基于密度峰值聚类算法的模态参数识别
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摘要
稀疏成分分析是解决欠定盲源分离问题的一种有效方法,其主要分为两步:计算振型矩阵和重构单模态信号。在计算振型矩阵时,针对无法预知源信号数量和高阶振动模态混叠的问题,利用一种基于密度峰值聚类算法识别模态振型。相比于传统的聚类算法,该方法具有以下特点:①利用决策图直观地选出聚类中心和聚类数目;②算法可以自动分离噪声点,对噪声不敏感。在重构单模态信号时,利用可以快速重构稀疏信号的SL0算法,重构出单模态时频域信号,提取出各阶模态频率。通过振动结构仿真算例验证了该方法的有效性。
The sparse component analysis is an efficient approach to handle the underdetermined blind source separation, which contains two steps: calculating the mixing matrix and second, reconstructing the sources. In the paper, the modal shapes were calculated by using the Density Peaks Clustering Algorithm to deal with the cases that the number of sources cannot be known a priori and high order modes are overlapped with each other. Compared to the traditional clustering algorithms, it has two advantages: determining the centers of clusters according to the decision graphs directly and being insensitive to noises. The SL0 algorithm a sparse recovery algorithm, was used to reconstruct the sources. Then the frequency of each mode was identified from the sources in time-frequency domain. The effectiveness of the proposed method was validated via adopting a six degree-of-freedom vibration system as a simulation example.
The sparse component analysis is an efficient approach to handle the underdetermined blind source separation, which contains two steps: calculating the mixing matrix and second, reconstructing the sources. In the paper, the modal shapes were calculated by using the Density Peaks Clustering Algorithm to deal with the cases that the number of sources cannot be known a priori and high order modes are overlapped with each other. Compared to the traditional clustering algorithms, it has two advantages: determining the centers of clusters according to the decision graphs directly and being insensitive to noises. The SL0 algorithm a sparse recovery algorithm, was used to reconstruct the sources. Then the frequency of each mode was identified from the sources in time-frequency domain. The effectiveness of the proposed method was validated via adopting a six degree-of-freedom vibration system as a simulation example.
引文
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[2] KERSCHEN G,PONCELET F,GOLINVAL J,et al.Physical interpretation of independent component analysis in structural dynamics[J].Mechanical Systems and Signal Processing,2007,21(4):1561-1575.
[3] ZHOU W,CHELIDZE D.Blind source separation based vibration mode identification[J].Mechanical Systems and Signal Processing,2007,21(8):3072-3087.
[4] PONCELET F,KERSCHEN G,GOLINVAL J,et al.Output-only modal analysis using blind source separation techniques[J].Mechanical Systems and Signal Processing,2007,21(6):2335-2358.
[5] 付志超,程伟,徐成.基于R-SOBI的结构模态参数辨识方法[J].振动与冲击,2010,29(1):108-111.FU Zhichao,CHENG Wei,XU Cheng.Modal parameter identification via robust second-order blind identification method[J].Journal of Vibration and Shock,2010,29(1):108-111.
[6] 张晓丹,姚谦峰.基于盲源分离的结构模态参数识别[J].振动与冲击,2010,29(3):150-153.ZHANG Xiaodan,YAO Qianfeng.Method of modal parameters identification based on blind sources separation[J].Journal of Vibration and Shock,2010,29(3):150-153.
[7] 姚谦峰,张晓丹.二阶统计量盲辨识在模态参数识别中的应用[J].工程力学,2011,28(10):72-77.YAO Qianfeng,ZHANG Xiaodan.Application of second-order staistics blind identification on identifying modal parameters[J].Engineering Mechanics,2011,28(10):72-77.
[8] GEORGIEV P,THEIS F J,CICHOCKI A,et al.Sparse component analysis and blind source separation of underdetermined mixtures[J].IEEE Transactions on Neural Networks,2005,16(4):992-996.
[9] YANG Y,NAGARAJAIAH S.Time-frequency blind source separation using independent component analysis for output-only modal identification of highly damped structures[J].Journal of Structural Engineering,2013,139(10):1780-1793.
[10] YU K,YANG K,BAI Y,et al.Estimation of modal parameters using the sparse component analysis based underdetermined blind source separation[J].Mechanical Systems and Signal Processing,2014,45(2):302-316.
[11] BOYD S,VANDENBERGHE L.Convex optimization[M].7th ed.NewYork:Cambridge University Press,2009.
[12] MOHIMANI H,BABAIEZADEH M,JUTTEN C,et al.A fast approach for overcomplete sparse decomposition based on smoothed l0-norm[J].IEEE Transactions on Signal Processing,2009,57(1):289-301.
[13] RODRIGUEZ A,LAIO A.Clustering by fast search and find of density peaks[J].Science,2014,344(6191):1492-1496.
[14] AMINI F,HEDAYATI Y.Underdetermined blind modal identification of structures by earthquake and ambient vibration measurements via sparse component analysis[J].Journal of Sound and Vibration,2016,366:117-132.
[15] REJU V G ?,KOH S N,SOOn I Y.An algorithm for mixing matrix estimation in instantaneous blind source separation[J].Signal Processing,2009,89:1762-1773.
[16] CHEN S S,DONOHO D L,SAUNDERS M A,et al.Atomic decomposition by basis pursuit[J].SIAM Journal on Scientific Computing,1998,20(1):33-61.
[17] XU Rui,WUNSCH D C,et al.Survey of clustering algorithms[J].Neural Networks,IEEE Transactions on,2005,16(3):645-678.
[18] JOHNSON E A,LAM H F,KATAFYGIOTIS L S,et al.Phase I IASC-ASCE structural health monitoring benchmark problem using simulated data[J].Journal of Engineering Mechanics,2004,130(1):3-15.