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A space-frequency multiplicative regularization for force reconstruction problems

机译：力重构问题的空频乘法正则化

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摘要

Dynamic forces reconstruction from vibration data is an ill-posed inverse problem. A standard approach to stabilize the reconstruction consists in using some prior information on the quantities to identify. This is generally done by including in the formulation of the inverse problem a regularization term as an additive or a multiplicative constraint. In the present article, a space-frequency multiplicative regularization is developed to identify mechanical forces acting on a structure. The proposed regularization strategy takes advantage of one's prior knowledge of the nature and the location of excitation sources, as well as that of their spectral contents. Furthermore, it has the merit to be free from the preliminary definition of any regularization parameter. The validity of the proposed regularization procedure is assessed numerically and experimentally. It is more particularly pointed out that properly exploiting the space-frequency characteristics of the excitation field to identify can improve the quality of the force reconstruction.
机译：根据振动数据重建动态力是一个不适定的逆问题。稳定重建的标准方法是使用有关数量的先验信息进行识别。通常通过在反问题的公式中包含正则项作为加法或乘法约束来完成。在本文中，开发了空频乘法正则化以识别作用在结构上的机械力。所提出的正则化策略利用了人们对激发源的性质和位置以及其光谱内容的先验知识。此外，它的优点是没有任何正则化参数的初步定义。提出的正则化程序的有效性通过数值和实验评估。尤其要指出的是，适当利用激发场的空间频率特性来识别可以提高力重建的质量。

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