Dynamic Parametrical Modeling Method of Nonlinear Systems with Multiple Outputs Based on REFOR Algorithm

doi:10.3901/JME.2018.23.073

Abstract

Abstract: 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.

Key words: cantilever beam, dynamic parametrical model, multiple outputs, nonlinear systems, REFOR algorithm

CLC Number:

TG156

LUO Zhong, LIU Haopeng, ZHU Yunpeng, WANG Fei, HAN Qingkai. Dynamic Parametrical Modeling Method of Nonlinear Systems with Multiple Outputs Based on REFOR Algorithm[J]. Journal of Mechanical Engineering, 2018, 54(23): 73-81.

References

[1] NORTON J P. An introduction to identification[M]. Courier Corporation,2009.
[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.