传递函数辨识(7):基于脉冲响应的递阶迭代参数估计方法
|
摘要
基于系统的脉冲响应观测数据,利用梯度搜索和牛顿搜索,研究和提出辨识系统传递函数参数的递阶(多新息)梯度迭代方法、递阶(多新息)牛顿迭代方法、递阶递推梯度迭代方法及递阶递推牛顿迭代方法等。文中的方法可以推广用于其他传递函数描述的动态系统参数辨识,如具有共轭极点、重极点传递函数参数的辨识以及任意非线性函数的参数估计。
Based on the impulse response data and using the gradient search and the Newton search,this paper presents the hierarchical(multi-innovation)gradient-based iterative method,hierarchical(multi-innovation)Newton iterative method,hierarchical recursive gradientbased iterative method,hierarchical recursive Newton iterative method for identifying the parameters of transfer functions with distinct poles.The proposed methods can be extended for the parameter identification of dynamical systems described by other transfer functions with conjugate poles and with same poles and nonlinear functions.
Based on the impulse response data and using the gradient search and the Newton search,this paper presents the hierarchical(multi-innovation)gradient-based iterative method,hierarchical(multi-innovation)Newton iterative method,hierarchical recursive gradientbased iterative method,hierarchical recursive Newton iterative method for identifying the parameters of transfer functions with distinct poles.The proposed methods can be extended for the parameter identification of dynamical systems described by other transfer functions with conjugate poles and with same poles and nonlinear functions.
引文
[1]丁锋.系统辨识新论[M].北京:科学出版社,2013.DING Feng.System Identification—New Theory and Methods[M].Beijing:Science Press,2013.
[2]丁锋.系统辨识—辨识方法性能分析[M].北京:科学出版社,2014.DING Feng.System Identification—Performance Analysis for Identification Methods[M].Beijing:Science Press,2014.
[3]丁锋.系统辨识—辅助模型辨识思想与方法[M].北京:科学出版社,2017.DING Feng.System Identification—Auxiliary Model Identification Idea and Methods[M].Beijing:Science Press,2017.
[4]丁锋.系统辨识—迭代搜索原理与辨识方法[M].北京:科学出版社,2018.DING Feng.System Identification—Iterative Search Principle and Identification Methods[M].Beijing:Science Press,2018.
[5]丁锋.系统辨识—多新息辨识理论与方法[M].北京:科学出版社,2016.DING Feng.System Identification—Multi-Innovation Identification Theory and Methods[M].Beijing:Science Press,2016.
[6]丁锋,徐玲,刘喜梅.传递函数辨识(1):阶跃响应两点法和三点法[J].青岛科技大学学报(自然科学版),2018,39(1):1-14.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part A:Two-point and three-point methods based on the step responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(1):1-14.
[7]丁锋,徐玲,刘喜梅.传递函数辨识(2):脉冲响应两点法和三点法[J].青岛科技大学学报(自然科学版),2018,39(2):1-15.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part B:Two-point and three-point methods based on the impulse responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(2):1-15.
[8]丁锋,徐玲,刘喜梅.传递函数辨识(3):正弦响应两点法和三点法[J].青岛科技大学学报(自然科学版),2018,39(3):1-15.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part C:Two-point and three-point methods based on the sine responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(3):1-15.
[9]丁锋,徐玲,刘喜梅.传递函数辨识(4):基于脉冲响应的递推参数估计[J].青岛科技大学学报(自然科学版),2018,39(4):1-15.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part D:Recursive parameter estimation methods based on the impulse responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(4):1-15.
[10]丁锋,徐玲,刘喜梅.传递函数辨识(5):基于脉冲响应的迭代参数估计[J].青岛科技大学学报(自然科学版),2018,39(5):1-14.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part E:Iterative parameter estimation methods based on the impulse responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(5):1-14.
