移动最小二乘法的时变结构模态参数辨识

doi:10.3901/JME.2016.03.079

机械工程学报 ›› 2016, Vol. 52 ›› Issue (3): 79-85.doi: 10.3901/JME.2016.03.079

移动最小二乘法的时变结构模态参数辨识

杨武, 刘莉, 周思达, 马志赛

北京理工大学飞行器动力学与控制教育部重点实验室北京 100081

收稿日期:2015-01-29 修回日期:2015-10-26 出版日期:2016-02-05 发布日期:2016-02-05
通讯作者: 刘莉，女，1964年出生，博士，教授，博士研究生导师。主要研究方向为飞行器结构总体设计、飞行器结构设计与分析等。 E-mail：liuli@bit.edu.cn
作者简介:杨武，男，1986年出生，博士研究生。主要研究方向为时变结构模态参数辨识。 E-mail：yangwu0629@163.com
基金资助:
北京理工大学基础研究基金资助项目(20120152009)

Modal Parameter Identification of Time-varying Structures via Moving Least Square Method

YANG Wu, LIU Li, ZHOU Sida, MA Zhisai

Key Laboratory of Dynamics and Control of Flight Vehicle of Ministry of Education, Beijing Institute of Technology, Beijing 100081

Received:2015-01-29 Revised:2015-10-26 Online:2016-02-05 Published:2016-02-05

摘要/Abstract

摘要： 研究时变结构模态参数辨识，基于泛函矢量时变自回归模型(Functional series vector time-dependent AR model, FS-VTAR)提出一种改进的移动最小二乘法的时变结构模态参数辨识方法。该方法源于无网格法中构造形函数进行局部近似的思想，引入带权正交基函数对移动最小二乘(Moving least square, MLS)的基函数进行改进，使得在辨识时间域内构造形函数矩阵过程中不再出现数值条件问题，从而提高了计算精度。把时变系数在形函数上线性展开，利用最小二乘法得到形函数的系数，从而得到时变系数。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：改进的移动最小二乘法相比于传统的FS-VTAR模型能有效地避免基函数形式的选择和很高的基函数阶数且更加高效，相比于移动最小二乘法能有效地避免辨识过程中的数值问题，具有更高的模态参数辨识精度。

关键词: 带权正交基函数, 模态参数辨识, 时变AR模型, 时变结构, 移动最小二乘法

Abstract: For modal parameter identification of time-varying structures, an improved identification approach is presented, which uses the moving least square method based on a functional series vector time-dependent AR model (FS-VTAR). The method stems from the local approximation using shape function in the mesh free method. The basis function of moving least square method (MLS) is improved by weighted orthogonal basis function, which makes numerical conditions problem of gaining the shape function matrix solve in the estimation time domain. The modal parameter identification precision is improved. 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 method, the time-varying coefficients are known. 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 improved MLS method avoids the form choice and high order of basis functions as well as high efficiency. Moreover, compared with MLS method, the improved MLS method solves efficiently the numerical conditions problem, and has higher modal parameter identification precision.

Key words: modal parameter identification, moving least square method, time-dependent AR model, time-varying structures, weighted orthogonal basis function

中图分类号:

TP391
TH113

杨武, 刘莉, 周思达, 马志赛. 移动最小二乘法的时变结构模态参数辨识[J]. 机械工程学报, 2016, 52(3): 79-85.

YANG Wu, LIU Li, ZHOU Sida, MA Zhisai. Modal Parameter Identification of Time-varying Structures via Moving Least Square Method[J]. Journal of Mechanical Engineering, 2016, 52(3): 79-85.

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移动最小二乘法的时变结构模态参数辨识

Modal Parameter Identification of Time-varying Structures via Moving Least Square Method

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