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Accelerating spectral digital image correlation computation with Taylor series image reconstruction

利用泰勒级数加速图像重建过程的频域数字图像相关方法

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Abstract

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.

摘要

本文介绍了一种基于泰勒级数的图像重建加速算法, 用于频域数字图像相关方法(SDIC)中对目标图像的重建. 泰勒级数图像重 建方法取代了之前的直接傅里叶变换(DFT)图像重建方法, 后者在对目标图像的重建过程中消耗了大量的计算时间. 泰勒级数中偏导 数的计算过程依托于傅里叶变换的理论原理, 通过对整个图像进行快速傅里叶变换(FFT)计算得到. 为了验证泰勒级数展开的不同阶 数对精度和效率的影响, 我们采用了三阶和四阶泰勒级数图像重建方法对模拟实验进行了分析, 并与DFT图像重建方法进行了比较. 由于这些改进, 使用三阶和四阶泰勒级数的图像重建方法在计算效率方面与DFT方法相比分别提高了57和46倍. 在分析精度方面, 在 应变范围为0–0.1且不添加图像噪声的情况下, 所提方法的精度随着扩展阶数的增加而提高. 当展开为四阶时, 其分析精度超过了DFT 图像重建方法. 此外, 当对模拟图像分别单独施加不同程度的高斯噪声时, 三阶和四阶泰勒级数展开方法的精度皆优于DFT方法. 最后, 我们给出了单轴拉伸条件下存在双侧裂纹的硅橡试样的分析实验结果.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12272145 and 11972013), the Ministry of Science and Technology of China (Grant No. 2018YFF01014200), and Hubei Provincial Natural Science Foundation of China (Grant No. 2022CFB288).

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Authors and Affiliations

  1. Department of Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Shihao Han  (韩世豪), Yuming He  (何玉明), Yiyu Hu  (胡轶宇) & Jian Lei  (雷剑)

  2. Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, Wuhan, 430074, China

    Shihao Han  (韩世豪), Yuming He  (何玉明), Yiyu Hu  (胡轶宇) & Jian Lei  (雷剑)

  3. Wuhan Sinorock Technology Co., Ltd, Wuhan, 430074, China

    Yongbo Yang  (杨永波)

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  1. Shihao Han  (韩世豪)
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  2. Yuming He  (何玉明)
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  3. Yiyu Hu  (胡轶宇)
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  4. Jian Lei  (雷剑)
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Contributions

Author contributions Yuming He and Shihao Han designed the research. Yuming He, Shihao Han, and Jian Lei wrote the first draft of the manuscript. Shihao Han and Yiyu Hu set up the experimental device and processed the experiment data. Jian Lei and Yiyu Hu helped organize the manuscript. Yongbo Yang participated in experimental design and manuscript revision. Yuming He, Shihao Han, Jian Lei, Yiyu Hu, and Yongbo Yang revised and edited the final version.

Corresponding author

Correspondence to Yuming He  (何玉明).

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Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Han, S., He, Y., Hu, Y. et al. Accelerating spectral digital image correlation computation with Taylor series image reconstruction. Acta Mech. Sin. 40, 423464 (2024). https://doi.org/10.1007/s10409-024-23464-x

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