多自由度非线性系统动态参数化模型建模方法研究
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摘要
针对多自由度非线性系统的动态模型辨识问题,基于NARX(Non-linear Autoregressive with Exogenous inputs)模型的建模方法,考虑系统的物理设计参数,建立非线性系统动态参数化模型.首先,根据系统输入、输出数据建立系统不同参数下的NARX模型,并通过EFOR(Extended Forward Orthogonal Regression)算法对不同参数下NARX模型进行修正,以统一辨识得到的系统模型结构.随后,建立NARX模型系数与物理设计参数间的函数关系,得到多自由度非线性系统的动态参数化模型.以单输入、单输出两自由度非线性系统为例,根据数值仿真结果,对系统的动态参数化模型建模过程进行说明.最后,以带非线性涂层阻尼的悬臂梁作为试验对象,建立其动态参数化模型以反映其动力学特性.试验结果表明,非线性系统动态参数化模型能准确预测多自由度非线性系统的输出响应,为非线性系统的分析与优化设计提供了理论基础.
For the identification problem of Multi-Degree of Freedom( MDOF) nonlinear systems,the dynamic parametrical model of a nonlinear system is presented based on the Non-linear Autoregressive with Exogenous inputs( NARX) model and considering the physical design parameters of interest of the systems. Firstly,the NARX model is established under the condition that different design parameters are considered,where each of the established NARX model is only related to the input and output data. These models are then unified to a common structure by using the proposed Extended Forward Orthogonal Regression( EFOR) algorithm. Secondly,the relationship between the coefficients of each unified NARX model and the corresponding physical design parameters are built in order to obtain the dynamic parametrical model of the MDOF nonlinear system. Furthermore,a Single Input Single Output( SISO) 2DOF nonlinear system is taken for a case study to clarify the modeling process of dynamic parametrical model in detail by using the results of numerical simulation. Finally,a cantilever beam with nonlinear coating damper is employed for an experimental validation of the proposed modeling method. The dynamic parametrical model of the beam is established to reflect its dynamic characteristics. The results indicate that the dynamic parametrical model of the non-linear systems can accurately predict the response of the nonlinear systems,which provides the theoretical basis for the analysis and design of nonlinear systems.
For the identification problem of Multi-Degree of Freedom( MDOF) nonlinear systems,the dynamic parametrical model of a nonlinear system is presented based on the Non-linear Autoregressive with Exogenous inputs( NARX) model and considering the physical design parameters of interest of the systems. Firstly,the NARX model is established under the condition that different design parameters are considered,where each of the established NARX model is only related to the input and output data. These models are then unified to a common structure by using the proposed Extended Forward Orthogonal Regression( EFOR) algorithm. Secondly,the relationship between the coefficients of each unified NARX model and the corresponding physical design parameters are built in order to obtain the dynamic parametrical model of the MDOF nonlinear system. Furthermore,a Single Input Single Output( SISO) 2DOF nonlinear system is taken for a case study to clarify the modeling process of dynamic parametrical model in detail by using the results of numerical simulation. Finally,a cantilever beam with nonlinear coating damper is employed for an experimental validation of the proposed modeling method. The dynamic parametrical model of the beam is established to reflect its dynamic characteristics. The results indicate that the dynamic parametrical model of the non-linear systems can accurately predict the response of the nonlinear systems,which provides the theoretical basis for the analysis and design of nonlinear systems.
引文
1李秀英,韩志刚.非线性系统辨识方法的新进展.自动化技术与应用,2004,23(10):5~7(Li X Y,Han Z G.New development on identification methods of nonlinear systems.Automation Technology and Application,2004,23(10):5~7(in Chinese))
2 Yao M H,Zhang W.Using the extended Melnikov method to study multi-pulse chaotic motions of a rectangular thin plate.International Journal of Dynamics and Control,2014,2(3):365~385
3 Yang X D,Zhang W.Nonlinear dynamics of axially moving beam with coupled longitudinal-transversal vibrations.Nonlinear Dynamics,2014,78(4):2547~2556
4 Astrom K J,Eykhoff P.System identification a survey.Automatica,1971,7(2):123~162
5 Li L M,Billings S A.Frequency domain truncation of Volterra series for weakly non-linear systems subject to harmonic excitation.International Journal of Control,2008,81(8):1291~1297
6 Wigren T.Recursive prediction error identification using the nonlinear Wiener model.Automatica,1993,29(4):1011~1025
7 Narendra K S,Gallman P G.An iterative method for the identification of nonlinear systems using a Hammerstein model.Automatic Control,IEEE Transactions on,1966,11(3):546~550
8 Billings S A.Nonlinear system identification:NARMAX methods in the time,frequency,and spatio-temporal domains.John Wiley&Sons,2013
9 Chen S,Billings S A.Representations of non-linear systems:the NARMAX model.International Journal of Control,1989,49(3):1013~1032
10 Chen S,Billings S A,Luo W.Orthogonal least squares methods and their application to non-linear system identification.International Journal of Control,1989,50(5):1873~1896
11 Billings S A,Chen S,Korenberg M J.Identification of MIMO non-linear systems using a forward-regression orthogonal estimator.International Journal of Control,1989,49 (6):2157~2189
12 Chiras N,Evans C,Rees D.Nonlinear gas turbine modeling using NARMAX structures.IEEE Transactions on Instrumentation and Measurement,2001,50(4):893~898.
