Accelerating spectral digital image correlation computation with Taylor series image reconstruction

• Published in: Acta mechanica Sinica 2024-06, Vol.40 (6), Article 423464
• Main Authors: Han, Shihao, He, Yuming, Hu, Yiyu, Lei, Jian, Yang, Yongbo
• Format: Article
• Language: English
• Subjects: Accuracy; Algorithms; Classical and Continuum Physics; Computational efficiency; Computational Intelligence; Computing time; Digital imaging; Engineering; Engineering Fluid Dynamics; Fast Fourier transformations; Fourier transforms; Image reconstruction; Random noise; Research Paper; Series expansion; Silicone rubber; Taylor series; Theoretical and Applied Mechanics
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-024-23464-x

In this paper, we introduce an accelerating algorithm based on the Taylor series for reconstructing target images in the spectral digital image correlation method (SDIC). The Taylor series image reconstruction method is employed instead of the previous direct Fourier transform (DFT) image reconstruction method, which consumes the majority of the computational time for target image reconstruction. The partial derivatives in the Taylor series are computed using the fast Fourier transform (FFT) of the entire image, following the principles of Fourier transform theory. To examine the impact of different orders of Taylor series expansion on accuracy and efficiency, we employ third- and fourth-order Taylor series image reconstruction methods and compare them with the DFT image reconstruction method through simulated experiments. As a result of these enhancements, the computational efficiency using the third- and fourth-order Taylor series improves by factors of 57 and 46, respectively, compared to the previous method. In terms of analysis accuracy, within a strain range of 0–0.1 and without the addition of image noise, the accuracy of the proposed method increases with higher expansion orders, surpassing that of the DFT image reconstruction method when the fourth order is utilized. However, when different levels of Gaussian noise are applied to simulated images individually, the accuracy of the third- or fourth-order Taylor series expansion method is superior to that of the DFT reconstruction method. Finally, we present the analyzed experimental results of a silicone rubber plate specimen with bilateral cracks under uniaxial tension.