Full-field measurements of high-frequency micro-vibration under operational conditions using sub-Nyquist-rate 3D-DIC and compressed sensing with order analysis

High-speed imaging is essential for high-frequency vibration measurement techniques that utilize images, such as digital image correlation (DIC). However, it poses challenges, including reduced displacement resolution due to decreased image resolution, increased measurement and calculation costs, and greater data volume. A previous method used compressed sensing to reconstruct time information from images captured with a high-resolution, low-speed camera, allowing high-frequency vibration measurements. However, this method was limited to steady vibrations since waveforms were reconstructed using the Fourier basis. In this study, order analysis is introduced into compressed sensing to measure operational vibrations, including rotation speed fluctuations, such as those in automobile engines. An out-of-plane vibration experiment on an aluminum plate confirmed the method’s accuracy in identifying mode shapes and displacement spectra of operational vibrations. The proposed method reconstructed vibrations (amplitude: several μm to several hundred μm, frequency: 33.3–133.2 Hz) using images captured at 10 fps. The modal assurance criterion (MAC) indicated 0.98 accuracy compared with finite element analysis. The mean squared error below 1 % compared to the frequency spectrum obtained with a laser Doppler vibrometer. Applied to automobile engine vibrations (amplitudes of a few μm), the method achieved errors under 2 % over a 1225 mm × 960 mm field of view. However, error increased for vibrations below the DIC displacement resolution. This method shows promise for analyzing vibrations in rotational machinery, such as engines and motors, through the full-field measurement of high-speed operational vibrations. In addition, the developed compressed sensing with order basis is expected to contribute to the advancement of the recovering missing signals and data compression.