Mode-shape magnification in high-speed camera measurements

If motion, identified using image-based methods, is too small to be seen with the naked eye, motion magnification can be used to help with the visualization. Established motion-magnification methods magnify (typically up to 1000 times) the band-passed content of the image data. Especially at higher frequencies, the amplitudes of measured displacements are often below the noise floor. In this research, a novel method for amplifying vibrations, based on experimental modal analysis (EMA), is introduced. The response of the examined structure to dynamic excitation is measured with a simplified, gradient-based, optical flow method and used to perform a hybrid modal analysis in conjunction with a reference accelerometer response measurement. Such a hybrid approach can: (a) identify structural dynamics significantly in the sub-pixel range, and (b) significantly below the image noise floor. The image of the vibrating structure is subdivided using a planar triangle mesh, which is then warped in accordance with the identified mode shape. A mesh-element-wise affine transformation is performed to obtain an image of the magnified mode shape. In the experimental part, the proposed method achieved magnification factors of approximately 40 thousand times, which is an order of magnitude deeper into noise than available before; additionally, the proposed approach is numerically significantly less demanding. The introduced mode-shape magnification presents an alternative to existing motion-magnification methods for applications where the harmonic displacement information is hidden by image noise.