaxation algorithm based on“least absolute deviation”criterion[J].Predictive Method Research,1990,9(2):16–18.(董祺.“残差绝对值和最小”准则的松弛算法[J].预测方法研究,1990,9(2):16–18.)
[24]WANG Guizeng,YE Hao.Principal Component Analysis and Partial Least Squares Method[M].Beijing:Tsinghua University Press,2012:41–59.(王桂增,叶昊.主元分析与偏最小二乘法[M].北京:清华大学出版社,2012:41–59.)
[25]QIN S J.Recursive PLS algorithms for adaptive data modeling[J].Computers&Chemical Engineering,1998,22(4/5):503–514.
[26]COATES M J,KURUOGLU E E.Time-frequency based detection in impulsive noise environments using alpha-stable noise model[J].Digital Signal Processing,2002,82(3):1917–1925.
[27]GUO Ying.The study on novel time delay estimation methods based on stable distribution[D].Dalian:Dalian University of Technology,2009.(郭莹.稳定分布环境下的时延估计新方法研究[D].大连:大连理工大学,2009.)
[28]CHEN Xiru,WU Yuehua.A problem about the relationship between the minimum Ll-norm estimate and linear programming[J].Journal of Nanjing Institute of Technology,1988,18(5):16–21.(陈希孺,吴月华.最小Ll模估计与线性规划的关系的一个问题[J].南京工业学院学报,1988,18(5):16–21.)