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Fuzzy-clustering-based all-factor automatous validation approach of modal parameters of structures
ZHOU Sida , ZHOU Xiaochen, LIU Li, YANG Wu
Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
Abstract:To solve the problem of modal parameter validation, an automatous validation approach of modal parameters was realize by using the fuzzy clustering analysis, which reduced the dependence of users' subjective experience on modal parameter validation, and improve the efficiency of modal parameter validation at modal analysis work. First, the modal parameters are divided into the scalar type and the vector type. Second, the scalar modal parameters were clustered by the convention fuzzy clustering approach. Third, the modal shape were fuzzy clustered by using a new proposed modal assurance criterion based metric function to solve the high-dimensional difficulty of fuzzy clustering. Then, combining the clustering results both of the scalar and the vector modal parameters, the all-factor automatous validation of modal parameters was accomplished. Finally, the proposed approach was validated by experimental results and illustrate that the proposed approach can automatously, accurately and high-efficiently validate the modal parameters.
Key words: modal validation     fuzzy clustering     all-factor     clustering of mode shapes     autonomous

1 模糊聚类

X={x1,x2,…,xN}Rp为一个含有N∈Ν1个元素的数据集合(其中Rp表示p维的实数集,Ν1为一维的自然数集,下同).用U∈RC×N表示N∈Ν1个元素的数据集合对CΝ1个聚类的隶属度矩阵.URC×N中的元素uij(i=1,2,…,C;j=1,2,…,N)表示第j个元素隶属于第i个聚类相对于其他聚类的程度.由于模糊聚类中的隶属度矩阵U∈RC×N表示的是一种概率的聚类划分,因此对于URC×N有如下的约束:

V={v1,v2,…,vC} ⊂ Rp表示由C∈Ν1个聚类原型组成的聚类原型集合,其中vi为第i个聚类的原型.

2 模态参数验证

2.1 标量型模态参数的模糊聚类

2.2 向量型参数(振型)的模糊聚类

2.3 两类模态参数的综合交叉验证

3 实验验证

 图 1 弹翼实验件Fig. 1 Test rig of a sample wing

 图 2 测点布置Fig. 2 Deployment of measurement locations

 图 3 原点频率响应函数Fig. 3 Origin frequency response function

 图 4 模糊聚类结果Fig. 4 Fuzzy clustering results

 图 5 布尔矩阵Fig. 5 Boolean matrix

 模态阶数 频率/Hz 阻尼比/% 辨识模型阶数 在总集合中序号 1 24.65 0.23 19 86 2 36.73 0.21 22 121 3 44.73 0.60 23 139 4 45.08 0.30 26 166 5 59.94 0.26 13 29 6 60.35 0.31 30 212
 图 6 验证后振型的MAC矩阵Fig. 6 MAC matrix of validated mode shapes

 图 7 模态指示函数的虚部[15]Fig. 7 Imaginary part of mode indicator function[15]

4 结 论

1) 方法考虑全部模态参数，最大化地使用辨识得到的信息，能够很好地去除虚假数学模型，且不易遗漏真实物理模态.

2) 在处理振型的模糊聚类时,为了解决高维和复数问题,提出了一种基于MAC的距离函数.

3) 验证实验结果表明,方法能够自动验证结构模态辨识得到的模态参数,且实施较为简单,不依赖使用者的经验.

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#### 文章信息

ZHOU Sida, ZHOU Xiaochen, LIU Li, YANG Wu

Fuzzy-clustering-based all-factor automatous validation approach of modal parameters of structures

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(5): 811-816.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0344