Strain field denoising for digital image correlation using a regularized cost-function

In digital image correlation (DIC), the widely used forward-additive Newton–Raphson (FA-NR) algorithm and the recently introduced equivalent but more efficient inverse-compositional Gauss–Newton (IC-GN) algorithm are capable of providing both displacements and displacement gradients (strains) for each calculation point. However, the obtained displacement gradients are seriously corrupted by various noises, and for this reason these directly computed strains are usually considered as useless information and therefore discarded. To extract strain distributions more accurately, much research efforts have been dedicated to how to smooth and differentiate the noisy displacement fields using appropriate numerical approaches. In this contribution, contrary to these existing strain estimation approaches, a novel and alternative strain estimation approach, based on denoising the noisy strain fields obtained by FA-NR or IC-GN algorithm using a regularized cost-function, is proposed. The effectiveness and practicality of the proposed strain estimation technique is carefully examined using both computer-simulated images with imposed homogeneous and inhomogeneous deformation, and experimentally obtained images. Experimental results reveal that the strains obtained by the proposed method are comparable to those determined by post-processing of the displacement fields using conventional pointwise least squares strain estimation approach.     

SU-8光刻胶应变分布光学全场检测方法

由于SU-8光刻胶的内应力将会影响高深宽比结构的全金属光栅的制作质量,本文针对近年来SU-8光刻胶应力测量困难的情况,提出了一种基于激光剪切散斑干涉技术的SU-8光刻胶应变分布测量的新方法。该方法通过对被测胶体加载前后两幅干涉图像的处理,直接得到被测胶体结构的全场应变分布情况,由胶体的应变变形数据即可反映出内应力的变化和分布趋势。同时使用ANSYS有限元分析软件对同一被测胶体进行应变仿真模拟研究,获得胶体结构的变形场仿真数据。组建了实验系统,进行了实验验证,结果表明:实际测量变形量约为1.189μm,仿真的最大变形量为1.088μm,测量误差在允许范围内,且测量的形变趋势与仿真模拟结果相一致,表明激光剪切散斑干涉技术可应用于SU-8光刻胶的应变分布全场无损检测。     

Path-independent digital image correlation with high accuracy,speed and robustness

The initial guess transferring mechanism is widely used in iterative DIC algorithms and leads to path-dependence. Using the known deformation at a processed point to estimate the initial guess at its neighboring points could save considerable computation time, and a cogitatively-selected processing path contributes to the improved robustness. In this work, our experimental study demonstrates that a path-independent DIC method is capable to achieve high accuracy, efficiency and robustness in full-field measurement of deformation, by combining an inverse compositional Gauss–Newton (IC-GN) algorithm for sub-pixel registration with a fast Fourier transform-based cross correlation (FFT-CC) algorithm to estimate the initial guess. In the proposed DIC method, the determination of initial guess accelerated by well developed software library can be a negligible burden of computation. The path-independence also endows the DIC method with the ability to handle the images containing large discontinuity of deformation without manual intervention. Furthermore, the possible performance of the proposed path-independent DIC method on parallel computing device is estimated, which shows the feasibility of the development of real-time DIC with high-accuracy.     

Single-step scanner-based digital image correlation (SB-DIC) method for large deformation mapping in rubber

The incremental digital image correlation (DIC) method has been applied in the past to determine strain in large deformation materials like rubber. This method is, however, prone to cumulative errors since the total displacement is determined by combining the displacements in numerous stages of the deformation. In this work, a method of mapping large strains in rubber using DIC in a single-step without the need for a series of deformation images is proposed. The reference subsets were deformed using deformation factors obtained from the fitted mean stress-axial stretch ratio curve obtained experimentally and the theoretical Poisson function. The deformed reference subsets were then correlated with the deformed image after loading. The recently developed scanner-based digital image correlation (SB-DIC) method was applied on dumbbell rubber specimens to obtain the in-plane displacement fields up to 350% axial strain. Comparison of the mean axial strains determined from the single-step SB-DIC method with those from the incremental SB-DIC method showed an average difference of 4.7%. Two rectangular rubber specimens containing circular and square holes were deformed and analysed using the proposed method. The resultant strain maps from the single-step SB-DIC method were compared with the results of finite element modeling (FEM). The comparison shows that the proposed single-step SB-DIC method can be used to map the strain distribution accurately in large deformation materials like rubber at much shorter time compared to the incremental DIC method.     