[11]丁锋,徐玲,刘喜梅.传递函数辨识(6):基于脉冲响应的递阶参数估计[J].青岛科技大学学报(自然科学版),2018,39(6):1-16.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part F:Hierarchical parameter estimation methods based on the impulse responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(6):1-16.
[12]陈垒.连续系统的传递函数模型辨识[D].无锡:江南大学,2012.CHEN Lei.Identification for Transfer Function Models of Continuous-Time Systems[D].Wuxi:Jiangnan University,2012.
[13]CHEN L,LI J H,DING R.Identification of the second-order systems based on the step response[J].Mathematical and Computer Modelling,2011,53(5/6):1074-1083.
[14]XU L,CHEN L,XIONG W L.Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration[J].Nonlinear Dynamics,2015,79(3):2155-2163.
[15]XU L.Application of the Newton iteration algorithm to the parameter estimation for dynamical systems[J].Journal of Computational and Applied Mathematics,2015,288:33-43.
[16]XU L.The damping iterative parameter identification method for dynamical systems based on the sine signal measurement[J].Signal Processing,2016,120:660-667.
[17]XU L,DING F.The parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle[J].IET Signal Processing,2017,11(2):228-237.
[18]XU L,DING F.Parameter estimation for control systems based on impulse responses[J].International Journal of Control,Automation and Systems,2017,15(6):2471-2479.
[19]徐玲.基于移动数据窗的传递函数多新息随机梯度辨识方法[J].控制与决策,2017,32(6):1091-1096.XU Ling.Moving data window based multi-innovation stochastic gradient identification method for transfer functions[J].Control and Decision,2017,32(6):1091-1096.
[20]ZHOU L C,LI X L,XU H G,et al.Multi-innovation stochastic gradient method for harmonic modelling of power signals[J].IET Signal Processing,2016,10(7):737-742.
[21]CAO Y N,LIU Z Q.Signal frequency and parameter estimation for power systems using the hierarchical identification principle[J].Mathematical and Computer Modelling,2010,52(5/6):854-861.
[22]XU L,XIONG W L,ALSAEDI A,et al.Hierarchical parameter estimation for the frequency response based on the dynamical window data[J].International Journal of Control,Automation and Systems,2018,16(4):1756-1764.
[23]WANG D Q.Least squares-based recursive and iterative estimation for output error moving average systems using data filtering[J].IET Control Theory and Applications,2011,5(14):1648-1657.
[24]PAN J,JIANG X,WAN X K,et al.A filtering based multiinnovation extended stochastic gradient algorithm for multivariable control systems[J].International Journal of Control,Automation and Systems,2017,15(3):1189-1197.
[25]王冬青.基于辅助模型的递推增广最小二乘辨识方法[J].控制理论与应用,2009,26(1):51-56.WANG Dongqing.Recursive extended least squares identification method based on auxiliary models[J].Control Theory and Applications,2009,26(1):51-56.
[26]WANG D Q,ZHANG W.Improved least squares identification algorithm for multivariable Hammerstein systems[J].Journal of the Franklin Institute,2015,352(11):5292-5307.
[27]WANG D Q.Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models[J].Applied Mathematics Letters,2016,57:13-19.
[28]LI J H.Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration[J].Applied Mathematics Letters,2013,26(1):91-96.
[29]WANG F F,LIU Y J,YANG E F.Least squares-based iterative identification methods for linear-in-parameters systems using the decomposition technique[J].Circuits,Systems and Signal Processing,2016,35(11):3863-3881.
[30]GUO L J,WANG Y J,WANG C.A recursive least squares algorithm for pseudo-linear ARMA systems using the auxiliary model and the filtering technique[J].Circuits,Systems and Signal Processing,2016,35(7):2655-2667.
[31]MENG D D.Recursive least squares and multi-innovation gradient estimation algorithms for bilinear stochastic systems[J].Circuits,Systems and Signal Processing,2017,36(3):1052-1065.
