基于小波多分辨率分析的时变结构参数识别研究

PHYSICAL PARAMETER IDENTIFICATION OF TIME-VARYING STRUCTURE BASED ON WAVELET MULTIRESOLUTION ANALYSIS

提出一种小波多分辨率分析的最优尺度选择方法,并将其应用于结构时变物理参数的识别。首先,从函数空间剖分的角度引入WMRA对时变参数进行多分辨率近似展开,将振动微分方程转化成多元线性回归方程,根据时变参数的频率范围及采样频率、线性方程组的个数等确定分解层数取值范围;其次,利用赤池信息准则(AIC)寻求最优分解尺度,为增强数据的稳定性,采用正交最小二乘算法(OLS)代替传统最小二乘算法(LS)对模型中小波系数进行估计并重构时变参数;最后,分别以突变和连续变化的两种时变参数的5层剪切框架模型进行数值模拟。分析结果表明:在预先确立的分解尺度范围内,采用无噪声干扰的响应信号进行识别时,识别精度随着分解尺度的增加而增加;采用噪声干扰的测量信号进行识别时,识别精度与分解尺度的增加无必然联系;通过选择适当的分解尺度,能够准确识别时变参数、提高方法的计算效率并保证很好的抗噪性能。

An optimal scale selection technique of wavelet multiresolution analysis is proposed, and applied to the identification of time-varying physical parameters. First, time-varying parameters were expressed approximately using wavelet multi-resolution analysis from the perspective of the function space subdivision, and the vibration differential equation can be transformed into a linear regression equation, and the decomposition layers scope was set for every time-varying parameter according to the initial information including the range of frequencies, sampling frequency and the number of linear equations. Then, the optimal decomposition scale was chosen using Akaike information criterion（AIC）. In order to enhance the stability of data, the orthogonal least squares algorithm（OLS） was used to estimate the wavelet coefficient instead of the least squares algorithm（LS）, and unknown time-varying parameters were reconstructed. Finally, five shear-beam frame models are simulated with two kinds of time-varying parameters cases（abruptly, smoothly）. Numerical results show that： in the scope of the decomposition scale preset, identification accuracy increases with decomposition scale when response contains noise, while identification accuracy and the increament of decomposition scale have no obvious connection under the condition that the response data contain noise; appropriate decomposition scale has a great influence on the identification accuracy; and optimal decomposition scale selection can identify the time-varying parameters accurately and improve the computational efficiency and anti-noise ability.