基于低秩Hankel矩阵逼近的模态参数识别方法

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (20) : 57-62.

论文

基于低秩Hankel矩阵逼近的模态参数识别方法

包兴先，李昌良，刘志慧

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Modal parameters identification based on low rank approximation of a Hankel matrix

BAO Xing-xian，LI Chang-liang，LIU Zhi-hui

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摘要

针对测量结构输出响应信号所受噪声干扰问题，提出利用低秩Hankel矩阵逼近方法对响应信号降噪。该方法利用结构脉冲响应信号构建Hankel矩阵，对其进行奇异值分解后计算奇异值相对变化率确定模型阶次，通过迭代低秩逼近方法获得降噪信号后进行模态参数识别。用数值算例研究矩阵维数对降噪效果、计算效率影响，并用悬臂梁模型实验验证该方法的有效性。

Abstract

Measured output signals are inevitably contaminated with noise. A low rank approximation of a Hankel matrix method was proposed to remove noise from the measured data, and then modal parameters were estimated from the filtered data. In the method, a Hankel matrix was constructed based on the impulse response function and then the singular value decomposition (SVD) was used to obtain the relative change ratio of the decreasing singular values. Theoretically the maximum change ratio corresponds to the model order. An iterative low rank approximation method was applied to get the filtered signals. The effects of chosen size of a Hankel matrix on the performance of the noise reduction and computational time were investigated. The effectiveness of the proposed method was verified by using measured signals from model test of a cantilever beam.

导出引用

包兴先;李昌良;刘志慧. 基于低秩Hankel矩阵逼近的模态参数识别方法[J]. 振动与冲击, 2014, 33(20): 57-62

BAO Xing-xian;LI Chang-liang;LIU Zhi-hui. Modal parameters identification based on low rank approximation of a Hankel matrix[J]. Journal of Vibration and Shock, 2014, 33(20): 57-62