Monitoring mechanical properties of structures such as bridges, buildings, or wind turbines, is important to detect early stage failures. Operational modal analysis (OMA) is a testing method to estimate these properties from vibration measurements. Taking advantage of works on motion estimation, several video modal analysis methods have emerged in the last decade.
Two approaches exist to estimate motion thanks to multi-scale pyramid decomposition of each frame: Wadhwa et al.  take the pyramid scales into account to estimate motion at each pixel, so that one single OMA is performed, whereas Yang et al.  determine the motion at a given scale.
Because no study compares phase-based motion estimation methods, we propose to assess their performances in  using synthetic videos that represent a vibrating vertical cantilever beam. We then compare estimated displacements to ground-truth ones. Videos are generated with different motion amplitudes to study sub-pixel efficiency.
In this experiment, the input force f (N) is represented by a time and space Dirac function to simulate a hammer impact at the free end of the beam. Besides, we set the beam volume to 900 x 30 x 6 mm3, its mass to 1.413 kg, and its Young modulus E to 210.109 Pa. Frame definition is set to 720 x 40 px and since the beam covers 97% of the frame height, the pixel size is 1.289 mm.
For illustration purposes, synthetic videos of the cantilever beam for different motion amplitudes (from 0.04 N to 10.47 N) in GIF format can be downloaded here. The framerate has been set here to 100 fps (limited by the GIF file format specification) instead of 436 fps. To avoid interpolation artefacts when playing the videos, we recommend the ImageGlass software.
 N. Wadhwa, J. G. Chen, J. B. Sellon, D. Wei, M. Rubinstein, R. Ghaffari, D. M. Freeman, Oral Büyüköztürk, P. Wang, S. Sun, S. H. Kang, K. Bertoldi, F. Durand, and William T. Freeman, "Motion microscopy for visualizing and quantifying small motions," Proceedings of the National Academy of Sciences, vol. 114, no. 44, pp. 11639–11644, Oct. 2017. DOI: 10.1073/pnas.1703715114.
 Y. Yang, C. Dorn, T. Mancini, Z. Talken, G. Kenyon, C. Farrar, and D. Mascareñas, "Blind identification of full-field vibration modes from video measurements with phase-based video motion magnification," Mechanical Systems and Signal Processing, vol. 85, pp. 567–590, Feb. 2017. DOI: 10.1016/j.ymssp.2016.08.041.
 C. Marinel, B. Mathon, O. Losson, and L. Macaire, "Comparison of phase-based sub-pixel motion estimation methods," 2022 IEEE International Conference on Image Processing (ICIP), Oct. 2022. DOI: 10.1109/ICIP46576.2022.9897338