基于多维振动响应GSC-TARMA模型的时变结构模态参数辨识

doi:10.3901/JME.2019.15.183

机械工程学报 ›› 2019, Vol. 55 ›› Issue (15): 183-192.doi: 10.3901/JME.2019.15.183

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基于多维振动响应GSC-TARMA模型的时变结构模态参数辨识

余磊^1,2, 刘莉^1,2, 马志赛^3,4, 康杰^1,2

1. 北京理工大学宇航学院北京 100081;
2. 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;
3. 天津大学机械工程学院天津 300350;
4. 天津大学非线性动力学与控制重点实验室天津 300350

收稿日期:2018-07-05 修回日期:2019-05-05 出版日期:2019-08-05 发布日期:2019-08-05
通讯作者: 刘莉(通信作者),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:余磊,男,1990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:bit_yulei@foxmail.com
基金资助:
国家自然科学基金（11802201）和中国博士后科学基金（2017M621075）资助项目。

Modal Parameter Estimation of Time-varying Structures Using GSC-TARMA Models Based on Vector Vibration Response Measurements

YU Lei^1,2, LIU Li^1,2, MA Zhisai^3,4, KANG Jie^1,2

1. School of Aerospace and Engineering, Beijing Institute of Technology, Beijing 100081;
2. Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, Beijing Institute of Technology, Beijing 100081;
3. School of Mechanical Engineering, Tianjin University, Tianjin 300350;
4. Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin University, Tianjin 300350

Received:2018-07-05 Revised:2019-05-05 Online:2019-08-05 Published:2019-08-05

摘要/Abstract

摘要： 针对多维振动响应测量信号下的仅输出时变结构模态参数辨识问题，基于广义随机约束时变自回归滑动平均模型（Generalized stochastic constraints time-dependent auto-regressive moving average，GSC-TARMA），拓展出广义随机约束向量时变自回归滑动平均模型（Generalized stochastic constraints vector time-dependent auto-regressive moving average，GSC-VTARMA）。为降低计算复杂度，进一步提出改进的GSC-VTARMA模型（GSC-VTARMA^*），并利用时变刚度数值系统与移动质量简支梁时变结构实验系统的非平稳振动响应信号对所提模型进行了验证。通过与单维GSC-TARMA模型和传统的泛函序列向量时变自回归滑动平均（Functional series vector time-dependent auto-regressive moving average，FS-VTARMA）模型进行对比，辨识结果表明：相较于GSC-VTARMA模型，GSC-VTARMA^*模型在保持辨识精度相同的前提下降低了计算复杂度；相较于单维GSC-TARMA模型，GSC-VTARMA^*模型具有更高的数据利用率与辨识鲁棒性；GSC-VTARMA^*模型具有与传统的FS-VTARMA模型相近的辨识精度，但由于采用了递推算法，该模型计算效率更高，在线辨识能力更强。

关键词: BPMN, 动态特性, 能耗单元, 耦合关系, 数控机床, 多维振动响应, 广义随机约束, 模态参数辨识, 时变结构

Abstract: The problem of output-only identification of time-varying structures based on vector vibration response measurements is considered. A generalized stochastic constraints vector time-dependent auto-regressive moving average (GSC-VTARMA) model is presented, which is an extension form of the generalized stochastic constraints time-dependent ARMA (GSC-TARMA) model. In order to reduce computation complexity, an improved generalized stochastic constraints vector time-dependent auto-regressive moving average (GSC-TARMA^*) model is subsequently proposed. The proposed model is validated by non-stationary vibration signals of a numerical system with time-varying stiffness and a laboratory time-varying structure consisting of a simply supported beam and a moving mass. The results indicate that the proposed GSC-VTARMA^* model achieves same identification accuracy but less computation complexity to the GSC-VTARMA model, and achieves better identification robustness and higher data utilization to the GSC-TARMA model. Furthermore, the proposed model shows a similar identification accuracy and lower computational cost than the traditional FS-VTARMA model. Due to the recursive algorithm used by the GSC-VTARMA^* model, its enhanced online identification capability has also been demonstrated.

Key words: BPMN, Coupling relationship, Dynamic characteristics, energy units, CNC Machining tools, generalized stochastic constraints, modal parameter estimation, time-varying structures, vector vibration responses

中图分类号:

TP391
TH113

余磊, 刘莉, 马志赛, 康杰. 基于多维振动响应GSC-TARMA模型的时变结构模态参数辨识[J]. 机械工程学报, 2019, 55(15): 183-192.

YU Lei, LIU Li, MA Zhisai, KANG Jie. Modal Parameter Estimation of Time-varying Structures Using GSC-TARMA Models Based on Vector Vibration Response Measurements[J]. Journal of Mechanical Engineering, 2019, 55(15): 183-192.

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基于多维振动响应GSC-TARMA模型的时变结构模态参数辨识

Modal Parameter Estimation of Time-varying Structures Using GSC-TARMA Models Based on Vector Vibration Response Measurements

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