基于Kriging形函数的线性时变结构模态参数辨识

doi:10.7527/S1000-6893.2014.0194

固体力学与飞行器总体设计

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基于Kriging形函数的线性时变结构模态参数辨识

杨武, 刘莉, 周思达, 马志赛

北京理工大学宇航学院飞行器动力学与控制教育部重点实验室, 北京 100081

收稿日期:2014-04-09 修回日期:2014-08-19 出版日期:2015-04-15 发布日期:2014-09-05
通讯作者: 刘莉Tel.: 010-68914534 E-mail: liuli@bit.edu.cn E-mail:liuli@bit.edu.cn
作者简介:杨武男, 博士研究生。主要研究方向: 时变结构模态参数辨识。Tel: 010-68913290 E-mail: yunlure@bit.edu.cn;刘莉女, 博士, 教授, 博士生导师。主要研究方向: 飞行器总体设计、飞行器结构分析与设计、飞行动力学与控制。Tel: 010-68914534 E-mail: liuli@bit.edu.cn;周思达男, 博士, 讲师, 硕士生导师。主要研究方向: 飞行器结构动力学分析、时变结构动力学系统分析与辨识。Tel: 010-68918752 E-mail: zhousida@bit.edu.cn;马志赛男, 博士研究生。主要研究方向: 时变系统参数辨识。Tel: 010-68913290 E-mail: zhisai.ma@gmail.com
基金资助:
北京理工大学基础研究基金(20120142009)

Modal parameter identification of linear time-varying structures using Kriging shape function

YANG Wu, LIU Li, ZHOU Sida, MA Zhisai

Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

Received:2014-04-09 Revised:2014-08-19 Online:2015-04-15 Published:2014-09-05
Supported by:
Beijing Institute of Technology Foundation for Basic Research (20120142009)

摘要/Abstract

摘要：

近年来,对航空航天飞行器随时间变化的动力学特性研究需求越来越迫切。仅输出参数化时域的时变时间序列模型以其结构简约、精度高且跟踪能力强而成为研究热点,尤其是泛函向量时变自回归(FS-VTAR)模型已经得到了广泛应用。然而传统的FS-VTAR模型在保证其辨识优势的同时却需要针对不同时变结构选择合适的基函数形式及较高的基函数阶数,该过程相当复杂且耗时。本文借鉴无网格法中移动最小二乘(MLS)法构造形函数的思想,提出一种基于Kriging形函数的线性时变结构模态参数辨识方法。该方法首先引入自适应于辨识信号的Kriging形函数;再把时变系数在形函数上线性展开,利用最小二乘(LS)法得到形函数的展开系数;最后把时变模型特征方程转换为广义特征值问题提取出模态参数。利用时变刚度系统非平稳振动信号验证该方法,结果表明:基于Kriging形函数的FS-VTAR模型相比于传统的FS-VTAR模型能有效地避免基函数形式的选择和较高的基函数阶数,且精度相当;相比于移动最小二乘法能有效地解决其数值条件问题且具有更高的模态参数辨识精度。

关键词: 时变结构, 模态参数辨识, Kriging, 形函数, 时变AR模型

Abstract:

Recently, it is essential and imperative to conduct the study of the time-varying dynamic characteristic of aerospace flight vehicle. Due to representation parsimony, high accuracy and improved tracking, the output-only parametric time-domain time-dependent time series models become the research hotspot. Above all, the function series vector time-dependent autoregressive (FS-VTAR) models are applied. Yet, the conventional FS-VTAR model needs to choose a suitable type and quite high order of basis function to certify its merit, which is complex and time-consuming. Stemmed from the moving least square (MLS) method via shape function in the mesh free method, a modal parameter identification method of time-varying structures via Kriging shape function is presented. Firstly, Kriging shape function adaptive to the signals is introduced to this method. Then, the time-varying coefficients are expanded into a linear combination of the shape functions. Once the unknown coefficients of shape functions are obtained via least square (LS) method, the time-varying coefficients are known. Finally, modal parameters are extracted from a generalized eigenvalue problem, which is transformed from an eigenvalue equation of the time-varying model. The identification approach is validated by non-stationary vibration signals of a system with time-varying stiffness. Compared with the traditional FS-VTAR model, the FS-VTAR method based on Kriging shape function avoids the form choice and high order of basis functions as well as high efficiency and has high precision. Moreover, compared with MLS method, this method solves efficiently the numerical conditions problem and has higher modal parameter identification precision.

Key words: time-varying structures, modal parameter identification, Kriging, shape function, time-dependent AR model

中图分类号:

杨武, 刘莉, 周思达, 马志赛. 基于Kriging形函数的线性时变结构模态参数辨识[J]. 航空学报, 2015, 36(4): 1169-1176.

YANG Wu, LIU Li, ZHOU Sida, MA Zhisai. Modal parameter identification of linear time-varying structures using Kriging shape function[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(4): 1169-1176.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于Kriging形函数的线性时变结构模态参数辨识

Modal parameter identification of linear time-varying structures using Kriging shape function

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