Towards Criteria Characterizing the Metrological Performance of Full-field Measurement Techniques

Users of full-field measurement methods like Digital Image Correlation (DIC) often aim to perform measurements with the best trade-off between spatial resolution, bias and measurement resolution. Whenever two full-field methods are compared, it is essential that these criteria are taken into consideration. Recently a metrological efficiency indicator for full-field measurements has been proposed and discussed. This indicator combines measurement resolution and spatial resolution. It has been shown to be invariant to the subset size in the case of Local DIC. The goal of this article is to discuss a method, which determines both the spatial and the measurement resolutions for a given bias for two different DIC methods, in order to obtain the metrological efficiency indicator for each of these methods. The benefit of this indicator is that it does not depend on setting parameters such as the subset size, which are chosen by the user. As such, it can be considered as intrinsic to each technique, thus enabling fair comparison. Local DIC and triangular finite element based Global DIC will be the subject of this investigation. With this setting, their respective subset and triangular element sizes will be related to the spatial resolution of both methods for a given acceptable bias. By using the metrological efficiency indicator, the performance of the two methods will be compared and discussed to a new level of detail. Generally speaking, the indicator shows that the metrological performance of both methods is similar, confirming their popularity. However, it will be shown that, depending on the choice of what an acceptable bias is, one of the method may be preferred to another. The results show that for the specific DIC versions used in the study, for cases for which a significant bias is acceptable, Local DIC outperforms Global DIC, while the opposite is true in the case for which the bias requirements are more stringent. Finally, the quadratic versions of both DIC versions are shown to significantly outperform their respective linear versions.

     

Spatial DIC Errors due to Pattern-Induced Bias and Grey Level Discretization

Digital image correlation (DIC) is an optical metrology method widely used in experimental mechanics for full-field shape, displacement and strain measurements. The required strain resolution for engineering applications of interest mandates DIC to have a high image displacement matching accuracy, on the order of 1/100th of a pixel, which necessitates an understanding of DIC errors. In this paper, we examine two spatial bias terms that have been almost completely overlooked. They cause a persistent offset in the matching of image intensities and thus corrupt DIC results. We name them pattern-induced bias (PIB), and intensity discretization bias (IDB). We show that the PIB error occurs in the presence of an undermatched shape function and is primarily dictated by the underlying intensity pattern for a fixed displacement field and DIC settings. The IDB error is due to the quantization of the gray level intensity values in the digital camera. In this paper we demonstrate these errors and quantify their magnitudes both experimentally and with synthetic images.

     

Identification of the Out-of-Plane Shear Modulus of a 3D Woven Composite

This study deals with the identification of macroscopic elastic parameters of a layer-to-layer interlock woven composite from a full-field measurement. As this woven composite has a coarse microstructure, the characteristic length of the weaving is not small as compared to the specimen size. A procedure based on an inverse identification method and full-field digital image correlation kinematic measurement is proposed to exploit a three-point bending test on short coupons to characterize the out-of-plane shear modulus. Each step of the proposed procedure is presented, and their respective uncertainty is characterized with the help of numerical simulations. The shear modulus is identified with an accuracy of about 1.5 % and is 15 % lower than the estimate obtained through Iosipescu tests. The proposed procedure shows a correlation between the ideal mesh size and the weaving period. It also reveals that the actual boundary conditions deviate from the ideal ones and hence a special attention is paid to their optimization.     

In-situ mechanical properties identification of 3D particulate composites using the Virtual Fields Method

This paper presents an identification procedure based on the Virtual Fields Method (VFM) for identifying in situ mechanical properties of composite materials constitutive phases from 3D full-field measurements. The new procedure, called the Regularized Virtual Fields Method (RVFM), improves the accuracy of the VFM thanks to the imposition of mechanical constraints derived from an appropriate homogenization model. The developed algorithms were validated through virtual experiments on particulate composites. The robustness of both the VFM and the RVFM was assessed in the presence of noisy strain data for various microstructures. A study was also carried out to investigate the influence of the size of region of interests on the reliability of the identified parameters. Accordingly, the optimum size of region of interest was determined based on full-field measurement requirements and accuracy of the identified parameters. This study enables determining, a priori, the required magnification level of 3D images for composites of any mechanical and morphological characteristics.     

