Vibration mode identification method for structures using image correlation and compressed sensing

Abstract

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.