All objects are subject to deformations of their shapes that correspond to their natural vibration modes. The analysis of these modes is extremely useful for structural design and structural health monitoring. Traditionally, expensive measurement equipment and many vibration sensors have been required to analyze vibration modes. Recently, a method that measures displacement from images (digital image correlation) has enabled the identification of vibration modes with a single camera. However, the identification of high-frequency vibration modes requires a high-speed camera, which increases costs and reduces spatial resolution. In this study, a low-cost and highly accurate method for identifying vibration modes and frequencies, randomized single-exposure sampling (RSES), was developed by applying compressed sensing to images captured with a strobe flash and a low-speed camera. This method extracts vibration modes using proper orthogonal decomposition and applies compressed sensing to the time function to recover high-speed vibrations from low-speed measurement results. The performance of RSES was evaluated by conducting vibration experiments on beams and comparing the results with the theoretical values using acceleration sensor measurements as boundary conditions. The results demonstrated that images captured at a shutter speed of 10 fps could measure the vibration modes and amplitudes of beams vibrating at a single frequency (ranging 170–3210 Hz). From 40 images, the amplitude of vibration could be measured with errors of less than 1 %, 2 %, and 26 % for vibrational frequencies of 170, 1130, and 3210 Hz, respectively. The larger error at 3210 Hz was attributed to the amplitude of vibration being only a few micrometers owing to the shaker limitations, a value close to the resolution of digital image correlation. This method can be used to accurately analyze structures that vibrate at high speeds, which is useful for vibration control design and other applications.

所有物体都会发生与其自然振动模式相对应的形状变形。这些模式的分析对于结构设计和结构健康监测非常有用。传统上，需要昂贵的测量设备和许多振动传感器来分析振动模式。最近，一种测量图像位移的方法（数字图像相关性）已经能够用单个相机识别振动模式。然而，高频振动模式的识别需要高速相机，这会增加成本并降低空间分辨率。在这项研究中，一种用于识别振动模式和频率的低成本且高精度的方法，随机单次曝光采样（RSES），是通过将压缩传感应用于闪光灯和低速相机拍摄的图像而开发的。该方法使用适当的正交分解提取振动模式，并将压缩传感应用于时间函数，以从低速测量结果中恢复高速振动。通过对梁进行振动实验并将结果与​​使用加速度传感器测量作为边界条件的理论值进行比较来评估 RSES 的性能。结果表明，以 10 fps 的快门速度拍摄的图像可以测量以单一频率（范围 170–3210 Hz）振动的光束的振动模式和振幅。从 40 张图像中，可以测量振动幅度，对于 170、1130 和 3210 Hz 的振动频率，误差小于 1%、2% 和 26%，分别。3210 Hz 处的较大误差归因于由于振动器的限制振动幅度仅为几微米，该值接近数字图像相关的分辨率。该方法可用于精确分析高速振动的结构，对于振动控制设计和其他应用非常有用。