基于加速度反演频域动载荷的一种正则化途径

发布时间：2018-07-06 14:23

本文选题：动态载荷 + 频响函数　；参考：《湖南大学学报(自然科学版)》2017年02期

【摘要】：基于加速度频响函数矩阵反演频域动载荷是病态逆问题,反求的结果精度差,对数据的小扰动敏感,基于Tikhonov正则化方法,提出一种反演途径,将测点响应与待求激励进行归一化变换,在此基础上引入变换后的频响函数矩阵和正则化泛函进行求解,应用广义交叉验证准则选取最优正则化参数.考虑简支矩形薄板上的4个动载荷的识别问题,分析激励点和响应测点的不同位置以及动载荷大小之间相差程度不同的4个算例,将本文方法与不采用归一化变换的正则化求解结果进行2种相对误差的均方根比较.结果表明,利用归一化变换可提高动载荷反演精度,增强正则化方法的抗噪能力,当测点之间的响应以及各动载荷大小相差较大时,明显改善了识别精度.
[Abstract]:The inversion of frequency domain dynamic load based on acceleration frequency response function matrix is a ill-conditioned inverse problem. The inverse result is poor in accuracy and sensitive to the small disturbance of data. Based on Tikhonov regularization method, an inversion approach is proposed. Based on the normalized transformation of the measured point response and the excitation to be solved, the transformed frequency response function matrix and regularization functional are introduced, and the optimal regularization parameters are selected by using the generalized cross validation criterion. Considering the identification of four dynamic loads on simply supported rectangular thin plates, four examples are analyzed for different positions of excitation points and response measuring points, as well as the difference between dynamic loads and the magnitude of dynamic loads. The results of this method are compared with the results of regularization without normalized transformation for two kinds of root-mean-square errors. The results show that the normalized transformation can improve the accuracy of dynamic load inversion and enhance the anti-noise ability of the regularization method.
【作者单位】：湖南大学机械与运载工程学院;北京强度与环境研究所;
【基金】：湖南省自然科学基金资助项目(11JJ3001)~~
【分类号】：O347.1

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