基于数据缩减的分频段小波模态参数快速识别

Sub-frequency band rapid modal identification using wavelet based on data reduction

针对利用小波进行模态参数识别效率较低的问题,提出了一种基于数据缩减的分频段小波模态参数快速识别算法。利用奇异值分解对协方差信号在保留数据信息量的情况下进行缩减以减少参与计算的数据量,对正功率谱密度矩阵的奇异值分解确定识别系统的模态阶数及相应的频率范围,利用小波变换对缩减后的数据进行各阶模态逐频段识别。相比原始算法,文中方法减少了小波分析的数据量并避免了一些无用频带的小波分解从而减少计算量。通过对一个3阶线性时不变系统以及一个大桥模型的参数识别验证了文中方法在保持识别精度的情况下大幅度地提升了计算效率。

In an attempt to overcome the low efficiency problem of model identification using wavelet transform,a rapid modal identification algorithm using wavelet based on data reduction is introduced.In the case of maintaining data signals the covariance signals are reduced by using singular value decomposition so as to diminish the amount of data which is involved in the analysis.The orders and the corresponding frequency range by singular value decomposition of the postive power spectrum matrix are determined,and then the modal parameters of each mode can be got by the continuous wavelet transform of the reduced signals according to the corresponding frequency range.Compared to the original algorithm,the method not only reduces the amount of data but also avoid some wavelet transform for useless frequency band.A numerical example on the parameter estimation of a linear time-invariant system of 3 degrees of freedom and one experimental example on the parameter estimation of a bridge model are presented to demonstrate that the method dramatically improves the compution efficiency in the case of maintaining identification accuracy.