基于模态空间时域精细积分的结构动力学参数辨识方法

潘耀宗; 赵岩

doi:10.21656/1000-0887.450071

基于模态空间时域精细积分的结构动力学参数辨识方法

doi: 10.21656/1000-0887.450071

潘耀宗^1,,
赵岩^{1, 2, ,}

1.
大连理工大学力学与航空航天学院工业装备结构分析优化与CAE软件全国重点实验室，辽宁大连 116024
2.
大连理工大学宁波研究院，浙江宁波 315016

（我刊编委赵岩来稿）

基金项目:

国家自然科学基金 11772084

国家自然科学基金 U1906233

国家重点研发计划 2017YFC0307203

详细信息

作者简介:
潘耀宗(1997—)，男，博士生(E-mail: panyaozong@mail.dlut.edu.cn)

通讯作者:
赵岩(1974—)，男，教授，博士生导师(通讯作者. E-mail: yzhao@dlut.edu.cn)

中图分类号: O32
计量
- 文章访问数: 30
- HTML全文浏览量: 13
- PDF下载量: 5
- 被引次数: 0
出版历程
- 收稿日期: 2024-03-20
- 修回日期: 2024-05-04
- 刊出日期: 2025-01-01

A Structural Dynamics Parameter Identification Method Based on the Modal Space Time-Domain Precise Integration

PAN Yaozong^1
,,
ZHAO Yan^{1, 2
, ,}

1.
State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China
2.
Ningbo Institute of Dalian University of Technology, Ningbo, Zhejiang 315016, P.R.China

(Contributed by ZHAO Yan, M.AMM Editorial Board)

摘要

摘要: 提出了一种基于模态空间时域精细积分的动力学参数辨识方法. 首先，基于时域测量信号和理论预测模型构造辨识方程，在模态空间内，由时域精细积分方法构造了理论预测模型；其次，通过矩阵、向量的Kronecker积运算法则推导了辨识模态的无约束向量的二次型函数，解析地给出了辨识振型的数学表达；最后，通过对辨识优化问题进行数学变换，仅需要辨识结构动力学特性的谱参数(频率和阻尼比)，极大地降低了辨识参数的维度. 数值算例中，进行了三自由度弹簧质量系统和高速受电弓的动力学参数辨识，辨识得到的固有频率、阻尼比与理论值相比，误差在8%以内；辨识振型与理论振型之间的夹角的余弦接近1，验证了辨识结果的准确性. 该文提出的方法能够有效地实现辨识谱参数(频率、阻尼)和空间参数(振型)的分离，具有非常好的求解效率和应用前景.
- 动力学参数辨识 /
- 时域精细积分法 /
- 最小二乘法 /
- 自振特性 /
- 动力学优化
Abstract: Based on the modal space time-domain precise integration, a dynamic parameter identification method was proposed. Firstly, an identification model was constructed based on the time-domain measurement signals and the theoretical prediction model with the time-domain precise integration method in the modal space. Secondly, the quadratic function of the unconstrained vector was derived through the Kronecker product of matrices, and the mathematical expressions of the mode shapes were analyzed and given. Finally, through mathematical transformations of the identification optimization problem, only the dynamics spectrum parameters (frequencies and damping ratios) need be identified, to greatly reduce the dimensionality of the identification parameters. In numerical examples, the dynamic parameter identification for the spring-mass system and the high-speed pantograph system were studied. The identified natural frequencies and damping ratios have errors less than 8% compared to the theoretical values. The cosine of the angle between the identified and the theoretical mode shapes is close to 1, which verifies the accuracy of the identification results. The proposed method can effectively achieve the separation of dynamic spectral parameters (frequencies, damping ratios) and spatial parameters (modal shapes), and has better solving efficiency and application prospects.
- dynamic parameter identification /
- time-domain precise integration method /
- least squares method /
- free vibration characteristic /
- dynamics optimization
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1) （我刊编委赵岩来稿）

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图 1 三自由度弹簧-质量系统

Figure 1. The 3-DOF spring-mass system

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图 2 系统激励与测量位移响应

Figure 2. System excitations and measurement displacement responses

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图 3 高速受电弓结构图

Figure 3. Structural diagram of the high-speed pantograph

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图 4 高速受电弓系统激励与测量加速度响应

Figure 4. Excitation and measurement acceleration response of high-speed pantograph system

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图 5 受电弓滑板振型辨识结果

Figure 5. Identification results of mode shapes of the pantograph strip

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图 6 受电弓理论响应与预测响应对比

Figure 6. Comparison between theoretical and predictive responses of the pantograph

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表 1 弹簧-质量系统动力学参数辨识结果

Table 1. Identification results of dynamic parameters of the spring-mass system

parameter		mode 1	mode 2	mode 3
f/Hz	identification	3.854	6.236	7.339
f/Hz	theory	3.854	6.238	7.340
ζ/%	identification	1.00	1.02	1.03
ζ/%	theory	1.00	1.00	1.00
γ	identification	1.65	0.54	0.75
γ	theory	1.65	0.50	0.70
C_MAC		1.000 0	0.999 7	0.999 0

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表 2 不同测量噪声水平谱参数辨识结果

Table 2. Dynamic spectral parameter identification results under different measurement noise levels

measurement noise level /%	mode 1		mode 2		mode 3
measurement noise level /%	f/Hz	ζ/%	f/Hz	ζ/%	f/Hz	ζ/%
5	3.854	1.00	6.238	1.01	7.340	1.01
10	3.854	1.00	6.237	1.02	7.340	1.02
15	3.854	1.00	6.236	1.02	7.339	1.03
20	3.854	1.01	6.236	1.03	7.339	1.05

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表 3 谱参数与空间参数耦合和解耦时结果对比

Table 3. Comparison of results of spectral parameters coupled and decoupled with spatial parameters

	mode 1			mode 2			mode 3			optimisation time /s
	f/Hz	ζ/%	γ	f/Hz	ζ/%	γ	f/Hz	ζ/%	γ	optimisation time /s
decoupled	3.854	1.00	1.65	6.237	1.02	0.52	7.340	1.02	0.73	22.40
coupled	3.854	1.00	1.65	6.237	1.02	0.52	7.340	1.02	0.73	121.84

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表 4 高速受电弓动力学参数辨识结果

Table 4. Identification results of dynamic parameters of the high-speed pantograph

parameter		mode 1	mode 2	mode 3	mode 4	mode 5	mode 6
f/Hz	identification	9.029	12.459	13.753	50.450	52.220	121.552
f/Hz	theory	9.035	12.472	13.764	50.585	52.376	123.320
ζ/%	identification	1.23	1.08	1.05	1.10	0.90	1.10
ζ/%	theory	1.00	1.00	1.00	1.00	1.00	1.00
γ/10^-4	identification	2.33	1.71	2.35	3.87	1.28	6.43
C_MAC		0.997 4	0.998 1	0.999 6	0.999 9	0.995 5	0.999 7

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表 5 高速受电弓模态试验动力学参数辨识结果

Table 5. Identification results of dynamic parameters of the high-speed pantograph modal test

	parameter	mode 1	mode 2	mode 3	mode 4	mode 5
proposed methodology	f/Hz	10.2	12.50	48.8	133.6	219.4
proposed methodology	ζ/%	0.46	0.36	3.95	2.711	1.84
ref. [17]	f/Hz	10.0	12.50	48.4	128.5	213.0

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