Random Error in Strain Calculation using Regularized Polynomial Smoothing (RPS) and Point-wise Least Squares (PLS) in Digital Image Correlation

•The estimations of random error and under-matched error caused by two strain calculation methods (point-wise least squares (PLS) and regularized polynomial smoothing method (RPS)) are proposed, based on two assumptions on the noise error of calculated displacement.•For the typical kernel function o...

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Bibliographic Details
Published in:	Optics and lasers in engineering Vol. 142; p. 106590
Main Authors:	Li, Xin, Fang, Gang, Zhao, Jiaqing, Zhang, Zhengming, Sun, Libin, Wang, Haitao, Wu, Xinxin
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.07.2021
Subjects:	Digital image correlation Displacement smoothing Self-Adaptive Algorithm Strain random error Strain random error Digital image correlation Displacement smoothing Self-Adaptive Algorithm
ISSN:	0143-8166, 1873-0302
Online Access:	Get full text
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Summary:	•The estimations of random error and under-matched error caused by two strain calculation methods (point-wise least squares (PLS) and regularized polynomial smoothing method (RPS)) are proposed, based on two assumptions on the noise error of calculated displacement.•For the typical kernel function of 3rd order polynomial, a self-adaptive algorithm minimizing the total error is proposed to choose the optimal parameters.•The self-adaptive algorithm can give the optimal parameters in restoring the displacement and strain field, and obtain a more accurate result if the provided displacement field conforms strictly to assumptions. The strain error analysis is greatly concerned recently as digital image correlation (DIC) is used to measure the heterogeneous deformation. This paper focuses on the estimation of random error and under-matched error caused by two strain calculation methods, i.e. the point-wise least squares (PLS) and the regularized polynomial smoothing method (RPS). Two assumptions are put forward on the noise error of the calculated displacement that are: a) it is pure random error without bias and b) in each strain window, it is the independent Gaussian white noise with zero-mean. Based on the assumptions, the random error of displacement and strain is estimated, and the under-matched error of displacement and strain is theoretically analyzed by the aid of Laplacian operator. These two error solutions are verified by some stimulated experiments. Then for the typical kernel function of 3rd order polynomial, a self-adaptive algorithm minimizing the total error is proposed to choose the optimal parameters, i.e. window size and parameter λ. Experiments show that when the original displacement noise conforms to the assumptions strictly, 1) the estimated random error and under-matched error agrees very well with the experimental value, 2) the self-adaptive algorithm can give the optimal parameters in restoring the displacement and strain field, and 3) the estimation of random error and under-matched error is affected by DIC noise greatly, and it is better to use low-pass Gaussian filter before utilizing self-adaptive algorithm.
ISSN:	0143-8166 1873-0302
DOI:	10.1016/j.optlaseng.2021.106590