基于最小一乘拟合的非均匀应变的数字图像相关测量

数字图像相关(DIC)方法是一种重要的位移和应变非接触式测量方法。为了对物体的非均匀应变进行准确测量,在DIC方法中引入位移最小一乘拟合,鉴于最小一乘拟合解析方法求解困难,采用基于模拟退火的混合粒子群算法进行求解。开展了虚拟剪切带形成的数值实验和相似材料断层滑移实验,并对非均匀变形条件下最小一乘拟合和最小二乘拟合的应变测量结果进行对比。研究发现:对于非均匀应变测量,最小一乘拟合的结果要优于最小二乘拟合;而对于均匀应变测量,两种方法具有相同的精度。     

针对裂尖变形场测量的包络单元局部数字图像相关方法

使用数字图像相关(DIC)方法测量平滑、准确的裂纹尖端位移场和应变场是学术界难题之一。目前常用的方法为基于子区的局部DIC方法,但其子区跨裂纹计算的结果无意义。经过改进的基于子区分割的DIC方法降低了子区内像素点数量,导致精度降低。提出一种基于Hermite单元的局部DIC(HELDIC)方法,依次分块计算感兴趣区域(ROI),利用较大单元包络分块区域剔除单元边界精度较低的数据,通过调整Hermite单元位置使得剔除的数据量最少,再使用所提改进的逐点最小二乘(PLS)方法平滑分块的位移场并得到应变场,从而提高裂纹尖端应变场的平滑度和精确度。实验结果表明,所提方法与传统局部DIC方法相比获得的变形场距离裂纹尖端及裂纹面更近,且在给定的单元和子区大小下的应变场平均误差降低30%以上,是计算裂尖变形场的有效方法。     

核能谱单能峰快速高精度高斯函数拟合算法研究

在核能谱分析中,高斯函数最小二乘拟合法是计算单能峰净峰面积常用的方法,该方法精度较高,但噪声敏感性较强,导致拟合出的高斯函数在峰位附近的残差向量较大。针对该问题,对高斯函数最小二乘拟合法进行了详细推导,分析了峰位附近残差向量较大的原因,提出了一种基于高斯函数最小二乘拟合法的高斯函数加权最小二乘拟合法,即在高斯函数最小二乘拟合法的基础上,引入了权重因子。该权重因子与取对数后数据权重削弱趋势相反或与数据本身趋势相符,以减小噪声敏感性。由于在求解高斯函数参数的过程中涉及到求逆矩阵运算,计算量较大,耗时较长,为了提高实时性,将求逆矩阵的运算过程转换为了简单的方程组运算,并给出了高斯函数的幅值、中心及方差参数的快速求解公式。将这两种方法用于55Fe的特征X射线单能峰的实际拟合中,结果表明,高斯函数加权最小二乘拟合法效果均较好,这说明该方法降低了噪声敏感性,减小了高斯函数在峰位附近的残差向量,进一步提高了拟合精度。另外,使用快速求解公式,也减小了运算量,增强了实时性,为在便携式设备中的有效使用提供了可能。     

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。     

Navier-Stokes方程的最小二乘等几何方法

基于Hermite多项式的C¹型单元构造复杂,限制了最小二乘有限元法的应用.引入高阶光滑的非均匀有理B样条作为基函数简化C¹型单元构造,提出求解黏性不可压流动Navier-Stokes方程的最小二乘等几何方法.用Newton法或Picard法对Navier-Stokes方程线性化,用线性化偏微分方程的余量定义最小二乘泛函,导出最小二乘变分方程,用NURBS构造高阶光滑的有限维空间来近似速度场和压力场.计算表明:本文方法计算的二维顶盖驱动流数值解能准确描述流动状况,计算的二维通道内圆柱绕流全局质量损失由最小二乘有限元法的6%降为0.018%,该方法可用于Navier-Stokes方程的求解,并且具有较好的质量守恒性.     

二维多相机全场数字图像相关变形测量方法

从理论上推导了数字图像相关(DIC)方法中应变精度的影响因素,指出应变计算精度会随着窗口尺寸的变小而下降。为了提高图像有效分辨率,针对细长平面试件提出了一种二维多相机全场DIC方法。该方法根据特征点检测及匹配算法定位特征点对的亚像素位置,通过DIC方法对特征点对进行高精度配准,利用发展的逐步优化单应矩阵方法求解图像变换关系,得到变形前后的无缝拼接图像。分别实施了纯平移和橡胶梁三点弯两组实验。在纯平移实验中,该方法计算得到的应变均值误差及均方根误差均在50με以内,验证了该方法的有效性;采用橡胶梁三点弯实验对比该方法与三维多相机全场DIC方法,并基于实验结果对该方法的优点与缺点进行了分析。     

梯度-曲面拟合法的亚像素位移测量算法

数字图像相关方法作为光学测量的一种测量方式在结构变形测量中有广泛应用,其中亚像素位移测量精度成为关键。基于亚像素位移测量精度影响因素的分析,研究了计算子区灰度插值、计算窗口大小以及拟合距离对亚像素位移测量的影响。提出了一种梯度-曲面拟合法的亚像素位移测量算法,即,先采用梯度法计算出结构的亚像素位移,再对计算子区进行亚像素插值,然后调整拟合距离进行亚像素曲面拟合。最后利用计算机模拟算例验证了该方法具有良好的计算效率、计算精度及抗噪声能力。     

S弯热应变分析及数值模拟

为了确定S弯结构在降温过程中的变形情况,基于卡氏定理对其一端建立温差位移和广义支反力之间的方程组,根据计算出的广义支反力求解该结构上各处的轴向应变.通过数值模拟对该方法计算出的最大应变和最小应变进行校核,两者非常吻合.可以认为:运用该方法计算类似结构的应变分布是可行的,计算出的结果具有较高的准确度.     

基于连续小波变换的FTIR光谱拟合算法

提出了一种基于连续小波变换的FTIR光谱拟合算法。在计算差减尺度因子时,同时考虑原始谱图及其连续小波变换谱图,从光谱最小二乘拟合的角度求解,克服了常规差谱算法中的参考峰及差减因子的人工选择问题。采用六种不同的小波进行光谱拟合,用计算得到的差减因子来定量酒精度,误差绝对值的平均值仅为0.047°~0.072°,误差标准差仅为0.056°~0.091°。实验结果表明,连续小波变换结合最小二乘拟合的光谱拟合模型能为FTIR差谱提供一种准确可靠的新方法。     

基于条纹中心线的载波散斑条纹解调方法

针对传统傅里叶变换法在处理含有多突起的载波散斑条纹图时,由于存在频谱展宽会出现严重的解调相位失真,提出了一种基于条纹中心线的载波散斑条纹解调方法.根据载波调制时所采用平行调制方式和倾斜调制方式,分别从理论上对相关的中心线解调法进行数学推导,并进一步采用最小二乘三次曲面拟合法获得被测物面全场的离面位移信息.实验结果表明:利用上述中心线解调法和曲面拟合法能解调出复杂的载波条纹图,并获得具有亚像素定位准确度、连续光滑的全场离面位移信息.     

Experimental determination of Representative Volume Element (RVE) size in woven composites

A systematic approach is proposed to estimate the length scales of the representative volume element (RVE) in orthogonal plain woven composites. The approach is based on experimental full-field deformation measurements at mesoscopic scales. Stereovision digital image correlation (DIC) is conducted to determine the full-field strain distribution in on- and off-axis specimens loaded axially in tension. A sensitivity analysis is carried out to optimize the image correlation parameters. Using the optimized set of image correlation parameters, full-field strains are measured and used in conjunction with a simple strain averaging algorithm to identify the length scales at which globally applied and spatially-averaged local strains converge in values. The size of a virtual window containing local strain data, the average of which has the same value as the global strain, is identified as the RVE dimensions for the examined material. The smallest RVE sizes found in this work are shown to be both strain and angle dependent. The largest RVE dimension obtained is reported as a unique, strain and orientation insensitive RVE size for the woven composite examined.     

数字散斑技术在混凝土单轴压缩试验中的应用

数字散斑技术作为一种新兴的测量方法,它具有非接触、全场量测、精度高、操作简单等特点,随着计算机技术的迅猛发展,数字散斑技术得到了广泛的应用与研究。针对混凝土在外荷载作用下具有明显的非均匀变化的特征,借助传统的测量方法很难得到混凝土表面的全场变形结果的问题,结合数字散斑相关方法测量技术,开展了混凝土单轴压缩试验,拍摄了混凝土表面在单轴压缩过程中的位移与应变矢量场,为分析混凝土试件的损伤区域奠定了基础;与电测法测量结果进行了对比,其测量结果表明,这两种测量方法误差相对较小,且数字散斑技术能更早的发现混凝土表面的破坏,验证了数字散斑相关方法的准确性和可靠性。借助数字散斑技术可以更加方便准确的得到材料表面的变形场,这也将在一定程度上促进土木工程领域的发展,具有广阔的应用前景。     

物体内部三维位移场分析的数字图像相关方法

提出了物体内部三维位移场的数字图像相关分析方法，对物体变形前后，或连续变形的两个相邻状态的内部三维结构的数字图像，通过相关运算获得三维位移场.文中给出了三维相关法的体搜索窗口、相关函数及亚像素运算的相关系数拟合函数.数字模拟结果证明了三维相关法的正确性及可靠性.位移计算精度为0.02像素. 关键词： 数字图像相关 三维相关 亚像素     

数字散斑亚像素小角位移测量的曲面拟合法

与传统测量方法相比,数字散斑相关法由于其目标特征单元网格划分的灵活性,能够更好地满足不同场合小角位移的测量需求。针对该方法亚像素小角位移测量的曲面拟合参数选择问题,研究了亚像素测量图像小角旋转前后的九点二次曲面拟合法,并根据计算机生成模拟散斑进行模拟实验分析,得到最佳误差效率优化条件下的曲面拟合法求解亚像素小角位移的最佳散斑尺寸3.5 pixel、计算窗口尺寸41×41 pixel和拟合窗口尺寸3×3 pixel。实验验证了上述测量参数的有效性,为进一步的曲面拟合法数字散斑成像角位移测量提供参考。     

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.     

Application of iteration and finite element smoothing technique for displacement and strain measurement of digital speckle correlation

In this paper, an improved method for measuring displacement in digital speckle correlation technology, which is based on an iterative and spatial-gradient algorithm, is developed. After obtaining full-field displacement, both finite element method and 2D generalized cross-validation (GCV) algorithm are adopted for smoothing the displacement field, and then the strain field can be obtained from the smoothed displacement field. The method is estimated by simulated speckle patterns and three-point bending experiment. All the results show the improved method can obtain a reasonable estimation of displacement and strain fields in digital speckle correlation 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.     

Random depth access full-field low-coherence interferometry applied to a small punch test

In small punch testing, with approximate preknowledge of the sample deformation, profile measurement need only be made at selected locations in depth. To date, profilometry through full-field low-coherence interferometry has not been applied to small punch testing—conventional methods typically measure the maximum displacement as the sample is deformed, ignoring useful shape and profile information. A modification of full-field low-coherence interferometry is presented, where a digital stepper motor is combined with piezoelectric transducer scanning to achieve random depth access three-dimensional micrometer profile measurement. Offering a rapid, inexpensive, and functional machine vision system, the measurement technique is applied to a small punch test.     

基于数字图像相关技术的隐框玻璃幕墙抗风压性能评估

为表征隐框玻璃幕墙面板在复杂边界条件与风荷载作用下产生的不对称挠曲变形并进行安全性评估,采用数字图像相关技术对幕墙样品进行非接触式全场测量。通过重建面板的空间挠曲形貌,建立基于面法线距离、表面高斯曲率、面内大主应变与应变能密度分布的玻璃幕墙抗风压性能综合评估方法。计算结果表明:初始形貌与结构耦合作用下面板挠曲后的最大面法线距离为6.02 mm,小于现行标准实验计算结果,幕墙的实际抗风压性能更优秀;面板四角区域呈双曲抛物面变形,同样存在安全隐患,在左上角出现全场最大面内大主应变257 με。因此该方法避免了传统仪器受限于指定测点数据的缺陷,能够反映玻璃面板变形的全场时空动态变化,为表征隐框玻璃幕墙的抗风压性能提供便捷且有效的技术手段。     

Incremental calculation for large deformation measurement using reliability-guided digital image correlation

Conventional digital image correlation (DIC) technique using a fixed reference image provides high-accuracy measurements but normally fails when serious decorrelation effect occurs in the deformed images due to large deformation, serious illumination fluctuations or other reasons. In this paper, an incremental reliability-guided digital image correlation (RG-DIC) technique, by combining the recently developed RG-DIC technique and an automatic reference image updating scheme, is proposed for large deformation measurement. In the incremental RG-DIC technique, a seed point is defined in the original reference image and searched in the deformed images, if the estimated correlation coefficient is larger than a preset threshold, which means no serious decorrelation effect exists in the deformed image, the RG-DIC technique is used to continue correlation analysis to obtain full-field displacements. Otherwise, the image recorded just before the current deformed image is chosen as an updated reference image to proceed with correlation analysis. Afterwards, the incremental displacements extracted by comparing the current deformed image and the updated reference image can be cumulated to determine the overall deformation. The effectiveness of the proposed technique is demonstrated by retrieving the full-field deformation of a foam sample subjected to large compressive deformation.