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利用小波多分辨率分析将结构的时变参数在多尺度上展开,截断高频细节成分,仅由展开的低频成分来近似描述时变参数(阻尼和刚度),将结构时变参数识别问题转化为时不变小波系数估计问题.基于Akaike信息准则(AIC)来优化确定各时变参数的小波分解层数.分解的小波系数采用最小二乘求解得到,为减小方程的病态问题,对模型进行Tikhonov正则化,然后重构识别出结构的时变参数.建立了一个三层剪切框架时变结构模型验证该方法的有效性.识别结果表明,该方法可以有效识别结构时变参数,时变刚度比时变阻尼识别效果更好,抗噪性更高.
The wavelet multi-resolution analysis is used to expand the time-varying parameters of the structure at multiple scales. The high-frequency detail components are truncated. The time-varying parameters (damping and stiffness) are approximated only by the unfolded low-frequency components, and the structural time-varying parameter identification problem is transformed. Time-invariant wavelet coefficient estimation problem. Based on Akaike Information Criterion (AIC), the time-varying parameter’s wavelet decomposition layer number is optimized and determined. The decomposed wavelet coefficients are obtained by least-squares solution. To reduce the ill-posed problem of the equation, the model is The Tikhonov regularization is performed, and then the time-varying parameters of the structure are reconstructed. A three-layer shear-frame time-varying structural model is established to verify the effectiveness of the method. The recognition results show that this method can effectively identify the structural time-varying parameters. The variable stiffness is better than the time-varying damping and the noise immunity is higher.