基于小波多分辨率分析的结构时变参数识别

Time-varying parameter identification of structure using wavelet multiresolution analysis

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 time-varying stiffness and damping were expanded into multi--scales using wavelet muiltresolution analysis, and then the time-varying parameters were estimated using only approximate component, so that a time-varying parameter identification was converted into a time-invariant wavelet coefficient estimation problem. A optimization method based on Akaike information criterion（AIC） was introduced to select the decomposition levels of parameters. The Tikhonov regularization method was used to estimate the least square solutions of the system, so that the wavelet coefficients were solved and the time-varying parameters could be identified. To validate the effectiveness of the meth- od, a numerical simulation of a three-story shear frame structure with time-varying stiffness and damping was presented. The results show that the identification result of time-varying stiffness is better than that of damping, and the anti-noise performs better than the damping.