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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 method for wavelet multi-resolution analysis is proposed and applied to the identification of structural time-varying physical parameters. Firstly, WMRA is introduced into the multi-resolution approximation of the time-varying parameters from the perspective of function space subdivision. The vibration differential equations are converted into multiple linear regression equations. According to the frequency range and sampling frequency of time-varying parameters, the number of linear equations Determine the value range of the decomposition layer; Second, use the Akaike Information Criterion (AIC) to find the optimal decomposition scale. To enhance the stability of the data, use Orthogonal Least Squares (OLS) instead of the traditional Least Squares (LS) algorithm. The wavelet coefficients in the model are estimated and the time-varying parameters are reconstructed. Finally, the 5-layer shear frame model with two time-varying parameters of mutation and continuous change is used for numerical simulation. The analysis results show that the recognition accuracy increases with the increase of the decomposition scale when the noise-free response signal is used to identify within the range of the pre-established decomposition scale; when the noise is used to identify the measurement signal, the recognition accuracy and decomposition scale The increase is not necessarily linked; by selecting appropriate decomposition scales, time-varying parameters can be accurately identified, the computational efficiency of the method can be improved, and good anti-noise performance can be ensured.