Errors In Digital Image Correlation Research Articles

Conditional diffusion model-based generation of speckle patterns for digital image correlation

Generating speckle images is crucial for calibrating errors in digital image correlation (DIC) algorithms, alleviating the scarcity of training data for deep learning-based DIC algorithms, and even for the broader application of digital speckle methods. Traditional methods for speckle image synthesis struggle to accurately replicate the brightness variations in the foreground and background of realistic speckle images, and these methods come with high computational costs. Additionally, there needs to be more scientific and systematic evaluation methods for the quality of generated DIC speckle images. Our study presents a high-fidelity method for generating DIC speckle images with cracks based on a conditional diffusion model. We established evaluation metrics for generated DIC speckle images based on multiscale spatial and spectrum domains. We verified them on an open-source dataset of DIC speckle images depicting cracks in stone masonry walls. The conditional diffusion model excels at forward tasks (DIC crack image segmentation) and inverse tasks (DIC speckle image generation), with particular strength in the latter. The proposed spatial and multiscale spectrum domain metrics allow for the comprehensive and accurate evaluation of the alignment between the synthetic and natural speckle images. The conditional diffusion model for DIC speckle image generation and evaluation proposed in this paper has the potential to enhance further the accuracy and robustness of DIC technology in experimental mechanics and engineering applications.

Optimization of speckle pattern based on integer programming method

The performance of digital image correlation (DIC) method heavily depends on the quality of the speckle pattern. Extensive studies have been conducted to evaluate the speckle pattern, in order to reduce the errors of DIC. It is generally understood that the sum of square of subset intensity gradients (SSSIG) is the most relevant metric to the accuracy of the DIC; and the higher SSSIG indicates the better quality of the speckle pattern. However, there are few works on the optimization of the speckle pattern. In this work, we propose an integer programming method (IPM) to obtain the subset having the highest SSSIG. The speckle pattern derived from the proposed IPM has a relatively high SSSIG and has a strong anti-noise capability. The regular patterns (e.g. checkerboard-type) can also be avoided by the proposed method. Both the simulation and experiment have been conducted to validate the effectiveness of the proposed method. The simulation results show that the standard deviation (STD) of the displacements obtained by using the proposed speckle pattern in this study is reduced by 25.2% and 10.7%, respectively, comparing with the results obtained by the conventional random speckle pattern and the optimized speckle pattern in our earlier work. In addition, the experimental results from a tensile testing also agreed to the results from the simulation.

Improving DIC Accuracy in Experimental Setups

Digital image correlation (DIC) is a common software tool to measure displacement and strain fields on the surface of a specimen during mechanical testing. Due to its low requirements on the experimental setup and the simple usability it is widely spread in the community of applied mechanics. Nevertheless, the real noise of the method often stays uninvestigated. Therefore, this work shows different approaches to measure errors in DIC. The present contribution proves lighting as the main error source and it shows that a series of static images allows to estimate the error level of the DIC before performing the experiment. To give a proof of concept of the improved DIC setup, three‐point bending tests on single struts of aluminum foam are performed and evaluated.

Measurement Affecting Errors in Digital Image Correlation

Optical full-field measurement methods such as Digital Image Correlation (DIC) are increasingly used in the area of experimental mechanics. The reliability for each measurement technique depends on the knowledge of its uncertainty and the sources of errors of the results. The aim of this work is to systemize the sources of errors related to digital image correlation (DIC) technique applied to strain measurements. The paper is concluded by some suggestions proposed in order to minimize the errors.

Displacement Measurement Errors in Digital Image Correlation Due to Displacement Mapping Function

In the classic subset-based local digital image correlation (DIC) technique, the displacement measurement errors due to the displacement mapping function have been an important factor to improve the measurement accuracy. In general, the first-order displacement mapping function is broadly used. But, in the real experiments, the order of the deformation of the test sample is higher than that of the used displacement mapping function. So the errors due to the undermatched displacement mapping functions are existent. Although the random errors due to the overmatched shape function have been studied, the root-mean square errors (RMSEs) due to the matched or mismatched displacement mapping function are not studied. In this paper, the RMSEs of the measured displacements due to the matched or mismatched displacement mapping function are investigated experimentally by employing the simulated and real experimental speckle patterns. Moreover, the relationships between the RMSE and the subset size or the image noise are thoroughly examined. Finally, the practical implementation of DIC is recommended in terms of the subset size and the image noise.