[32]DING J L.Multi-innovation stochastic gradient algorithm for multi-input output-error systems using the filtering technique[J].ICIC Express Letters,2016,10(12):2927-2933.
[33]WANG D Q,GAO Y P.Recursive maximum likelihood identification method for a multivariable controlled autoregressive moving average system[J].IMA Journal of Mathematical Control and Information,2016,33(4):1015-1031.
[34]LI J H,ZHENG W X,GU J P,et al.Parameter estimation algorithms for Hammerstein output error systems using Levenberg-Marquardt optimization method with varying interval measurements[J].Journal of the Franklin Institute,2017,354(1):316-331.
[35]CHEN J,WANG X P.Identification of Hammerstein systems with continuous nonlinearity[J].Information Processing Letters,2015,115(11):822-827.
[2]丁锋.系统辨识—辨识方法性能分析[M].北京:科学出版社,2014.DING Feng.System Identification—Performance Analysis for Identification Methods[M].Beijing:Science Press,2014.
[3]丁锋.系统辨识—辅助模型辨识思想与方法[M].北京:科学出版社,2017.DING Feng.System Identification—Auxiliary Model Identification Idea and Methods[M].Beijing:Science Press,2017.
[4]丁锋.系统辨识—迭代搜索原理与辨识方法[M].北京:科学出版社,2018.DING Feng.System Identification—Iterative Search Principle and Identification Methods[M].Beijing:Science Press,2018.
[5]丁锋.系统辨识—多新息辨识理论与方法[M].北京:科学出版社,2016.DING Feng.System Identification—Multi-Innovation Identification Theory and Methods[M].Beijing:Science Press,2016.
[6]丁锋,徐玲,刘喜梅.传递函数辨识(1):阶跃响应两点法和三点法[J].青岛科技大学学报(自然科学版),2018,39(1):1-14.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part A:Two-point and three-point methods based on the step responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(1):1-14.
[7]丁锋,徐玲,刘喜梅.传递函数辨识(2):脉冲响应两点法和三点法[J].青岛科技大学学报(自然科学版),2018,39(2):1-15.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part B:Two-point and three-point methods based on the impulse responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(2):1-15.
[8]丁锋,徐玲,刘喜梅.传递函数辨识(3):正弦响应两点法和三点法[J].青岛科技大学学报(自然科学版),2018,39(3):1-15.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part C:Two-point and three-point methods based on the sine responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(3):1-15.
[9]丁锋,徐玲,刘喜梅.传递函数辨识(4):基于脉冲响应的递推参数估计[J].青岛科技大学学报(自然科学版),2018,39(4):1-15.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part D:Recursive parameter estimation methods based on the impulse responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(4):1-15.
[10]丁锋,徐玲,刘喜梅.传递函数辨识(5):基于脉冲响应的迭代参数估计[J].青岛科技大学学报(自然科学版),2018,39(5):1-14.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part E:Iterative parameter estimation methods based on the impulse responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(5):1-14.
[11]丁锋,徐玲,刘喜梅.传递函数辨识(6):基于脉冲响应的递阶参数估计[J].青岛科技大学学报(自然科学版),2018,39(6):1-16.DING Feng,XU Ling,LIU Ximei.Transfer function identification.Part F:Hierarchical parameter estimation methods based on the impulse responses[J].Journal of Qingdao University of Science and Technology(Natural Science Edition),2018,39(6):1-16.
[12]陈垒.连续系统的传递函数模型辨识[D].无锡:江南大学,2012.CHEN Lei.Identification for Transfer Function Models of Continuous-Time Systems[D].Wuxi:Jiangnan University,2012.
[13]CHEN L,LI J H,DING R.Identification of the second-order systems based on the step response[J].Mathematical and Computer Modelling,2011,53(5/6):1074-1083.
[14]XU L,CHEN L,XIONG W L.Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration[J].Nonlinear Dynamics,2015,79(3):2155-2163.