Color Stereo-Digital Image Correlation Method Using a Single 3CCD Color Camera

This paper presents a novel color stereo-digital image correlation (stereo-DIC) method using a single 3CCD color camera for full-field shape, motion, and deformation measurements without any sacrifice of the camera sensor spatial resolution. With the aid of a specially designed color separation device using a beam splitter and two optical bandpass filters, images of blue and red colors are simultaneously recorded by the 3CCD camera from two different optical paths. The blue and red channel sub-images extracted from the recorded color images can be analyzed using the regular stereo-DIC algorithm to obtain the full-field three dimensional (3D) information of a test object surface. The effectiveness and accuracy of the proposed technique are demonstrated by a series of real shape, in-plane and out-of-plane translation, and 3D deformation tests.     

使用单彩色相机的单相机三维数字图像相关方法

介绍了一种基于单个彩色相机的新型全靶面、单相机三维数字图像相关(3D-DIC)方法。借助于设计巧妙的颜色分光光路,被测物体表面图像可以通过两条不同的光路达到相机靶面,采集的标定靶和实验件表面的彩色图像可以分离得到蓝色和红色子图像。通过使用3D-DIC分析标定靶和实验件表面分离后的蓝色和红色子图像,可以获得物体表面的三维形貌和变形。形貌测量、面内和离面平移、以及静动态三维变形实验验证了该单彩色相机3D-DIC方法的有效性和测量精准度。由于可避免双相机同步,且能实现无分辨率损失的全靶面三维形貌和变形测量,本文方法在需要实现瞬态位移和变形测量的爆炸、冲击、振动等领域中具有广阔重要的应用前景。     

Full-Field High-Strain Gradient Evaluation from Wrapped ESPI Data Using Phasors

Electronic Speckle Pattern Interferometry (ESPI) is a sensitive optical method commonly used for making full-field measurements of surface displacements. It would be very desirable to be able to extend the technique also to determine surface strains. This would provide a full-field, non-contact strain measurement method that avoids the substantial installation burden of strain gauges. A mathematical approach is described where the ESPI data from an in-plane interferometer are numerically differentiated to determine surface strains. This is a challenging process because numerical differentiation is very sensitive to the presence of noise and ESPI data are inherently noisy. In addition, the phase information from ESPI data are wrapped modulo-2π. The resulting phase discontinuities make it difficult to use local averaging to smooth the data. A technique is described here where phasors are used to avoid the need for phase unwrapping. The effect of noise is reduced by a localized multiple smoothing technique that is effective in preserving spatial resolution, even near very high strain concentrations. Example measurements are shown and the effectiveness of the proposed method is illustrated.     

A novel architecture for a super-resolution PIV algorithm developed for the improvement of the resolution of large velocity gradient measurements

Three different particle image processing algorithms have been developed for the improvement of PIV velocity measurements characterized by large velocity gradients. The objectives of this study are to point out the limitations of the standard processing methods and to propose a complete algorithm to enhance the measurement accuracy. The heart of the PIV image processing is a direct cross-correlation calculation in order to obtain complete flexibility in the choice of the size and the shape of the interrogation window (IW). An iterative procedure is then applied for the reduction of the size of IW at each measurement location. This procedure allows taking into account the local particle concentration in the image. The results of this first iterative processing, applied to synthetic images, show both a significant improvement of measurement accuracy and an increase of the spatial resolution. Finally, a super-resolution algorithm is developed to further increase the spatial resolution of the measurement by determining the displacement of each particle. The computer time for a complete image processing is optimized by the introduction of original data storage in Binary Space Partitions trees. It is shown that measurement errors for large velocity gradient flows are similar to those obtained in simpler cases with uniform translation displacements. This last result validates the ability of the developed super-resolution algorithm for the aerodynamic characterization of large velocity gradient flows.     

Thermoelastic stress analysis under nonadiabatic conditions

Thermoelastic stress analysis is a full-field stress measurement technique complementary to local techniques like strain gages. Generally, the heat transfer inside the material is neglected with respect to the frequency of the cyclical loading. An adiabaticity criterion is established to assert this simplification as a function of the thermal diffusion length and the spatial stress gradients. Under nonadiabatic conditions, heat diffusion attenuates the spatial temperature gradients, which leads to an underestimation of stress concentrations. Analytical and numerical considerations allow for the quantification of the spatial resolution. Finally, several inverse techniques can restore the thermally attenuated contrasts.     

Measurement of Local Thermal Deformations in Heterogeneous Microstructures via SEM Imaging with Digital Image Correlation

It is challenging to measure accurately and with high spatial resolution the local thermal strains in heterogeneous microstructures due of the complex nature of the thermal deformations and local boundary conditions. In the enclosed study, a digital image correlation (DIC) based, thermal strain mapping technique is described that is able to probe thermal deformations with sub-micron spatial resolution and sub-nanometer displacement accuracy for both homogeneous and heterogeneous materials, including cross-sections of IC packages. The full-field thermal deformation maps of different materials within a nanostructured IC chip cross-section are established from room temperature up to 160 °C, uncovering the heterogeneous nature of the specimen while accurately measuring the highly non-uniform displacement and strain fields across the multiple material constituents. As described in this work, the DIC-enabled technique is capable of high resolution mapping of local thermo-mechanical deformations in heterogeneous materials, providing a methodology that can improve our understanding of complex material systems under controlled thermal-environmental conditions.     

Spatial resolution and noise considerations in determining scalar dissipation rate from passive scalar image data

The effects of photonic shot noise and finite spatial resolution on the scalar dissipation rate were investigated for the analytical profile of a passive scalar layer subjected to a compressive strain, and the results were applied to interpret measured data from spray mixing data from an internal combustion engine. A Monte Carlo approach was employed. The measured scalar dissipation rate is underestimated, and the layer width measured at 20% of the peak height is overestimated by the finite resolution. The ratio of the local scalar spread value to the noise level, the spread-noise ratio, was found to describe the noise effects, which principally results in an overestimation of the scalar dissipation rate, especially at high resolution levels. The Nyquist resolution provides a good compromise between the sampling bias at low resolution and the noise bias at high resolution. Top hat filtering the raw data prior to calculation of the scalar dissipation rate was found to, effectively, reduce spatial resolution, whereas median filtering preserved the resolution. Both filters had a comparable effect on noise reduction. The evaluation of experimental data showed that a significant fraction of data reside at low spread-noise ratio and are biased by noise. The peak scalar dissipation rate is, however, not biased by noise and a method of estimating spatial resolution based on the peak scalar dissipation rate is described.     

On the resolution limit of digital particle image velocimetry

This work analyzes the spatial resolution that can be achieved by digital particle image velocimetry (DPIV) as a function of the tracer particles and the imaging and recording system. As the in-plane resolution for window-correlation evaluation is related by the interrogation window size, it was assumed in the past that single-pixel ensemble-correlation increases the spatial resolution up to the pixel limit. However, it is shown that the determining factor limiting the resolution of single-pixel ensemble-correlation are the size of the particle images, which is dependent on the size of the particles, the magnification, the f-number of the imaging system, and the optical aberrations. Furthermore, since the minimum detectable particle image size is determined by the pixel size of the camera sensor in DPIV, this quantity is also considered in this analysis. It is shown that the optimal magnification that results in the best possible spatial resolution can be estimated from the particle size, the lens properties, and the pixel size of the camera. Thus, the information provided in this paper allows for the optimization of the camera and objective lens choices as well as the working distance for a given setup. Furthermore, the possibility of increasing the spatial resolution by means of particle tracking velocimetry (PTV) is discussed in detail. It is shown that this technique allows to increase the spatial resolution to the subpixel limit for averaged flow fields. In addition, PTV evaluation methods do not show bias errors that are typical for correlation-based approaches. Therefore, this technique is best suited for the estimation of velocity profiles.     

数字图像相关技术中插值偏差的理论估计

数字图像相关测量的普及提出了建立散斑质量评价体系要求,即发展针对不同的数字散斑图能够评估测量精度的标准方法.其中,数字图像相关计算中插值误差引起亚像素位移系统偏差(插值偏差)的估计是评价散斑质量的重要参数,然而至今插值偏差与散斑图结构及其插值方法之间的深层机制仍然不明,而且缺乏快速有效的手段估计插值偏差的量级.基于傅里叶方法获得了插值偏差的解析表达式.在满足采样定理的情况下,对其简化得到了插值偏差的带限近似形式和正弦近似形式.插值偏差的正弦近似形式解释了插值偏差随亚像素平移呈正弦形式变化的现象.基于插值偏差的正弦近似公式,提出了决定插值算法用于相关匹配优劣的插值偏差核概念,它表征了插值算法对散斑图特定频率的偏差响应,插值偏差是由插值偏差核与图像功率谱乘积的积分决定的.基于理论分析,提出了一种通过散斑频谱和插值偏差核估计插值偏差的简便有效算法,较之于传统的散斑图平移方法有明显的速度优势.分析了模板大小对估计精度的影响,并通过模拟进行了验证.解释了插值偏差产生的深层机理,解决了长久以来插值偏差难以快速估计的问题.不仅可以用于插值偏差估计,也可以用于插值算法优化,滤波模板选取等问题.对建立散斑质量评价体系,从而制作方便用户的水转印标准散斑也有推动作用.      

Spectral characteristics of background error covariance and multiscale data assimilation

The spatial resolutions of numerical atmospheric and oceanic circulation models have steadily increased over the past decades. Horizontal grid spacing down to the order of 1 km is now often used to resolve cloud systems in the atmosphere and sub‐mesoscale circulation systems in the ocean. These fine resolution models encompass a wide range of temporal and spatial scales, across which dynamical and statistical properties vary. In particular, dynamic flow systems at small scales can be spatially localized and temporarily intermittent. Difficulties of current data assimilation algorithms for such fine resolution models are numerically and theoretically examined. An analysis shows that the background error correlation length scale is larger than 75 km for streamfunctions and is larger than 25 km for water vapor mixing ratios, even for a 2‐km resolution model. A theoretical analysis suggests that such correlation length scales prevent the currently used data assimilation schemes from constraining spatial scales smaller than 150 km for streamfunctions and 50 km for water vapor mixing ratios. These results highlight the need to fundamentally modify currently used data assimilation algorithms for assimilating high‐resolution observations into the aforementioned fine resolution models. Within the framework of four‐dimensional variational data assimilation, a multiscale methodology based on scale decomposition is suggested and challenges are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

An advanced off-axis holographic particle image velocimetry (HPIV) system

Holographic PIV (HPIV) is the most promising candidate for the next generation full-field velocimetry that can measure high spatial resolution instantaneous three-dimensional (3D) velocity fields. To explore the maximum performance capabilities of HPIV including spatial resolution, off-axis holography based HPIV has become a major direction of development. A fully automated off-axis HPIV system based on an injection-seeded dual-pulsed YAG laser and 3D data processing software has been implemented in the laser flow diagnostics lab (LFD). In our system, 90-degree particle scattering, dual reference beams, in situ reconstruction/data processing, and 3D velocity extraction based on a fast “concise cross correlation” (CCC) algorithm are utilized. The off-axis HPIV system is tested for an acoustically excited air jet and the wake of a surface-mounted tab in a water channel flow, giving instantaneous 3D velocity fields for both flows. Experimental data of instantaneously measured 3D flow structures using this technique show great promise. Received: 12 August 1998/Accepted: 20 October 1999     

数字图像相关中的亚像素位移定位算法进展

数字图像相关方法 (DIC) 已经作为一种常用的光学计量有效手段应用于实验力学及其它科学研究和工程应用领域中. 经过 20 多年的发展, 该方法日渐成熟和完善. 作为提高测量精度的亚像素位移定位算法被认为是该方法的关键技术之一. 本文对二维数字图像相关的基本原理及其中为提高测量精度而提出的各种亚像素位移定位算法做了概括性的介绍. 在总结已有研究成果的基础上, 分析了各种方法优缺点. 并对数字图像相关方法的最新进展作了简要介绍, 随着算法精度、效率以及硬件设备性能的提高, 该方法必将会获得更广泛的应用.      

Real-time Bayesian data assimilation with data selection,correction of model bias,and on-the-fly uncertainty propagation

The work introduces new advanced numerical tools for data assimilation in structural mechanics. Considering the general Bayesian inference context, the proposed approach performs real-time and robust sequential updating of selected parameters of a numerical model from noisy measurements, so that accurate predictions on outputs of interest can be made from the numerical simulator. The approach leans on the joint use of Transport Map sampling and PGD model reduction into the Bayesian framework. In addition, a procedure for the dynamical and data-based correction of model bias during the sequential Bayesian inference is set up, and a procedure based on sensitivity analysis is proposed for the selection of the most relevant data among a large set of data, as encountered for instance with full-field measurements coming from digital image/volume correlation (DIC/DVC) technologies. The performance of the overall numerical strategy is illustrated on a specific example addressing structural integrity on damageable concrete structures, and dealing with the prediction of crack propagation from a damage model and DIC experimental data.     

A Stereovision Deformation Measurement System for Transfer Length Estimates in Prestressed Concrete

This work proposes a novel, stereo-vision based test setup for the accurate measurement of relatively small surface strain fields that develop in prestressed concrete prismatic beams after strand release, with the goal of providing an effective and accurate alternative to existing measurement techniques. To this end, the enclosed paper discusses the proposed StereoDIC system configuration, introduces the technique for acquiring full-field shape, deformation and strain measurements using 3D Digital Image Correlation (StereoDIC), verifies the proposed technique through high fidelity laboratory and computer simulations and proposes a computational algorithm that automates the calculation of the transfer length using these measurements. Our studies show that the proposed approach is an effective and accurate non-contacting technique for determining the small surface strain fields in full-scale, prestressed concrete beam specimens, providing essential data to reliably estimate the transfer length in prestressed concrete beams. Though implementation of the procedure in industrial scale facilities is beyond the scope of this paper, discussion regarding this extension is provided.     

Development and assessment of a single-image fringe projection method for dynamic applications

A single-image fringe projection profiling method suitable for dynamic applications was developed by combining an accurate camera calibration procedure and improved phase extraction procedures. The improved phase extraction process used a modified Hilbert transform with Laplacian pyramid algorithms to improve measurement accuracy. The camera calibration method used an accurate pinhole camera model and pixel-by-pixel calibration of the phase-height relationship. Numerical simulations and controlled baseline experiments were performed to quantify key error sources in the measurement process and verify the accuracy of the approach. Results from numerical simulations indicate that the resulting phase error can be reduced to less than 0.02 radians provided that parameters such as fringe spacing, random measured intensity noise, fringe contrast and frequency of spatial intensity noise are carefully controlled. Experimental results show that the effects of random temporal and spatial noise in typical CCD cameras for single fringe images limits the accuracy of the method to 0.04 radians in most applications. Quantitative results from application of the fringe projection method are in very good agreement with numerical predictions, demonstrating that it is possible to design both a fringe projection system and a measurement process to achieve a prespecified accuracy and resolution in the point-to-point measurement of the spatial (X, Y, Z) positions.     

Limits on the resolution of correlation PIV iterative methods. Fundamentals

The spatial resolution of correlation particle image velocimetry (PIV) is a frequently addressed issue that still raises scientific interest. In conventional non-iterative PIV, the spatial resolution limits are of common knowledge (Willert and Gharib (1991) Exp Fluids 10:181–193; Raffel et al. (1998) ISBN 3-540-63683-8, Springer, Berlin Heidelberg New York, among others). On the contrary, those advanced iterative multipass methods that use image distortion techniques or multigrid techniques present a more complex scenario. One of the concepts that raises more debate is the limiting effect of the interrogation window size. This paper focuses on the subject, trying to clarify key points. The results indicate that iterative algorithms using an appropriate weighting function eliminate the window size from the ensemble of spatial resolution limits.