MODAL PARAMETER IDENTIFICATION OF COVARIANCE-BASED STOCHASTIC SUBSPACE IDENTIFICATION BASED ON WELCH METHOD
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摘要: 对工程结构进行环境激励下的模态参数识别具有重要意义, 而随机子空间法作为适合环境激励下模态参数识别的时域方法, 由于噪声和复杂激励的原因, 会产生虚假模态、真实模态遗漏、系统自动定阶难和计算效率等问题, 这些问题阻碍了该方法在实际工程中的广泛应用. 本文提出了基于Welch法的随机子空间方法, 通过Welch法对振动响应在频域进行去噪、降低环境激励和其他不确定性因素影响的处理, 把结构固有模态从噪声和激励频率中突显出来, 形成富含更多结构模态的Toeplitz矩阵, 然后进行奇异值分解和状态矩阵计算, 最后进行特征值分析. 为了实现自动定阶, 对不同奇异值分量构建的状态矩阵得到的特征参数, 进行模糊C均值聚类分析和模态的平均相位偏移分析, 剔除虚假模态, 实现结构模态参数的自动识别. 并把本文所提出方法应用于一座大跨悬索桥的实测加速度响应分析, 和一座七十层的高层建筑的加速度响应分析, 跟频域分解法、传统随机子空间法和基于相关分析的随机子空间法的计算结果进行了比较, 发现基于Welch方法的随机子空间法相比于传统随机子空间法和基于相关分析的随机子空间法, 在避免模态遗漏和计算效率方面有显著提高, 而相对于频域分解法则在自动识别和剔除虚假模态方面有明显优势.Abstract: It is of great significance to identify the modal parameters of engineering structures under environmental excitations. However, the stochastic subspace identification method (SSI), as a time-domain method suitable for the identification of modal parameters under environmental excitations, will produce false modes, loss of real modes, computational efficiency, problem in automatic determination of the system order and other problems due to noise and complex excitations. These problems limit the wide application of this method in practical engineering. In this paper, a stochastic subspace identification method based on the Welch method is proposed. The Welch method is used to reduce the effect of noise, environmental excitations and other uncertainties on vibration response in the frequency domain. It aims to highlight the inherent structural modes from the noise and excitation frequencies. Then, a Toeplitz matrix which contains more structural modes is constructed, and the singular value decomposition of the matrix is performed. Finally, the discrete state matrix is calculated and the eigenvalues are analyzed. In order to determine the modal orders automatically and eliminate the false modes, fuzzy C-means clustering analysis (FCM) and modal mean phase deviation (MPD) analysis are performed on the characteristic parameters obtained from the discrete state matrix constructed by different singular value components. The method proposed in this paper is applied to the measured acceleration response analysis of a long-span suspension bridge and the acceleration response analysis of a 70-story high-rise building. The results are compared with those of frequency-domain decomposition method, traditional stochastic subspace identification method and stochastic subspace identification method based on correlation analysis to verify the effectiveness of the proposed method. It is found that compared with the traditional SSI and the SSI based on correlation analysis, SSI based on Welch method has significant improvement in avoiding modal loss and computing efficiency, and has obvious advantages in automatically identifying and eliminating false modes compared with the frequency domain decomposition method.
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图 1 基于Welch法的随机子空间法的流程图
Figure 1. Flow of stochastic subspace identification based on Welch method
图 4 频域分解法FDD、传统SSI、基于相关分析的SSI和基于Welch法的SSI的某大跨悬索桥的频率识别
Figure 4. Frequency identification of a long-span suspension bridge by FDD, traditional SSI, SSI based on correlation analysis and SSI based on Welch method
图 5 对各聚类所对应的振型进行MPD分析得到的MPD分布图
Figure 5. the distribution of MPD obtained by MPD analysis of vibration modes corresponding to each cluster
图 6 使用基于Welch法的SSI和FDD法得到的悬索桥的三阶振型分量对比
Figure 6. Comparison of three orders mode shape components of suspension bridges obtained by using SSI based on Welch method and FDD
图 8 某大厦的第68层处测点的加速度响应
Figure 8. Acceleration response of a certain measuring point in a high-rise building
表 1 大跨悬索桥的频率识别结果(Hz)
Table 1. The identified frequency results of long-span suspension bridge (Hz)
Mode No. FDD Traditional
SSISSI based on
correlationSSI based on
Welch method1 0.1343 0.1348 2 0.1678 0.1708 3 0.2289 0.2362 0.2344 4 0.2747 5 0.3662 0.3666 0.3688 6 0.4608 0.4579 7 0.5646 0.5624 0.5645 0.5618 8 0.6775 9 0.7935 0.7895 0.7948 10 0.9155 0.91 0.9137 11 1.041 1.038 1.038 12 1.12 1.125 1.118 13 1.288 1.281 1.286 1.354 14 1.419 1.418 1.414 15 1.541 1.549 1.541 16 1.672 1.697 1.668 17 1.785 1.778 1.792 1.79 18 1.904 1.906 1.906 19 2.028 1.988 1.985 
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表 2 某大厦的频率识别结果(Hz)
Table 2. The identified frequency results of a building (Hz)
Mode No. FDD Traditional SSI SSI based on
correlationSSI based on
Welch method1 0.174 0.1721 0.1727 2 0.383 0.3795 0.3813 0.385 3 0.6744 0.6723 0.6727 4 0.7309 0.7309 0.7304 0.7302 5 0.9933 0.9948 0.9946 6 1.291 1.286 1.289 7 1.408 1.41 1.408 8 1.465 1.466 1.467 9 1.605 1.584 1.605 1.605 10 1.785 1.788 11 1.962 1.959 1.968 12 2.118 2.139 13 2.284 2.308 2.281 2.279 14 2.493 2.5 2.496 2.495 15 2.8 2.799 16 3.157 3.152 17 3.365 3.372 3.374 18 3.621 3.632 19 4.881 4.893
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