13 Espinoza M,Suykens J A K,Belmans R,et al.Electric load forecasting.Control Systems,IEEE,2007,27(5):43~57
14 Coca D,Billings S A.Identification of coupled map lattice models of complex spatio-temporal patterns.Physics Letters A,2001,287(1):65~73
15 De Hoff R L,Rock S M.Development of simplified nonlinear models from multiple linearizations.Decision and Control including the 17th Symposium on Adaptive Processes,1978 IEEE Conference on.IEEE,1979:316~318
16 Van Mien H D,Normand-Cyrot D.Nonlinear state affine identification methods:applications to electrical power plants.Automatica,1984,20(2):175~188
17 Wei H L,Lang Z Q,Billings S A.Constructing an overall dynamical model for a system with changing design parameter properties.International Journal of Modelling,Identification and Control,2008,5(2):93~104
18 Worden K,Tomlinson G R.Nonlinearity in structural dynamics:detection,identification and modelling.CRC Press,2000
19 Worden K,Manson G,Tomlinson G R.A harmonic probing algorithm for the multi-input Volterra series.Journal of Sound and Vibration,1997,201(1):67~84
20 郭抗抗,曹树谦.压电发电悬臂梁的非线性动力学建模及响应分析.动力学与控制学报,2014,12(1):18~23(Guo K K,Cao S Q.Nonlinear modeling and analysis of piezoelectric cantilever energy harvester.Journal of Dynamics and Control,2014,12(1):18~23(in Chinese))
2 Yao M H,Zhang W.Using the extended Melnikov method to study multi-pulse chaotic motions of a rectangular thin plate.International Journal of Dynamics and Control,2014,2(3):365~385
3 Yang X D,Zhang W.Nonlinear dynamics of axially moving beam with coupled longitudinal-transversal vibrations.Nonlinear Dynamics,2014,78(4):2547~2556
4 Astrom K J,Eykhoff P.System identification a survey.Automatica,1971,7(2):123~162
5 Li L M,Billings S A.Frequency domain truncation of Volterra series for weakly non-linear systems subject to harmonic excitation.International Journal of Control,2008,81(8):1291~1297
6 Wigren T.Recursive prediction error identification using the nonlinear Wiener model.Automatica,1993,29(4):1011~1025
7 Narendra K S,Gallman P G.An iterative method for the identification of nonlinear systems using a Hammerstein model.Automatic Control,IEEE Transactions on,1966,11(3):546~550
8 Billings S A.Nonlinear system identification:NARMAX methods in the time,frequency,and spatio-temporal domains.John Wiley&Sons,2013
9 Chen S,Billings S A.Representations of non-linear systems:the NARMAX model.International Journal of Control,1989,49(3):1013~1032
10 Chen S,Billings S A,Luo W.Orthogonal least squares methods and their application to non-linear system identification.International Journal of Control,1989,50(5):1873~1896
11 Billings S A,Chen S,Korenberg M J.Identification of MIMO non-linear systems using a forward-regression orthogonal estimator.International Journal of Control,1989,49 (6):2157~2189
12 Chiras N,Evans C,Rees D.Nonlinear gas turbine modeling using NARMAX structures.IEEE Transactions on Instrumentation and Measurement,2001,50(4):893~898.
13 Espinoza M,Suykens J A K,Belmans R,et al.Electric load forecasting.Control Systems,IEEE,2007,27(5):43~57
14 Coca D,Billings S A.Identification of coupled map lattice models of complex spatio-temporal patterns.Physics Letters A,2001,287(1):65~73
15 De Hoff R L,Rock S M.Development of simplified nonlinear models from multiple linearizations.Decision and Control including the 17th Symposium on Adaptive Processes,1978 IEEE Conference on.IEEE,1979:316~318
16 Van Mien H D,Normand-Cyrot D.Nonlinear state affine identification methods:applications to electrical power plants.Automatica,1984,20(2):175~188
17 Wei H L,Lang Z Q,Billings S A.Constructing an overall dynamical model for a system with changing design parameter properties.International Journal of Modelling,Identification and Control,2008,5(2):93~104
18 Worden K,Tomlinson G R.Nonlinearity in structural dynamics:detection,identification and modelling.CRC Press,2000
19 Worden K,Manson G,Tomlinson G R.A harmonic probing algorithm for the multi-input Volterra series.Journal of Sound and Vibration,1997,201(1):67~84
20 郭抗抗,曹树谦.压电发电悬臂梁的非线性动力学建模及响应分析.动力学与控制学报,2014,12(1):18~23(Guo K K,Cao S Q.Nonlinear modeling and analysis of piezoelectric cantilever energy harvester.Journal of Dynamics and Control,2014,12(1):18~23(in Chinese))