Spatial uncertainty of measurement errors in digital image correlation

Digital image correlation is a widely used optical metrology for shape, motion, and deformation measurement. Although a number of studies have been carried out on the measurement errors of digital image correlation, the spatial uncertainty of the measurement errors, which stems from the randomness of speckle patterns, is seldom researched. In this work, a theoretical model is built for the spatial uncertainty of measurement errors. Analytical formulae for the spatial variances of both the mean bias error and the standard deviation error are derived. The influences of subset size, speckle coverage, and speckle radius on the spatial uncertainty are investigated. Numerical simulations demonstrate the correctness of the proposed model.

Shortcut in DIC error assessment induced by image interpolation used for subpixel shifting

In order to characterize errors of Digital Image Correlation (DIC) algorithms, sets of virtual images are often generated from a reference image by in-plane sub-pixel translations. This leads to the determination of the well-known S-shaped bias error curves and their corresponding random error curves. As images are usually shifted by using interpolation schemes similar to those used in DIC algorithms, the question of the possible bias in the quantification of measurement uncertainties of DIC softwares is raised and constitutes the main problematic of this paper. In this collaborative work, synthetic numerically shifted images are built from two methods: one based on interpolations of the reference image and the other based on the transformation of an analytic texture function. Images are analyzed using an in-house subset-based DIC software and results are compared and discussed. The effect of image noise is also highlighted. The main result is that the a priori choices to numerically shift the reference image modify DIC results and may lead to wrong conclusions in terms of DIC error assessment.

Random Errors in Digital Image Correlation Due to Matched or Overmatched Shape Functions

The random errors of subset-based digital image correlation due to the use of matched or overmatched shape functions are investigated. Governing formulations that can quantitatively predict these random errors are derived. Theoretical results reveal that all these random errors are in linear proportion to the noise level of the speckle images and inverse proportion to the sum of square of subset intensity gradients of the interrogated subsets. However, for matched or overmatched cases, zero-order and first-order shape functions give rise to the same magnitude of random errors, while the random errors induced by second-order shape functions are approximately twice that resulted from the regularly used first-order shape functions. The correctness of the derived theoretical formulations is verified using numerical tests, and also shows good accordance with previously reported experimental results.

The errors in digital image correlation due to overmatched shape functions

In subset-based digital image correlation (DIC), a proper shape function must be chosen to approximate the underlying displacement field of the target subsets to ensure an accurate subset matching. Shape functions with varying orders of Taylor’s expansions (e.g. zero-, first- and second-order) have been proposed. However, since the actual deformation occurring in the deformed subsets cannot be known a priori in most practical measurements, problems of mismatch (undermatched or overmatched) inevitably arise, which lead to additional errors in the measurement displacements. Although systematic errors due to undermatched shape functions have been thoroughly studied, the displacement errors associated with overmatched shape functions are still not sufficiently clear to us. In this paper, the systematic and random errors caused by the use of overmatched shape functions are first examined using numerical translation tests with precisely controlled subpixel motions. The results reveal that overmatched shape functions will not introduce additional systematic error but can induce increased random error, while the latter is negligibly small when a larger subset is used. Thus, it can be made explicit that second-order shape functions, capable of depicting more complex local deformation, can be used for practical DIC applications as a default, because this effectively eliminates the possible systematic error associated with the use of first-order shape functions, while the possibly increased random errors are small enough if using a relatively larger subset. Two sets of images with inhomogeneous deformation are also used to verify the accuracy of DIC measurements using second-order shape functions.