Initial guess by improved population-based intelligent algorithms for large inter-frame deformation measurement using digital image correlation

Digital image correlation (DIC) has received a widespread research and application in experimental mechanics. In DIC, the performance of subpixel registration algorithm (e.g., Newton-Raphson method, quasi-Newton method) relies heavily on the initial guess of deformation. In the case of small inter-frame deformation, the initial guess could be found by simple search scheme, the coarse-fine search for instance. While for large inter-frame deformation, it is difficult for simple search scheme to robustly estimate displacement parameters and deformation parameters simultaneously with low computational cost. In this paper, we proposed three improving strategies, i.e. Q-stage evolutionary strategy (T), parameter control strategy (C) and space expanding strategy (E), and then combined them into three population-based intelligent algorithms (PIAs), i.e. genetic algorithm (GA), differential evolution (DE) and particle swarm optimization (PSO), and finally derived eighteen different algorithms to calculate the initial guess for qN. The eighteen algorithms were compared in three sets of experiments including large rigid body translation, finite uniaxial strain and large rigid body rotation, and the results showed the effectiveness of proposed improving strategies. Among all compared algorithms, DE-TCE is the best which is robust, convenient and efficient for large inter-frame deformation measurement.     

A fast digital image correlation method for deformation measurement

Fast and high-accuracy deformation analysis using digital image correlation (DIC) has been increasingly important and highly demanded in recent years. In literature, the DIC method using the Newton-Rapshon (NR) algorithm has been considered as a gold standard for accurate sub-pixel displacement tracking, as it is insensitive to the relative deformation and rotation of the target subset and thus provides highest sub-pixel registration accuracy and widest applicability. A significant drawback of conventional NR-algorithm-based DIC method, however, is its extremely huge computational expense. In this paper, a fast DIC method is proposed deformation measurement by effectively eliminating the repeating redundant calculations involved in the conventional NR-algorithm-based DIC method. Specifically, a reliability-guided displacement scanning strategy is employed to avoid time-consuming integer-pixel displacement searching for each calculation point, and a pre-computed global interpolation coefficient look-up table is utilized to entirely eliminate repetitive interpolation calculation at sub-pixel locations. With these two approaches, the proposed fast DIC method substantially increases the calculation efficiency of the traditional NR-algorithm-based DIC method. The performance of proposed fast DIC method is carefully tested on real experimental images using various calculation parameters. Results reveal that the computational speed of the present fast DIC is about 120-200 times faster than that of the traditional method, without any loss of its measurement accuracy     

A novel speckle pattern—Adaptive digital image correlation approach with robust strain calculation

Digital image correlation (DIC) has seen widespread acceptance and usage as a non-contact method for the determination of full-field displacements and strains in experimental mechanics. The advances of imaging hardware in the last decades led to high resolution and speed cameras being more affordable than in the past making large amounts of data image available for typical DIC experimental scenarios. The work presented in this paper is aimed at maximizing both the accuracy and speed of DIC methods when employed with such images. A low-level framework for speckle image partitioning which replaces regularly shaped blocks with image-adaptive cells in the displacement calculation is introduced. The Newton-Raphson DIC method is modified to use the image pixels of the cells and to perform adaptive regularization to increase the spatial consistency of the displacements. Furthermore, a novel robust framework for strain calculation based also on the Newton-Raphson algorithm is introduced. The proposed methods are evaluated in five experimental scenarios, out of which four use numerically deformed images and one uses real experimental data. Results indicate that, as the desired strain density increases, significant computational gains can be obtained while maintaining or improving accuracy and rigid-body rotation sensitivity.     

Determination of displacement distributions in bolted steel tension elements using digital image techniques

Digital imaging methods have found a great interest in various engineering fields to study stress-deformation characteristics of materials. Recent enhancements in visual instrumentation with the availability of cost-effective hardware and software products make the digital imaging techniques a viable tool to replace direct strain or displacement measurement methods in engineering applications. In this study, deformation characteristics of bolted steel connections are investigated by calculating in-plane displacement distributions using digital image correlation method (DIC). Validation of the method is presented by comparing the strains measured in standard tension specimens using electrical resistance strain gages and the DIC method. Finite element analysis of the connection specimen is also performed to compare the in-plane displacement distributions calculated from both methods. Results from the validation process indicate that the strains obtained from the DIC method compare well with the results of strain gages. The findings also indicate that the displacement distributions calculated from the finite element method may differ from those of the DIC method in terms of distribution pattern, and the location and magnitude of the extreme values of displacements. It is suggested that the proposed method can be used to determine the in-plane displacement distributions for the bolted connections, hence to evaluate their deformation characteristics under loading.     

Experimental study on the micromechanical behavior of a PBX simulant using SEM and digital image correlation method

The micro-scale mechanical behavior of a polymer-bonded explosive (PBX) simulant was experimentally studied using a scanning electron microscope (SEM) imaging system and digital image correlation (DIC) method. The semi-circular bend (SCB) test was chosen for the study. During the testing, a series of SEM images of the specimen was acquired in situ. The natural micro-structural features of the specimen were used as random speckle pattern for DIC analysis. The displacement and strain fields at the area of interest were obtained by DIC. The deformation and damage of PBX were analyzed. Heterogeneous strain fields demonstrated the damage evolution underneath the specimen surface and predicted possible micro-crack growth. Based on the contour plots of the correlation coefficient, the formation and extension of microscopic cracks were quantitatively analyzed.     

Processing discontinuous displacement fields by a spatio-temporal derivative technique

In this paper, a digital image correlation (DIC) method coupling cross-correlation with spatio-temporal differential techniques was proposed for assessing discontinuous displacement fields. The accuracy and robustness of the algorithm was assessed on a set of numerical tests by processing computer generated speckled-pattern images. Fracture mechanical tests in mode I were considered, in which both in-plane and out-of-plane rigid-body movements were taken into account. The ability for recovering the analytical asymptotic displacement field in mode I was analysed, and stress intensity factor, crack opening displacement and crack tip location were used as quantitative parameters for validation purposes. Throughout these tests, the results obtained with the proposed method were systematically compared to the ones from Aramis DIC-2D commercial code. Globally, the results computed from both methods are in good agreement with reference values. However, due to the high spatial resolution (point-wise characteristic), a better matching of the displacements in the neighbour of discontinuities could be obtained by the proposed method.     

Accurate kinematic measurement at interfaces between dissimilar materials using conforming finite-element-based digital image correlation

Digital image correlation (DIC) is now an extensively applied full-field measurement technique with subpixel accuracy. A systematic drawback of this technique, however, is the smoothening of the kinematic field (e.g., displacement and strains) across interfaces between dissimilar materials, where the deformation gradient is known to be large. This can become an issue when a high level of accuracy is needed, for example, in the interfacial region of composites or joints. In this work, we described the application of global conforming finite-element-based DIC technique to obtain precise kinematic fields at interfaces between dissimilar materials. Speckle images from both numerical and actual experiments processed by the described global DIC technique better captured sharp strain gradient at the interface than local subset-based DIC.     

Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements

Digital image correlation (DIC) method using iterative least squares algorithm (ILS) for displacement field measurement and pointwise least squares algorithm (PLS) for strain field measurement is proposed in this paper. A more general and practical intensity change model is employed with consideration of the linear intensity change of the deformed image, followed by an iterative least squares algorithm for calculating displacement field with sub-pixel accuracy. The concept of correlation function is not used in the ILS method, even though we prove that the algorithm is actually equivalent to the optimization of the sum of squared difference correlation function using improved Newton–Raphson method. Besides, different from the conventional strain estimation approaches based on smoothing the displacement fields first and followed by differentiation of the smoothed displacement fields, a simple yet effective PLS algorithm is proposed for extracting strain fields from the computed displacement fields. The effectiveness and accuracy of the proposed techniques is verified through numerical simulation experiments. A practical application of the algorithms to residual plastic deformation field measurement of GH4169 alloy subjected to tensile fatigue is also presented.     

Whole-field thickness strain measurement using multiple camera digital image correlation system

Three Dimensional digital image correlation(3D-DIC) has been widely used by industry, especially for strain measurement. The traditional 3D-DIC system can accurately obtain the whole-field 3D deformation. However, the conventional 3D-DIC system can only acquire the displacement field on a single surface, thus lacking information in the depth direction. Therefore, the strain in the thickness direction cannot be measured. In recent years, multiple camera DIC (multi-camera DIC) systems have become a new research topic, which provides much more measurement possibility compared to the conventional 3D-DIC system. In this paper, a multi-camera DIC system used to measure the whole-field thickness strain is introduced in detail. Four cameras are used in the system. two of them are placed at the front side of the object, and the other two cameras are placed at the back side. Each pair of cameras constitutes a sub stereo-vision system and measures the whole-field 3D deformation on one side of the object. A special calibration plate is used to calibrate the system, and the information from these two subsystems is linked by the calibration result. Whole-field thickness strain can be measured using the information obtained from both sides of the object. Additionally, the major and minor strain on the object surface are obtained simultaneously, and a whole-field quasi 3D strain history is acquired. The theory derivation for the system, experimental process, and application of determining the thinning strain limit based on the obtained whole-field thickness strain history are introduced in detail.     

单周期条纹双四步相移投影仪的标定方法

针对投影仪标定方法中存在畸变及倾斜投影引起条纹周期、条纹级数变化的问题,提出一种单周期条纹双四步相移投影仪的标定方法.设计生成横向和纵向各两组单周期条纹图像,经投影仪投影到带有圆形标识的标定板上,相机同步采集标定板图像,叠加由双四步相移获得的两幅相位主值图,对叠加相位主值图相位展开,利用展开的绝对相位值计算投影仪像素坐标值,最终将投影仪标定转换为成熟的相机标定.实验结果表明:仿真投影仪标定实验准确度的最大重投影误差约为0.4pixel,均方根误差为0.132 96pixel;实际投影仪标定实验准确度的最大反投影误差约为0.46pixel,均方根误差为0.143 12pixel;实验结果与仿真结果的最大反投影误差相差15%,均方根误差相差7.6%.与现有的采用三频相位展开进行投影仪标定的方法相比,投影光栅图像数可减少8幅.该方法改善了现有投影仪标定方法的不足,标定准确度和标定效率均得到提高.     

Large deformation measurement scheme for 3D digital image correlation method

Difficulties often arise for digital image correlation (DIC) technique when serious de-correlation occurs between the reference image and the deformed image due to large deformation. An updating reference image scheme could be employed to deal with large deformation situation, however that will introduce accumulated errors. A large deformation measurement scheme, combining improved coarse search method and updating reference image scheme, is proposed in this paper. For a series of deformation images, the correlation calculation begins with a seed point and spreads out. An improved coarse search method is developed to calculate the initial correlation parameters for the seed point, which guarantees that the correlation calculation can be carried out successfully even in large deformation situation. Only for extremely large deformation, the reference image is updated. Using this method, not only extremely large deformation can be measured successfully but also the accumulated error could be controlled. A polymer material tensile test and a foam compression test are used to verify the proposed scheme. Experimental results show that up to 450% tensile deformation and 83% compression deformation can be measured successfully.     

Strain field estimation based on digital image correlation and radial basis function

Two methods based on digital image correlation (DIC) and radial basis function (RBF) were proposed to obtain the accurate strain field in this paper. One is a combined method. RBF was applied to remove the noisy discrete displacement data first. After that, the strain was computed by a local least-squares algorithm. The other is a partial derivative of RBF (PD-RBF) based strain estimation method which integrated denoising with differential process. The effectiveness and accuracy of the proposed methods were verified through two numerical simulation experiments. A practical application on the normal strain measurement of an aluminum alloy beam under symmetric four-point bending via an outer loading frame was also presented. The measurement results are in good accordance with the data obtained by strain gauges. Furthermore, a shape parameter selection method based on rate of convergence was suggested. The new method simplifies the choice of the good shape parameter.     

Improve accuracy of laser beam width measurement using a genetic algorithm

Beam width measurements of laser beams based on CCD by the second moment method as proposed by International Standardization Organization, are excessively sensitive to the noise far from light beam center. A novel method of noise elimination based on the analysis of the influence from CCD noise on laser beam width measurement result is proposed. The appropriate integral region could be obtained by genetic algorithm to improve accuracy of laser beam width measurement. The experimental results show that method could tolerate heavy CCD noise, and define the corresponding integral region according to requested precision.     

面内位移测量的基于梯度的数字图像相关方法

将整像素位移搜索和基于微区统计性质的亚像素位移梯度算法相结合的数字图像相关方法具有计算简单、求解效率高等优点。该方法的基本假设是变形前后的子区做刚体平移,这则与有位移梯度存在的实际情况相矛盾。首先分析了该基本假设的理论误差,在基于梯度的数字图像相关方法中,得出变形子区做刚体平移的假设和在Newton-Rapshon方法中子区均匀变形的假设所获得的变形子区中心位移在理论上为相同的结论。然后用四组实验来验证该方法在实际实验条件下的计算精度和稳定性,并在铝板试件的单向拉伸实验中,将该方法与N-R方法在有应变存在情况下的计算结果作比较,结果表明该方法计算的位移和理论位移符合得很好,但其计算速度和效率要远优越于N-R方法。     

Single-lens 3D digital image correlation system based on a bilateral telecentric lens and a bi-prism: Systematic error analysis and correction

Recently, we proposed a single-lens 3D digital image correlation (3D DIC) method and established a measurement system on the basis of a bilateral telecentric lens (BTL) and a bi-prism. This system can retrieve the 3D morphology of a target and measure its deformation using a single BTL with relatively high accuracy. Nevertheless, the system still suffers from systematic errors caused by manufacturing deficiency of the bi-prism and distortion of the BTL. In this study, in-depth evaluations of these errors and their effects on the measurement results are performed experimentally. The bi-prism deficiency and the BTL distortion are characterized by two in-plane rotation angles and several distortion coefficients, respectively. These values are obtained from a calibration process using a chessboard placed into the field of view of the system; this process is conducted after the measurement of tested specimen. A modified mathematical model is proposed, which takes these systematic errors into account and corrects them during 3D reconstruction. Experiments on retrieving the 3D positions of the chessboard grid corners and the morphology of a ceramic plate specimen are performed. The results of the experiments reveal that ignoring the bi-prism deficiency will induce attitude error to the retrieved morphology, and the BTL distortion can lead to its pseudo out-of-plane deformation. Correcting these problems can further improve the measurement accuracy of the bi-prism-based single-lens 3D DIC system.     

数字图像相关中基于位移场局部最小二乘拟合的全场应变测量

为了从含噪声的位移场中计算得到可靠的应变场,提出一种基于位移场局部最小二乘拟合的全场应变求解方法。介绍了数字图像相关方法的原理,阐述了基于位移场局部最小二乘拟合的全场应变求解方法,并讨论了计算区域边界、孔洞及裂纹附近区域等情况下的应变计算。对均匀变形和中心带圆孔的薄铝板拉伸实验的计算结果表明,该方法能有效地从原始位移场数据中提取全场应变信息。在均匀变形情况下应选择大的应变计算窗口,计算结果更逼近真值;在非均匀变形情况下,如果位移场中包含较强的噪声,则应选择较大的应变计算窗口,而位移场精度很高时可选择更小的应变计算窗口。