Influence of the Analysis Window on the Metrological Performance of the Grid Method
This paper deals with the grid method in experimental mechanics. It is one of the full-field methods available for estimating in-plane displacement and strain components of a specimen submitted to a load producing slight local deformation. This method consists in, first, depositing a regular grid on the surface of a specimen, and, second, comparing images of the grid before and after deformation. A possibility is to perform windowed Fourier analysis to measure these deformations as changes of the local grid aspect. The aim of the present study is to investigate the choice of the analysis window and its influence on the metrological performances of the grid method. Two aspects are taken into account, namely the reduction of the harmonics of the grid line profile, which are not pure sine because of manufacturing constraints, and the transfer of the digital noise from the imaged grid to the mechanical measurements. A theoretical study and a numerical assessment are presented. In addition, the interested reader can find in this paper a calculation of the Wigner–Ville transform of a triangular function which, to the best of the present authors’ knowledge, is not available in the existing literature.
KeywordsImage-based contactless measurement Displacement and strain maps Grid method Windowed Fourier analysis Spatially correlated noise Derivative of a random process Wigner–Ville transform
This work is partially funded by GdR CNRS ISIS (Timex project).
- 1.Abrahamsen, P.: A review of Gaussian random fields and correlation functions. Technical report, Norwegian Computing Center, Oslo (1997)Google Scholar
- 7.Cohen, L.: Time-Frequency Analysis. Prentice-Hall, Upper Saddle River (1995)Google Scholar
- 12.Grédiac, M., Sur, F., Blaysat, B.: The grid method for in-plane displacement and strain measurement: a review and analysis. Strain (2016). To be publishedGoogle Scholar
- 19.JCGM member organizations: International vocabulary of metrology. Basic and General Concepts and Associated Terms (VIM) (2008)Google Scholar
- 23.Molimard, J., Surrel, Y.: Grid method, moiré and deflectometry. In: Grédiac, M., Hild, F. (eds.) Full-field Measurements and Identification in Solid Mechanics, pp. 61–89. Wiley, Hoboken (2012)Google Scholar
- 25.Murthagh, F., Starck, J., Bijaoui, A.: Image restoration with noise suppression using a multiresolution support. Astron. Astrophys. 112, 179–189 (1995)Google Scholar
- 26.Peevers, A.W.: A real time 3D signal analysis/synthesis tool based on the short time Fourier transform. Technical report, Department of Electrical Engineering, University of California, Berkeley (2004)Google Scholar
- 29.Reu, P.L., Quintana, E., Lon, K.: Using sampling moiré to extract displacement information from X-ray images of molten salt batteries. In: Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 3, pp. 331–336 (2014)Google Scholar
- 31.Sur, F., Blaysat, B., Grédiac, M.: Determining displacement and strain maps immune from aliasing effect with the grid method (2016). Submitted for publicationGoogle Scholar