| Citation: | JIA Weizhou, PENG Jingbo, XIE Shousheng, et al. Nonlinear polynomial model's structure and parameter integration identification[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(6): 1303-1311. doi: 10.13700/j.bh.1001-5965.2017.0442(in Chinese)
|
An integration algorithm of nonlinear polynomial model structure identification and parameter identification was proposed for the linear parametric polynomial assembled model, which had wider significance in the field of nonlinear systems. The algorithm combined optimal-selecting process based on contribution items with poor-eliminating process based on redundant items in structure identification. In the optimal-selecting process, the recursive modified Gram-Schmidt (RMGS) algorithm based on output vector residual was used to select the better terms in the vector space, and some redundant non-model terms were allowed to be selected, according to the maximizing drop of the output vector projection residual. In the poor-eliminating process, the algorithm adopted the model structure poor-eliminating strategy based on modified orthogonal sequence to deal with the contribution of the orthogonal vector equally. The structure items with small contribution to the actual output were deleted from the optimal set. The structure and parameters were determined by the system completeness index. Two examples of typical nonlinear polynomial model identification simulation demonstrate the effectiveness of the algorithm.
| [1] |
DING F, LIU X P, LIU G.Identification methods for Hammerstein nonlinear systems[J].Digital Signal Processing, 2011, 21(2):215-238. doi: 10.1016/j.dsp.2010.06.006
|
| [2] |
RUGH W J.Nonlinear system theory-The Volterra Wiener approach[M].Baltimore:Johns Hopkins University Press, 1981:412-414.
|
| [3] |
LEONTARITIS I J, BILLINGS S A.Input-output parametric models for nonlinear system, part:Stochastic nonlinear system[J].International Journal of Control, 1985, 41(2):1863-1878. https://www.researchgate.net/publication/312895401_Input-Output_Parametric_Models_for_Non-Linear_Systems_Part_I_and_Part_II
|
| [4] |
CHEN S, BILLINGS S A, GRANT P M.Non-linear system identification using neural networks[J].International Journal of Control, 1990, 51(6):1191-1214. doi: 10.1080/00207179008934126
|
| [5] |
欧文, 韩崇昭, 王文正.Volterra泛函级数在非线性系统辨识中的应用[J].控制与决策, 2002, 17(2):239-242. http://industry.wanfangdata.com.cn/dl/Detail/Periodical?id=Periodical_kzyjc200202029
OU W, HAN C Z, WANG W Z.Application of Volterra series in the identification of nonlinear system[J].Control and Decision, 2002, 17(2):239-242(in Chinese). http://industry.wanfangdata.com.cn/dl/Detail/Periodical?id=Periodical_kzyjc200202029
|
| [6] |
SUGENO M, KANG G.Structure identification of fuzzy model[J].Fuzzy Sets and Systems, 1988, 28(1):15-33. doi: 10.1016/0165-0114(88)90113-3
|
| [7] |
李应红, 尉询楷, 刘建勋.支持向量机的工程应用[M].北京:国防工业出版社, 2004:44-50.
LI Y H, YU X K, LIU J X.Engineering application of support vector machines[M].Beijing:National Defense Industry Press, 2004:44-50(in Chinese).
|
| [8] |
KOZA J R.Genetic programming:On the programming of computers by means of natural selection[M].Cambridge:MIT Press, 1992:23-25.
|
| [9] |
周霞, 沈炯.多目标免疫GEP算法及其在多项式NARMAX模型辨识中的应用[J].控制与决策, 2014, 29(6):1009-1015. http://www.cqvip.com/QK/91549X/201406/49935271.html
ZHOU X, SHEN J.A immune based multiobjective GEP algorithm for identifying polynomial NARMAX model[J].Control and Decision, 2014, 29(6):1009-1015(in Chinese). http://www.cqvip.com/QK/91549X/201406/49935271.html
|
| [10] |
程长明. 基于Volterra级数的非线性系统辨识及应用研究[D]. 上海: 上海交通大学, 2015: 98-120. http://cdmd.cnki.com.cn/Article/CDMD-10248-1016787797.htm
CHENG C M. Nonlinear system identification and application based on Volterra series[D]. Shanghai: Shanghai Jiao Tong University, 2015: 98-120(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10248-1016787797.htm
|
| [11] |
陈森林, 高正红.基于多小波展开的Volterra级数非线性系统建模方法[J].西北工业大学学报, 2017, 35(3):428-434. http://cdmd.cnki.com.cn/Article/CDMD-10614-2007101123.htm
CHEN S L, GAO Z H.Nonlinear system modeling using multi-wavelet expansion based Volterra series[J].Journal of Northwestern Polytechnical University, 2017, 35(3):428-434(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10614-2007101123.htm
|
| [12] |
CHEN S, BILLINGS S A, LUO W. Orthogonal least squares methods and their application to nonlinear system identification[R]. Sheffield: The University of Sheffield, 1988.
|
| [13] |
王晓, 谢剑英, 贾青.非线性NARMAX模型结构与参数一体化辨识的改进算法[J].信息与控制, 2000, 29(2):102-110. http://www.cqvip.com/qk/90854X/199709/2660656.html
WANG X, XIE J Y, JIA Q.New modified integrated algorithm for structure determination and parameter estimation for nonlinear stochastic systems[J].Information and Control, 2000, 29(2):102-110(in Chinese). http://www.cqvip.com/qk/90854X/199709/2660656.html
|
| [14] |
WEI H L, BILLINGS S A, LIU J. Term and variable selection for nonlinear system identification[R]. Sheffield: The University of Sheffield, 2003.
|
| [15] |
翟旭升, 王海涛, 谢寿生, 等.基于自适应遗传算法的多项式模型结构与参数一体化辨识[J].控制与决策, 2011, 26(5):761-767. http://www.cnki.com.cn/Article/CJFDTOTAL-DNDX200801007.htm
ZHAI X S, WANG H T, XIE S S, et al.Polynomial model structure and parameter integration identification based on adaptive genetic algorithm[J].Control and Decision, 2011, 26(5):761-767(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-DNDX200801007.htm
|
| [16] |
HONG X, CHEN S, GAO J.Nonlinear identification using orthogonal forward regression with nested optimal regularization[J].IEEE Transactions on Cybernetics, 2015, 45(12):2925-2936. doi: 10.1109/TCYB.2015.2389524
|
| [17] |
龚怀云, 寿纪麟, 王锦森.应用泛函分析[M].西安:西安交通大学出版社, 1995:160-178.
GONG H Y, SHOU J L, WANG J S.Applied functional analysis[M].Xi'an:Xi'an Jiaotong University Press, 1995:160-178(in Chinese).
|
| [18] |
王惠文, 夏棒.快速Gram-Schmidt回归方法[J].北京航空航天大学学报, 2013, 39(9):1259-1262. http://bhxb.buaa.edu.cn/CN/abstract/abstract12735.shtml
WANG H W, XIA B.Quick Gram-Schmidt regression method[J].Journal of Beijing University of Aeronautics and Astronautics, 2013, 39(9):1259-1262(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract12735.shtml
|
Figures(10) / Tables(3)
Copyright © Journal of Beijing University of Aeronautics and Astronautics
Address: Editorial Department of Journal of Beijing University of Aeronautics and Astronautics, 37 Xueyuan Road, Haidian District, Beijing Post Code: 100191 Email: jbuaa@buaa.edu.cn
Supported by:
Beijing Renhe Information Technology Co., Ltd.
DownLoad:
