北京航空航天大学学报 ›› 2018, Vol. 44 ›› Issue (6): 1303-1311.doi: 10.13700/j.bh.1001-5965.2017.0442

• 论文 • 上一篇    下一篇

非线性多项式模型结构与参数一体化辨识

贾伟州, 彭靖波, 谢寿生, 刘云龙, 李腾辉, 何大伟   

  1. 空军工程大学 航空航天工程学院, 西安 710038
  • 收稿日期:2017-07-03 出版日期:2018-06-20 发布日期:2018-06-28
  • 通讯作者: 彭靖波.E-mail:pjb1209@126.com E-mail:pjb1209@126.com
  • 作者简介:贾伟州 男,硕士研究生。主要研究方向:航空推进系统综合控制;彭靖波 男,博士,副教授,硕士生导师。主要研究方向:航空发动机分布式控制与故障诊断;谢寿生 男,博士,教授,博士生导师。主要研究方向:航空推进系统综合控制与状态监控。
  • 基金资助:
    国家自然科学基金(51476187,51506221)

Nonlinear polynomial model's structure and parameter integration identification

JIA Weizhou, PENG Jingbo, XIE Shousheng, LIU Yunlong, LI Tenghui, HE Dawei   

  1. Aeronautics and Astronautics Engineering Institute, Air Force Engineering University, Xi'an 710038, China
  • Received:2017-07-03 Online:2018-06-20 Published:2018-06-28

摘要: 针对非线性系统领域具有更广泛意义的线参数多项式组合模型,提出一种非线性多项式模型结构辨识和参数辨识一体化算法。该算法将结构辨识中基于贡献项的择优过程与基于冗余项的劣汰过程结合。在择优过程中,根据输出向量投影残差下降的最大化,采用基于输出向量残差化的递归改进Gram-Schmidt(RMGS)算法,在向量空间的全集中择优,并允许部分冗余非模型项选入。在劣汰过程中,为平等对待正交化向量的贡献,采用基于改进正交化次序的模型结构劣汰策略,在优选集合里逐个删除对实际输出贡献相对较小的结构项,以系统完备性指标为约束,确认结构与参数。2类典型非线性多项式模型辨识仿真算例对比验证了算法的有效性。

关键词: 非线性系统辨识, 多项式模型, 一体化辨识, 递归改进Gram-Schmidt(RMGS)算法, 改进正交化次序

Abstract: 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.

Key words: nonlinear system identification, polynomial model, integration identification, recursive modified Gram-Schmidt (RMGS) algorithm, modified orthogonal sequence

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