基于REFOR算法的多输出非线性系统动态参数化建模方法研究
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摘要
针对多输出非线性系统动态模型的辨识问题,提出一种新的非线性系统动态参数化建模方法,即冗余向前延拓正交(Redundant extended forward orthogonal regression,REFOR)算法。该算法旨在消除传统向前延拓正交(Extended forward orthogonal regression,EFOR)算法因遗漏某些重要模型项而造成所建模型精度较低的问题。首先,基于系统在各工况下辨识所得非线性有源自回归(Non-linear autoregressive with exogenous inputs,NARX)模型,利用REFOR算法统一各模型结构得到模型系数与设计参数间的函数关系,进而建立多输出非线性系统的动态参数化模型。其次,以四自由度非线性系统为例,说明了REFOR算法的优势及其在系统建模中的应用。最后,利用REFOR算法建立悬臂梁的动态参数化模型,并将REFOR预测输出与试验测得输出进行对比,试验结果表明,基于REFOR算法建立的非线性系统动态参数化模型,能准确预测系统的输出响应,为非线性系统建模方法的优化设计提供了理论基础。
In allusion to the identification problem of nonlinear systems with multiple outputs, a new algorithm of nonlinear systems' dynamic parametrical modeling method, called the redundant extended forward orthogonal regression(REFOR) is proposed in this study, which aims to avoid the missing of some significant model terms when using extended forward orthogonal regression(EFOR) algorithm. Firstly, based on non-linear autoregressive with exogenous inputs(NARX) model, which correspond to different cases of parameter properties, a common-structured model is built via REFOR, and a functional relationship between the coefficients of unified model term and the design parameters is established. A dynamic parametrical model of nonlinear systems with multiple outputs is constructed as a consequence. Further, a 4th degree of freedom(4DOF) nonlinear system is taken as a case study to clarify the advantage of REFOR and its application in modeling. Finally, a dynamic parametrical model of cantilever beam is established via REFOR, and a contrast between REFOR's output and corresponding real measurement is given. The results indicate that the REFOR based dynamic parametrical model can accurately predict output response of nonlinear systems, which provide a theoretical basis for the optimal design of nonlinear systems' modeling methods.
In allusion to the identification problem of nonlinear systems with multiple outputs, a new algorithm of nonlinear systems' dynamic parametrical modeling method, called the redundant extended forward orthogonal regression(REFOR) is proposed in this study, which aims to avoid the missing of some significant model terms when using extended forward orthogonal regression(EFOR) algorithm. Firstly, based on non-linear autoregressive with exogenous inputs(NARX) model, which correspond to different cases of parameter properties, a common-structured model is built via REFOR, and a functional relationship between the coefficients of unified model term and the design parameters is established. A dynamic parametrical model of nonlinear systems with multiple outputs is constructed as a consequence. Further, a 4th degree of freedom(4DOF) nonlinear system is taken as a case study to clarify the advantage of REFOR and its application in modeling. Finally, a dynamic parametrical model of cantilever beam is established via REFOR, and a contrast between REFOR's output and corresponding real measurement is given. The results indicate that the REFOR based dynamic parametrical model can accurately predict output response of nonlinear systems, which provide a theoretical basis for the optimal design of nonlinear systems' modeling methods.
引文
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[2]黄涛,杨开明,杨进,等.柔性结构的多输入多输出运动系统辨识方法[J].机械工程学报,2016,52(11):42-49.HUANG Tao,YANG Kaiming,YANG Jin.Identification of multiple input multiple output motion system with flexible structures[J].Journal of Mechanical Engineering,2016,52(11):42-49.
[3]FJ III D,PEARSON R K,OGUNNAIKE B A.Identification and control using Volterra models[M].Springer Science&Business Media,2012.
[4]LI S,LI Y.Model predictive control of an intensified continuous reactor using a neural network Wiener model[J].Neurocomputing,2016,185:93-104.
[5]GOTMARE A,PATIDAR R,GEORGE N V.Nonlinear system identification using a cuckoo search optimized adaptive Hammerstein model[J].Expert systems with applications,2015,42(5):2538-2546.
[6]PIRODDI L.Simulation error minimisation methods for NARX model identification[J].International Journal of Modelling,Identification and Control,2008,3(4):392-403.
[7]RUANO A E,FLEMING P J,TEIXEIRA C,et al.Nonlinear identification of aircraft gas-turbine dynamics[J].Neurocomputing,2003,55(3):551-579.
[8]GE S S,ZHANG J,LEE T H.Adaptive MNN control for a class of non-affine NARMAX systems with disturbances[J].Systems&Control Letters,2004,53(1):1-12.
[9]CHEN S,BILLINGS S A.Representations of non-linear systems:the NARMAX model[J].International Journal of Control,1989,49(3):1013-1032.
[10]TONG H.Threshold models in non-linear time series analysis[M].Springer Science&Business Media,2012.
[11]刘昊鹏,朱云鹏,罗忠,等.多自由度非线性系统动态参数化模型建模方法研究[J].动力学与控制学报[J],2017,15(1):15-24.LIU Haopeng,ZHU Yunpeng,LUO Zhong,et al.Modeling method on dynamic parametrical model of nonlinear multi-degree of freedom system[J].Journal of Dynamics and Control,2017,15(1):15-24.
[12]BILLINGS S A,VOON W S F.Piecewise linear identification of non-linear systems[J].International Journal of Control,1987,46(1):215-235.
[13]HABER R,VAJK I,KEVICZKY L.Nonlinear system identification by"linear"systems having signal-dependent parameters[J].IFAC Proceedings Volumes,1982,15(4):499-504.
[14]VAN MIEN H D,NORMAND-CYROT D.Nonlinear state affine identification methods:applications to electrical power plants[J].Automatica,1984,20(2):175-188.
[15]DIEKMANN K,UNBEHAUEN H.On-line parameter estimation in a class of nonlinear systems via modified least-squares and instrumental variable algorithms[J].IFAC Proceedings Volumes,1985,18(5):149-153.
[16]WEI H L,LANG Z Q,BILLINGS S A.Constructing an overall dynamical model for a system with changing design parameter properties[J].International Journal of Modelling,Identification and Control,2008,5(2):93-104.
[17]BILLINGS S A.Nonlinear system identification:NARMAX methods in the time,frequency,and spatio-temporal domains[M].John Wiley&Sons,2013.
[18]WORDEN K,TOMLINSON G R.Nonlinearity in structural dynamics:Detection,identification and modelling[M].CRC Press,2000.