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小波有限元以区间B样条小波尺度函数为插值函数构造小波有限元单元,并通过单元转换矩阵建立小波空间与物理空间各参数之间的关系。采用动态规划法与Tikhonov正则化法识别移动荷载,避免了直接处理反问题时的振荡与数值计算病态解等问题。算例采用所测得的部分离散点的动态响应数据为已知信息,验证了小波有限元的优越性及小波的多尺度特性,仿真结果表明,在相同条件下与传统有限元模型相比,小波有限元模型单元较少,识别精度较高;且可根据不同的识别精度要求自由选取所需的小波尺度。
The finite element of wavelet is used to construct the wavelet finite element unit by using the interval B-spline wavelet scaling function as the interpolation function. The relationship between the wavelet space and the parameters of the physical space is established through the unit transformation matrix. The dynamic programming method and the Tikhonov regularization method are used to identify the moving loads and avoid the problems of direct oscillation and numerical solution of the inverse problems when dealing with inverse problems. The example uses the measured dynamic response data of some discrete points as known information to verify the superiority of the wavelet finite element and the multi-scale characteristics of the wavelet. The simulation results show that under the same conditions, compared with the traditional finite element model, The wavelet finite element model has fewer elements and higher recognition accuracy, and can select the desired wavelet scale according to different recognition accuracy requirements.