The Virtual Point Transformation (VPT) makes it possible to experimentally identify the full DoF FRF matrix by projecting the measured displacements onto the Interface Deformation Modes (IDMs). The VP FRFs were already successfully used in Frequency-Based Substructuring (FBS); however, the VPT is susceptible to deviations in the impact location and orientation, as well as to deviations in the sensor’s sensitivity and positioning. Uncertainties associated with the sensors can be decreased by using the expanded VPT. This expanded VPT allows the projection of a directly measured rotational response onto the Interface Deformation Modes (IDMs). The consistency of the transformation is achieved by using a rotational weighting matrix, which is formulated to minimize the norm of the overall displacements due to the rotational residual at the VP for each rotational sensor. The rotational response is measured using a direct piezoelectric rotational accelerometer. In this paper the application of the expanded virtual point transformation and the possible advantages are explored on a complex and engineering-like test structure. Both transformations, standard and expanded, are performed for each VP to enable a side-by-side comparison.

中文翻译：

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扩展虚拟点变换在复杂测试结构上的性能

虚拟点变换 (VPT) 可以通过将测量的位移投影到界面变形模式 (IDM) 上来通过实验识别完整的 DoF FRF 矩阵。VP FRF 已成功用于基于频率的子结构化 (FBS)；然而，VPT 容易受到冲击位置和方向的偏差以及传感器灵敏度和定位的偏差的影响。通过使用扩展的 VPT，可以减少与传感器相关的不确定性。这种扩展的 VPT 允许将直接测量的旋转响应投影到界面变形模式 (IDM) 上。变换的一致性是通过使用一个旋转加权矩阵来实现的，由于每个旋转传感器的 VP 处的旋转残差，它被公式化以最小化整体位移的范数。使用直接压电旋转加速度计测量旋转响应。在本文中，扩展的虚拟点变换的应用和可能的优势在复杂的和类似工程的测试结构上进行了探索。为每个 VP 执行标准和扩展两种转换，以实现并排比较。