Simultaneous estimation of both the location and force history of an impact applied on a lattice truss core sandwich panel is inversely carried out utilizing velocity signals collected by means of a scanning laser Doppler vibrometer. The algorithm assumes that several impact forces are exerted concurrently on a number of specified locations on a panel, provided that the magnitude of all impact forces but one is actually equal to zero. This condition equates to a scenario where an impact occurs at only one location. The purpose is therefore to detect the actual impact location among all potential locations, together with its force history, through minimizing error functions. Two algorithms, the one-to-one (even-determined) approach and the superposition approach, are considered. The one-to-one approach solves the reconstruction problem independently for each pair of impact and measurement points. However, in the superposition approach, the impact forces at all potential locations are concurrently reconstructed through a single matrix equation. It is shown that the one-to-one approach fails to detect the true impact location while the superposition approach recognizes the actual impact location based on some qualitative evaluating criteria. Adopting the superposition approach, for a problem with four possible impact locations, two scenarios one with four and one with 12 measurement points, are investigated. It is observed that the additional measurement points do not necessarily enhance the efficiency and accuracy of the proposed method. It is found that different arrangements of measuring points lead to identification of the location and the magnitude of the impact force, though the use of four evenly distributed measurement points seems to be most effective in simultaneous identification of the location and magnitude of the impact force. Further, a quantitative index based on the concept of similarity search for time-series using wavelet transformation is proposed and it is demonstrated that the index can successfully identify the true impact force location in a fully automated way.

中文翻译：

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复合板上冲击位置和力大小的同时识别

利用扫描激光多普勒测振仪收集的速度信号，同时估计施加在格构桁架芯夹芯板上的冲击的位置和力历史。该算法假设多个冲击力同时施加在面板上的多个指定位置上，前提是所有冲击力的大小实际上都为零。这种情况相当于仅在一个位置发生影响的情况。因此，目的是通过最小化误差函数来检测所有潜在位置中的实际撞击位置及其力历史。考虑了两种算法，一对一（偶数确定）方法和叠加方法。一对一的方法为每对冲击点和测量点独立解决重建问题。然而，在叠加方法中，所有潜在位置的冲击力通过单个矩阵方程同时重建。结果表明，一对一的方法无法检测到真实的撞击位置，而叠加法则基于一些定性的评估标准来识别实际的撞击位置。采用叠加法，针对有四个可能的撞击位置的问题，研究了一种有四个测量点和一种有12个测量点的两种情况。据观察，额外的测量点并不一定会提高所提出方法的效率和准确性。研究发现，测量点的不同布置导致了冲击力的位置和大小的识别，尽管使用四个均匀分布的测量点似乎在同时识别冲击力的位置和大小方面最有效。此外，提出了一种基于小波变换时间序列相似性搜索概念的定量指标，并证明该指标可以以全自动方式成功识别真实冲击力位置。