Error Estimation of DIC for Heterogeneous Strain States

Digital image correlation (DIC) involves certain errors during correlation, which are highly influenced by factors, e.g. image qualities, DIC parameters, and furthermore, degrees of deformation or strain states. In this contribution, attention is paid to the influence of strain states on the uncertainty of DIC, including the magnitude and the heterogeneity of the strains. A series of 2D-DIC numerical experiments are carried out on tensile specimens associated with finite element analysis (FEA). The specimens are made of 3 materials, i.e. steel DC06, steel DX54D+Z, and aluminium alloy Al6016, and cut into 3 different geometries, i.e. standard and 2 complex designs. Initial images were taken from these real specimens, which were all painted manually with random speckle patterns. Deformed images were obtained by imposing FE displacement fields on these undeformed initial images. Consequently, the errors source from imaging system are avoided, and only intrinsic errors of DIC itself are taken into account. The hardening behaviours of those materials in 3 different orientations were introduced to FEA for simulation, namely rolling direction (RD), transverse direction (TD) and 45o w.r.t. RD (45o). In FEA, homogeneous and heterogeneous strain states are achieved through applying uniaxial tension on two ends of the standard and complex specimens, respectively. The strain states are characterized by different material properties and geometries of specimens. DIC calculation are performed at various load steps to investigate the influence of the magnitude of the strain. Errors of the fields are compared among the different specimens to study the influence of the heterogeneity. In this contribution, the qualities of the speckle patterns are considered, since different patterns are applied to each experiment.

Experimental and Numerical Methods for Exact Subpixel Shifting

An approach to quantifying the errors in digital image correlation (DIC) is presented using experimentally produced images. The challenge arises in creating exact subpixel shifted images in an experiment. This was accomplished via numerical binning of an ultra-high resolution image. The shifted images are then used for a preliminary analysis of 2D correlation software uncertainty and investigation of speckle pattern quality. Because it is often necessary to use numerically shifted images, for uncertainty quantification for instance, the optimum method of Fourier shifting is also presented.

Assessment of measuring errors in DIC using deformation fields generated by plastic FEA

In this article, systematic errors that arise from different implementations of digital image correlation (DIC) techniques are analyzed. In particular, we investigate the influence of the adopted correlation function, the interpolation order, the shape function and the subset size on the derived displacements. These errors are estimated using numerically deformed images that were obtained by imposing finite element (FE) displacement fields on an undeformed image yielding plastic deformation of the specimen. This FE procedure simulates realistic experimental heterogeneous deformations at various load steps. It is shown that DIC is able to reproduce these displacements up to a satisfactory level if conscious choices in the above-mentioned implementations are made.

Systematic Errors in Digital Image Correlation Due to Undermatched Subset Shape Functions

Systematic Errors in Digital Image Correlation Due to Undermatched Subset Shape Functions

Systematic errors in digital image correlation due to undermatched subset shape functions

Digital image correlation techniques are commonly used to measure specimen displacements by finding correspondences between an image of the specimen in an undeformed or reference configuration and a second image under load. To establish correspondences between the two images, numerical techniques are used to locate an initially square image subset in a reference image within an image taken under load. During this process, shape functions of varying order can be applied to the initially square subset. Zero order shape functions permit the subset to translate rigidly, while first-order shape functions represent an affine transform of the subset that permits a combination of translation, rotation, shear and normal strains. In this article, the systematic errors that arise from the use of undermatched shape function, i.e., shape functions of lower order than the actual displacement field, are analyzed. It is shown that, under certain conditions, the shape functions used can be approximated by a Savitzky-Golay low-pass filter applied to the displacement functions, permitting a convenient error analysis. Furthermore, this analysis is not limited to the displacements, but naturally extends to the higher-order terms included in the shape functions. This permits a direct analysis of the systematic strain errors associated with an undermatched shape function. Detailed numerical studies are presented for the case of a second-order displacement field and first- and second-order shape functions. Finally, the relation of this work to previously published studies is discussed.

Systematic errors in digital image correlation caused by intensity interpolation

Recently, digital image correlation as a tool for surface defor- mation measurements has found widespread use and acceptance in the field of experimental mechanics. The method is known to reconstruct displacements with subpixel accuracy that depends on various factors such as image quality, noise, and the correlation algorithm chosen. How- ever, the systematic errors of the method have not been studied in detail. We address the systematic errors of the iterative spatial domain cross- correlation algorithm caused by gray-value interpolation. We investigate the position-dependent bias in a numerical study and show that it can lead to apparent strains of the order of 40% of the actual strain level. Furthermore, we present methods to reduce this bias to acceptable lev- els. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)00911-9)