2 L. Bang-Jian et al. In this paper, a novel method to reduce error will be proposed which is different from existing solutions which focus on random error and based on image pre-filtering. The new strategy is developed from the system error reduction perspective to improve the measurement accuracy. Due to the fact that systematic error is related with interpolation, noise, shape function, correlation criterion and so on, a few effective methods to reduce the systematic error are studied. In this paper, a strategy will be put forward based on the shape feature of systematic errors in translation measurement using DIC. To sum up, the improvement of the translation or displacement measurement accuracy plays an important role in practical applications, especially in motion and dimension measurement. The quasi odd function feature of the system error in DIC will be exhibited by simulation experiments. Subsequently the strategy will be proposed based on the quasi odd function feature. And the system error reduction will be derived mathematically in detail. Finally, the open access speckle image data will be applied to verify the effectiveness of the developed strategy. 1.2 Algorithm 1.2.1 Quasi Odd Function Feature of DIC System Error In this part, the open access speckle images from DIC Challenge Datasets (https://sem.org/dic-challenge/) are applied to implement the experiment which can show the quasi odd function feature of the system error. In detail, the reference speckle image is selected from the DIC Challenge 2D Datasets. Subsequently by translating, one deformed speckle image set is built. The Fourier Shift theorem [1, 15] is used to translate the reference speckle image to form the deformed set. The displacements are from 0.5 to 0.5 pixels and the displacement interval is 0.1 pixels. The subset based local DIC algorithm with first order shape function and bi-cubic interpolation is used to calculate the displacements. And the subset size is set as 25 25 pixels and the area of interest (AOI) is 100 100 pixels. And the mean bias error is used to quantify the system error. In addition, 2 2, 4 4, 6 6, 8 8 and 10 10 kernel based bi-cubic interpolations are used to demonstrate the quasi odd function feature too. As showed in Fig. 1.1, the quasi odd function feature of DIC system error for different interpolations is evident. 1.2.2 Strategy On the basis of the quasi odd function feature of DIC system error, a system error reduction strategy is developed. As displayed in Fig. 1.1, the system errors of the symmetric displacements are opposite numbers to each other. So the system error of the displacement can be reduced or removed by the system error of the symmetric displacement. In the proposed Fig. 1.1 The quasi odd function feature of system error induced by different bi-cubic interpolation methods in digital image correlation (DIC)
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