[15]XU L.Application of the Newton iteration algorithm to the parameter estimation for dynamical systems[J].Journal of Computational and Applied Mathematics,2015,288:33-43.
[16]XU L.The damping iterative parameter identification method for dynamical systems based on the sine signal measurement[J].Signal Processing,2016,120:660-667.
[17]XU L,DING F.The parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle[J].IET Signal Processing,2017,11(2):228-237.
[18]XU L,DING F.Parameter estimation for control systems based on impulse responses[J].International Journal of Control,Automation and Systems,2017,15(6):2471-2479.
[19]徐玲.基于移动数据窗的传递函数多新息随机梯度辨识方法[J].控制与决策,2017,32(6):1091-1096.XU Ling.Moving data window based multi-innovation stochastic gradient identification method for transfer functions[J].Control and Decision,2017,32(6):1091-1096.
[20]ZHOU L C,LI X L,XU H G,et al.Multi-innovation stochastic gradient method for harmonic modelling of power signals[J].IET Signal Processing,2016,10(7):737-742.
[21]CAO Y N,LIU Z Q.Signal frequency and parameter estimation for power systems using the hierarchical identification principle[J].Mathematical and Computer Modelling,2010,52(5/6):854-861.
[22]XU L,XIONG W L,ALSAEDI A,et al.Hierarchical parameter estimation for the frequency response based on the dynamical window data[J].International Journal of Control,Automation and Systems,2018,16(4):1756-1764.
[23]WANG D Q.Least squares-based recursive and iterative estimation for output error moving average systems using data filtering[J].IET Control Theory and Applications,2011,5(14):1648-1657.
[24]PAN J,JIANG X,WAN X K,et al.A filtering based multiinnovation extended stochastic gradient algorithm for multivariable control systems[J].International Journal of Control,Automation and Systems,2017,15(3):1189-1197.
[25]王冬青.基于辅助模型的递推增广最小二乘辨识方法[J].控制理论与应用,2009,26(1):51-56.WANG Dongqing.Recursive extended least squares identification method based on auxiliary models[J].Control Theory and Applications,2009,26(1):51-56.
[26]WANG D Q,ZHANG W.Improved least squares identification algorithm for multivariable Hammerstein systems[J].Journal of the Franklin Institute,2015,352(11):5292-5307.
[27]WANG D Q.Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models[J].Applied Mathematics Letters,2016,57:13-19.
[28]LI J H.Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration[J].Applied Mathematics Letters,2013,26(1):91-96.
[29]WANG F F,LIU Y J,YANG E F.Least squares-based iterative identification methods for linear-in-parameters systems using the decomposition technique[J].Circuits,Systems and Signal Processing,2016,35(11):3863-3881.
[30]GUO L J,WANG Y J,WANG C.A recursive least squares algorithm for pseudo-linear ARMA systems using the auxiliary model and the filtering technique[J].Circuits,Systems and Signal Processing,2016,35(7):2655-2667.
[31]MENG D D.Recursive least squares and multi-innovation gradient estimation algorithms for bilinear stochastic systems[J].Circuits,Systems and Signal Processing,2017,36(3):1052-1065.
[32]DING J L.Multi-innovation stochastic gradient algorithm for multi-input output-error systems using the filtering technique[J].ICIC Express Letters,2016,10(12):2927-2933.
[33]WANG D Q,GAO Y P.Recursive maximum likelihood identification method for a multivariable controlled autoregressive moving average system[J].IMA Journal of Mathematical Control and Information,2016,33(4):1015-1031.
[34]LI J H,ZHENG W X,GU J P,et al.Parameter estimation algorithms for Hammerstein output error systems using Levenberg-Marquardt optimization method with varying interval measurements[J].Journal of the Franklin Institute,2017,354(1):316-331.
[35]CHEN J,WANG X P.Identification of Hammerstein systems with continuous nonlinearity[J].Information Processing Letters,2015,115(11):822-827.