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Operational modal analysis using SVD of power spectral density transmissibility matrices

机译：基于SVD的功率谱密度透射矩阵的运作模式分析

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摘要

This paper proposes the singular value decomposition of power spectrum density transmissibility matrices with different references, (PSDTM-SVD), as an identification method of natural frequencies and mode shapes of a dynamic system subjected to excitations under operational conditions. At the system poles, the rows of the proposed transmissibility matrix converge to the same ratio of amplitudes of vibration modes. As a result, the matrices are linearly dependent on the columns, and their singular values converge to zero. Singular values are used to determine the natural frequencies, and the first left singular vectors are used to estimate mode shapes. A numerical example of the finite element model of a beam subjected to colored noise excitation is analyzed to illustrate the accuracy of the proposed method. Results of the PSDTM-SVD method in the numerical example are compared with obtained using frequency domain decomposition (FDD) and power spectrum density transmissibility (PSDT). It is demonstrated that the proposed method does not depend on the excitation characteristics contrary to the FDD method that assumes white noise excitation, and further reduces the risk to identify extra non-physical poles in comparison to the PSDT method. Furthermore, a case study is performed using data from an operational vibration test of a bridge with a simply supported beam system. The real application of a full-sized bridge has shown that the proposed PSDTM-SVD method is able to identify the operational modal parameter. Operational modal parameters identified by the PSDTM-SVD in the real application agree well those identified by the FDD and PSDT methods.
机译：本文提出了具有不同参考的功率谱密度透射率矩阵的奇异值分解（PSDTM-SVD），作为在运行条件下受激励的动力系统固有频率和振型的识别方法。在系统极点，建议的透射率矩阵的行收敛到相同的振动模式振幅比。结果，矩阵线性依赖于列，并且它们的奇异值收敛到零。奇异值用于确定固有频率，而第一个左奇异矢量用于估计众数形状。分析了有色噪声激励下光束的有限元模型的数值示例，以说明所提方法的准确性。将数值示例中的PSDTM-SVD方法的结果与使用频域分解（FDD）和功率谱密度透射率（PSDT）获得的结果进行比较。结果表明，与假设白噪声激励的FDD方法相反，所提出的方法不依赖于激励特性，与PSDT方法相比，该方法进一步降低了识别额外的非物理极点的风险。此外，使用来自具有简单支撑梁系统的桥梁的运行振动测试中的数据进行案例研究。全尺寸桥梁的实际应用表明，所提出的PSDTM-SVD方法能够识别运行模态参数。在实际应用中，由PSDTM-SVD识别的运行模态参数与FDD和PSDT方法识别的模态参数非常吻合。

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