三维射流PIV图像处理方法的研究及其精度分析

本文利用三台照相机系统记录三维射流的流动，通过照相机系统的标定、三维空间粒子的重构、空间粒子的对应及误对应向量的判断和消除等，建立了一种三个图像记录设备组成的三维PIV图像处理算法，并对其精度进行了分析，通过对三维射流图像的处理和分析表明，该方法是切实可行的。     

Diffraction Assisted Image Correlation: A Novel Method for Measuring Three-Dimensional Deformation using Two-Dimensional Digital Image Correlation

Digital Image Correlation (DIC) provides a full-field non-contact optical method for accurate deformation measurement of materials, devices and structures. The measurement of three-dimensional (3D) deformation using DIC in general requires imaging with two cameras and a 3D-DIC code. In the present work, a new experimental technique, namely, Diffraction Assisted Image Correlation (DAIC) for 3D displacement measurement using a single camera and 2D-DIC algorithm is presented. A transmission diffraction grating is placed between the specimen and the camera, resulting in multiple images which are then used to obtain apparent in-plane displacements using 2D-DIC. The true in-plane and out-of-plane displacements of the specimen are obtained from the apparent in-plane displacements and the diffraction angle of the grating. The validity and accuracy of the DAIC method are demonstrated through 3D displacement measurement of a small thin membrane. This technique provides new avenues for performing 3D deformation measurements at small length scales and/or dynamic loading conditions.     

Measurement of curved-surface deformation in cylindrical coordinates

Stereo vision is used to measure the strain field of a round tension test specimen in a cylindrical coordinate system. Initially, the displacement fields of the specimen are measured relative to a world coordinate system erected by the stereo vision. Through coordinate transformations, the measured displacement fields expressed in world coordinates are then converted to the displacement fields expressed in cylindrical coordinates. By differentiating the axial and circumferential displacements in the axial and circumferential directions, the axial, circumferential and shear strains are determined. Results indicate that the measured mean value of the axial strains is in good agreement with the measurements of the extensometer and the strain gage. The Poisson's ratio obtained by the circumferential and axial strains is close to .33 in the elastic state. The mean error of the computed shear strain is approximately .03 percent in the smaller elastic deformation and .08 percent in the larger plastic deformation.     

Three-dimensional displacement measurements using digital image correlation and photogrammic analysis

The application of digital image correlation and stereoscopic principles is used to determine three-dimensional displacements. Two pairs of stereo images of a speckled surface before and after deformation are digitized and correlated to determine the three-dimensional displacements. The images are interpolated so as to account for subpixel displacements. A sequential decision technique and a coarsefine search are employed to increase computer efficiency and decrease run time. Very accurate results are obtained, expecially when the magnification is increased. The effect of camera tilt is shown to be negligible. Theory and experimental verification are presented.     

Sensitivity of in-Plane Strain Measurement to Calibration Parameter for out-of-Plane Specimen Rotations

In practice, out-of-plane motions usually are not avoidable during experiments. Since 2D–DIC measurements are vulnerable to parasitic deformations due to out-of-plane specimen motions, three-dimensional digital image correlation (StereoDIC or 3D–DIC) oftentimes is employed. The StereoDIC method is known to be capable of accurate deformation measurements for specimens subjected to general three-dimensional motions, including out-of-plane rotations and displacements. As a result, there has been limited study of the deformation measurements obtained when using StereoDIC to measure the displacement and strain fields for a specimen subjected only to out-of-plane rotation. To assess the accuracy of strain measurements obtained using stereovision systems and StereoDIC when a specimen undergoes appreciable out of plane rotation, rigid body out-of-plane rotation experiments are performed in the range ?40⁰?≤?θ?≤?40⁰ using a two-camera stereovision system. Results indicate that (a) for what would normally be considered “small angle” calibration processes, the measured normal strain in the foreshortened specimen direction due to specimen rotation increases in a non-linear manner with rotation angle, with measurement errors exceeding ±1400με and (b) for what would normally be considered “large angle” calibration processes, the magnitude of the errors in the strain are reduced to ±300με. To theoretically assess the effect of calibration parameters on the measurements, two separate analyses are performed. First, theoretical strains due to out-of-plane rigid body rotation are determined using a pinhole camera model to project a series of three-dimensional object points into the image plane using large angle calibration parameters and then re-project the corresponding sensor plane coordinates back into the plane using small angle calibration parameters. Secondly, the entire imaging process is also simulated in order to remove experimental error sources and to further validate the theory. Results from both approaches confirmed the same strain error trends as the experimental strain measurements, providing confidence that the source of the errors is the calibration process. Finally, variance based sensitivity analyses show that inaccuracy in the calibrated stereo angle parameter is the most significant factor affecting the accuracy of the measured strain.     

New aspects of surface displacement and strain analysis by speckle interferometry

The application of two allied laser-speckle-interferometric techniques to the measurement of surface displacements and strains is described. One technique uses the ‘double-aperture speckle camera’ and the other uses a similar interferometer called a ‘double-aperture speckle-shearing camera’. Although these cameras are not new, the theory for their application to general deformation of a flat surface was presented only recently with ‘new’ equations governing the formation of fringes. These equations are reviewed briefly and particular applications of them are presented. Three experiments demonstrating the use of the cameras are described. The good results obtained verify the validity of the new equations.     

Strain tensor for large three-dimensional surface deformation of sheet metal from an object grating

Grating techniques are used to determine the three-dimensional deformation and the tangential strain of sheet metal. A grating is fixed on the surface and taken by stereo CCD cameras in different deformation states. By suitable line-following software, the grating coordinates in the images are determined with subpixel accuracy. Using photogrammetric methods, the three-dimensional coordinates are calculated from the image coordinates. The strain usually is determined by means of a deformation gradient, which is calculated from every deformed triangle. In this paper, the gradient is determined in the center of four neighboring meshes using a polynomial approximation of the displacement function in a reference position. The influence of the nontangential deformation is considered. By simulation, a flat sheet metal is deformed to a rotational symmetric surface. The difference of the known exact strain is compared with the numerically derived strain with respect to different grating pitches. The proposed method yields good results even in the case of large spatial deformation. It is applied to the deformation of a hatlike test specimen.     

Target-free Stereo PIV: a novel technique with inherent error estimation and improved accuracy

A novel, accurate and simple stereo particle image velocimetry (SPIV) technique utilising three cameras is presented. The key feature of the new technique is that there is no need of a separate calibration phase. The calibration data are measured concurrently with the PIV data by a third paraxial camera. This has the benefit of improving ease of use and reducing the time taken to obtain data. This third camera also provides useful velocity information, considerably improving the accuracy of the resolved 3D vectors. The additional redundancy provided by this third perspective in the stereo reconstruction equations suggests a least-squares approach to their solution. The least-squares process further improves the utility of the technique by means of the reconstruction residual. Detailed error analysis shows that this residual is an accurate predictor of resolved vector errors. The new technique is rigorously validated using both pure translation and rotation test cases. However, while this kind of validation is standard, it is shown that such validation is substantially flawed. The case of the well-known confined vortex breakdown flow is offered as an alternative validation. This flow is readily evaluated using CFD methods, allowing a detailed comparison of the data and evaluation of PIV errors in their entirety for this technique.     

A quantitative study of three-dimensional Lagrangian particle tracking algorithms

A neural network particle finding algorithm and a new four-frame predictive tracking algorithm are proposed for three-dimensional Lagrangian particle tracking (LPT). A quantitative comparison of these and other algorithms commonly used in three-dimensional LPT is presented. Weighted averaging, one-dimensional and two-dimensional Gaussian fitting, and the neural network scheme are considered for determining particle centers in digital camera images. When the signal to noise ratio is high, the one-dimensional Gaussian estimation scheme is shown to achieve a good combination of accuracy and efficiency, while the neural network approach provides greater accuracy when the images are noisy. The effect of camera placement on both the yield and accuracy of three-dimensional particle positions is investigated, and it is shown that at least one camera must be positioned at a large angle with respect to the other cameras to minimize errors. Finally, the problem of tracking particles in time is studied. The nearest neighbor algorithm is compared with a three-frame predictive algorithm and two four-frame algorithms. These four algorithms are applied to particle tracks generated by direct numerical simulation both with and without a method to resolve tracking conflicts. The new four-frame predictive algorithm with no conflict resolution is shown to give the best performance. Finally, the best algorithms are verified to work in a real experimental environment.     

Elasticity solutions for free vibrations of annular plates from three-dimensional analysis

This article, examines the vibrational characteristics of annular plates by using the three-dimensional elasticity theory. It aims to raise the quality of the investigation beyond that provided by the two-dimensional plate theories by resorting to a full three-dimensional analysis. A polynomials–Ritz model based on sets of orthogonally generated polynomial functions to approximate the spatial displacements of the plates in cylindrical polar coordinates is presented. The model is then used to extract the full vibration spectrum of natural frequencies and mode shapes. The vibration responses due to the variations of boundary conditions and thickness are investigated. Frequency parameters and three-dimensional deformed mode shapes are presented in vivid graphical forms. The accuracy of the method is validated through appropriate convergence and comparison studies.     

Viscoplastic parameter estimation by high strain-rate experiments and inverse modelling – Speckle measurements and high-speed photography

A methodology based on inverse modelling for estimating viscoplastic material parameters at high strain-rate conditions is presented. The methodology is demonstrated for a mild steel exposed for compression loading in a split Hopkinson pressure bar arrangement. By using dog-bone shaped specimens nonhomogeneous states of deformation are obtained throughout the entire deformation process. The resulting nonhomogeneous deformation of the specimens is evaluated using digital speckle photography (DSP) to give in-plane point-wise displacement and strain fields. The photographs are captured with a high-speed camera of image converter type, which acquire time resolved images during the impact loading. The experiments are simulated using finite element analysis (FEA), where the material model suggested by Johnson–Cook for high-strain rate conditions are utilised. Experimental and FE-calculated field information are compared in order to estimate the viscoplastic parameter in the Johnson–Cook material model. The estimation is performed by minimising least-square functions that contain the differences in displacements and strains, respectively. The quality of the estimated parameters is studied from statistical point of view.     

A 3D Shape Measurement Technique that Makes Use of a Printed Line Pattern

The in-house validation of finite element models for bird strike events is currently carried out by means of experimental tests on flat plates. High displacement speeds in these experiments require a low exposure time of the high-speed camera (up to 1/50,000 s). In order to acquire images of sufficient quality, a special, high-intensity light source has to be used, which does not always turn out to be possible. Therefore, the regions with high displacement speeds often result in blurry images. In such cases, a printed line pattern to estimate the shape of the plate during the test, offers major advantages over a speckle pattern in terms of the reconstruction and optimization of the blurry regions. In this article, a stereo vision technique is presented that was developed to reconstructs 3D shape maps using images of impacted plates with printed line patterns. It is shown that two cameras are necessary to calculate accurate shape maps in case of large deflections. The resulting shapes can be used for the validation of numerical simulations.     

Influence of Camera Rotation on Stereo-DIC and Compensation Methods

Camera rotation during stereo digital image correlation (DIC) measurements is always present in some amount and is caused by environmental vibrations during testing (e.g. blast testing, testing in industrial environments, vibration testing Helffrick et al., Mech Syst Signal Process 25(3):917–927, 2011, etc.). The impact of changing extrinsic parameters on stereo-DIC measurements was investigated in this paper by simulating several DIC experiments with a shaking camera system. To obtain an appropriate order of magnitude of the camera motion, the actual camera rotation during a test was observed and reported. The impact hereof was investigated by analyzing static images and by simulating camera rotation with a stereo-DIC simulator presented in Balcaen et al. (Exp Mech 57(5):703–718, 2017). Insight on this underestimated error source is explained by investigating which rotations are more critical to the resulting displacements and strains. Two possible compensation methods were investigated and their capability of compensating camera motion was evaluated.     

Surface deformation measurements of a cylindrical specimen by digital image correlation

Planar digital image correlation has been extended to measure surface deformations of cylindrical specimens without physical contact for high-temperature situations. A single CCD camera acquires the surface image patterns of a section of a specimen in the undeformed and deformed states to determine two-dimensional displacements on a projection plane. Axial, circumferential and shear deformations are determined through curvature transformation on the two-dimensional projection displacement field. The resolution of this technique was determined for a cylinder of 22.23-mm diameter to be 3.5 μm for the axial displacement, 0.05 percent for the axial and shear strains and 0.08 percent for the circumferential strain when correlation computations are carried out over a field of 5 mm×5 mm.     

A 3D Displacement Control by Digital Image Correlation for the Multiaxial Testing of Materials with a Stewart Platform

A Digital Image Correlation technique is proposed to control a quasi-static 6 degrees of freedom testing machine. This machine is based on a hexapod architecture, allowing displacements of several tens of centimeters and degrees, and with force capacities of several tens of kN and kN.m. The control technique is based on the measurement of the set of actuator lengths, from images of the end-effector of the machine. A firstattempt is shown with a single camera. Thoughrelevant, the results present too high uncertainties for the aimed applications. Several cameras are then used to improve the 3D rigid body motion displacement measurement of the end-effector. Thecamera positions are free, with an automatic calibration method assessing the needed coefficients for the control. The set of actuator lengths is then searched by global minimization of the difference between the current image and the reference image of each camera (i.e., the minimization is not performed independently for each camera). The algorithm is implemented on Graphical Processing Units to achieve computation times lower than 50 ms. An in-depth experimental validation of the whole setup is performed. For an actuator length range of 200 μm, the actuator length uncertainties are around 0.4 μm with 3 cameras. The errors of displacement of the end-effector are less than 2 μm, partially due to the validation setup itself.     

复合材料层合板的三维研究

本文提出了固支复合材料各向异性层合圆板受均布横向载荷作用下的满足三维弹性力学基本微分方程和边界条件的解析解答。文中采用一种发展的摄动方法进行求解，板中的每个应力和位移都展开为无量纲厚度参数ε的摄动级数，并采用二维板理论解答作为其相应三维摄动解答的一个基本解的形式，通过摄动方法逐级求解而获得完整的三维解答。文中以解析形式和数值形式给出了高精确度的三维应力和位移结果，结果表明，本文求解三维问题的解析方法是合理有效的。     

A displaced-line velocity diagnostic and its application in a visualization engine

A technique for measuring three-dimensional velocity by imaging the displacement of a marked fluid line is described, together with its use in an automotive visualization engine. In a flow seeded with 2–3 μ phosphorescing particles, a line is excited by a UV laser beam, deformed by the local velocity field, and detected by stereo low-light-level video cameras. The derivation of velocity from digitized images is discussed and capabilities of the diagnostic are assessed. Some image data taken in the engine are shown and quantitative two-component velocity plots along the line are presented.     

Advances in light microscope stereo vision

The increasing research focus on small-scale mechanical systems has generated a need for deformation and strain measurement systems for microscale applications. Optical measurement systems, such as digital image correlation, present an obvious choice due to their non-contacting nature. However, the transfer of measurement technology developed for macroscale applications to the microscale presents unique challenges due to the differences in the required highmagnification optics. In this paper we illustrate the problems involved in calibrating a stereo microscope using traditional techniques and present a novel methodology for acquiring accurate, three-dimensional surface shape and deformation data on small-scale specimens. Experimental results demonstrate that stereo microscope systems can be accurately and reliably calibrated using a priori distortion estimation techniques in combination with traditional bundle-adjustment. The unique feature of the present methodology is that it does not require a precision calibration target but relies solely on point correspondences obtained by image correlation. A variety of experiments illustrate the measurement performance of a stereo microscope system. It is shown that the surface strains obtained from the full-field, three-dimensional measurements on tensile specimens undergoing large rigid-body motions are within ±50 microstrain of strain gage measurements for strains ranging from 0 to 2000 microstrain. H. W. Schreier was a PhD Student from Ecole Mines des Albi in France     

Normal surface displacement around a circular hole by reflection holographic interferometry

In a previous paper¹, a fringe-compensation technique was developed to improve the possibilities of stress analysis by real-time holographic interferometry. The technique is specially well suited for the measurement of small displacements in the direction of viewing. As an application of this method, the surface displacements caused by strains in the thickness direction are measured around a circular hole in a plate loaded in tension in its plane. Independent prior knowledge of the in-plane displacement is required, however, in data processing. An analytical solution to the problem is used for that purpose. The experimental results are compared to those obtained theoretically from the classical two-dimensional analysis, and from a three-dimensional analysis. The two-dimensional theory assumes a state of ‘generalized plane stress’. The three-dimensional theory, made by Alblas², takes into account the existence of stresses in the thickness direction, and the variation of the in-plane stresses through the thickness. Both theories give the same results away from the hole. They differ significantly, however, when the hole boundary is approached, where the proximity of the hole induces three-dimensional effects. The experimentally measured displacement is found to be in good agreement with both theories away from the hole. Close to the hole, a large departure from the two-dimensional results is observed. The experimental results here are close to those of three-dimensional results. The experiment is thus in good agreement with the three-dimensional theory over the whole field. But the two-dimensional theory is valid only at large distances from the hole.     

弹性力学问题的一阶有限元解法

求解弹性力学问题的应力时,如果采用常规的位移有限元法,需要先求得单元的节点位移,再经过求导运算得到。为了解决这种求解方式引起的应力精度下降的问题,提出了弹性力学问题的一阶多变量形式,使得应力与位移精度同阶,并推导了弱形式。采用有限元方法,对弹性力学问题给出了一阶解法的二维、三维数值算例,并且将一阶解法的结果与常规位移有限元法的解进行了比较。数值计算结果表明,一阶解法有效提高了应力的精度,并且应力的误差和节点位移的误差具有相同的收敛阶,验证了本文方法的有效性,为提高有限元法的应力精度提供了新的思路。