Digital Image Correlation (DIC) technology facilitates non-contact,real-time monitoring and analysis of the dynamic mechanical behavior of materials by tracking speckle patterns on the surface of samples.Nevertheless,in the context of Split Hopkinson Pressure Bar (SHPB) testing,characterized by high strain rates and complex loading conditions,DIC technology encounters several challenges,including limited measurement accuracy and inadequate adaptability to environmental variations.In order to fully grasp the application status and optimization methods of DIC technology in SHPB test,based on the principle of SHPB test and DIC technology,the relevant research results on the improvement of large deformation measurement accuracy were summarized from the aspects of incremental correlation,shape function,initial value estimation and deep learning algorithm.Subsequently,based on the specific requirements of SHPB tests, practical optimization strategies for DIC technology were proposed, focusing on speckle fabrication techniques and material mechanical characteristics feedback.These strategies include the utilization of high-speed cameras and the optimization of image processing algorithms to improve the efficacy of the image acquisition and processing system.Additionally,efforts are made to augment the environmental adaptability of DIC technology,ensuring its stable operation in challenging conditions such as high temperature and high pressure.Combined with other testing methodologies,the implementation of multi-parameter measurement and comprehensive analysis facilitates a more thorough understanding of the dynamic mechanical behavior of materials.The application and optimization of DIC technology in SHPB testing are intended to enhance measurement accuracy,broaden the scope of applications,and advance the intelligence of the testing system.This approach is expected to yield more precise evaluations of the dynamic mechanical properties of materials,thereby providing substantial support for advancements in materials science and related engineering disciplines.
目前室内研究材料动态力学行为的常见设备为分离式霍普金森压杆(Split Hopkinson Pressure Bar,SHPB),用于分析各类材料在高应变率(102~104 s-1)下的动态力学特征(臧小为,2011)。传统SHPB测试装置通过贴在入射杆和透射杆的应变片信号,结合一维应力波理论间接推导材料的动态应力—应变关系。试验过程中,材料与杆之间的摩擦力以及惯性力会影响材料的真实受力(Kajberg et al.,2007),导致材料自身的真实变形过程无法准确呈现。范亚夫等(2015)通过铝合金的动态拉伸性能试验证实,电测方法所测得的材料变形与实际变形存在差异。常用的应变测量方法分别有电阻应变片法(Gilat et al.,2009)、半导体应变片法(宋力等,2006)和PVDF压电计法(席道瑛等,1995;郭弦等,2015),这些接触式测量方法不仅要求应变片与杆之间具有良好的黏附性,而且对材料的断裂和破坏分析只能通过后效观察,无法反映材料变形的过程特征。此外,这些方法对于高应变率下微小尺寸材料的变形测量精度不高,也无法在直径小于3 mm的杆中使用应变片。
DIC技术是通过光电摄像机或数码相机采集图像并数字化,对比材料表面的散斑变化,对选定区域进行匹配运算,进而得出相应的应变场和位移场(Zhou et al.,2024)。DIC基本原理如图2所示,以参考图像上的为中心点,选取(2M+1)×(2M+1)的参考子图像,通过函数匹配和相关算法获得具有最大相关性的变形子图像,变形子图像中是参考子图像的对应点。两点之间的函数关系式(韩红亮等,2022)表示为
目前在DIC测试中制作散斑常用的方法有喷枪、喷涂料和记号笔等,这些制作方法可以提高对比度,但重复操作性较差、操作较为复杂且对试件具有一定的伤害,特别是对于一些耐腐蚀性较差的材料。为此,学者们利用计算机设计数字高质量散斑图像,再通过其他方法将其转移或复制到被测材料表面,此方法在理论上适用于所有材料,且可重复操作性较好,每次转移相同的数字散斑场,得到的试验散斑是一致的。通过直接转移和间接打印方式制作散斑的方法一般有丝网印刷、水转印和光敏印章复制等(陈振宁,2018)。然而,印刷和水转印等方法对时间和材料的损失是不可避免的,且应用场景和条件存在一定的局限性(Thai et al.,2022)。Zhang et al.(2023)根据岩石表面深层纹理特征信息,通过局部二元模型在岩石表面建立LBP高质量数字散斑场,很好地弥补了传统散斑、印刷和水转印等方法的固有缺陷,图3所示是基于表面纹理信息的岩石变形测量方法的步骤。未来,基于表面纹理特征信息制作散斑的方法具有广泛的应用前景。为实现这一目标,需综合考虑材料表面的粗糙度、反射率和折射率等关键因素,并根据目标材料的特性进行针对性调整与优化。通过设计合理的标记点或斑纹布局,可以获得更贴近实际效果的散斑图像,从而提升整体应用性能。
2.2 材料力学性质对DIC测量的影响
不同材料的力学特性不同,在高应变率下会有不同的动态力学响应。对于金属材料而言,其在高应变率下表现出显著的应变率依赖性,如应变硬化(朱正洪等,2024)和热软化效应(Huang et al.,2016),DIC系统必须能够在极短的时间尺度内准确测量应变分布,这对图像捕捉的帧率和分析算法的实时处理能力提出了较高的要求;许多金属材料在宏观上表现为各向同性,但在微观结构(如晶粒)层面可能存在各向异性(Dai et al.,2020),DIC分析需要识别并量化这种微观尺度的各向异性。对于聚合物而言,其在高应变率下常表现出大范围的非线性变形(罗鑫等,2014),包括黏弹性和塑性行为,DIC系统需要应对这种非线性响应,并提供精确的全场应变分布;此外,许多聚合物对温度变化敏感,可能在试验过程中由于内部摩擦和塑性变形产生热量,DIC分析需要考虑这种温度效应对材料响应的影响。对于复合材料而言,其应力—应变响应极其复杂,涉及纤维(冻瑞岚等,2023)、基体(聂明明等,2023)和界面(佘欢等,2024)的相互作用,DIC技术必须能够区分这些不同成分的贡献,并准确测量各向异性的应变分布。因此,构建不同材料在高应变率下的本构模型至关重要。在此基础上,结合材料特性和试验条件,自动调整参数并优化DIC算法,包括提升时间分辨率、优化动态时间窗口等,以实现对各类材料高速变形过程的精确追踪。
3 DIC技术在SHPB试验中的发展与应用
20世纪80年代初期,DIC方法分别由日本学者Yamaguchi (1981)和美国学者Peters et al.(1982)独立提出。1981年,Yamaguchi(1981)确定了散斑位移与物体变形量之间的关系,提出一种测量物体微小变形的方法;1982年,Perters et al.(1982)提出用数字散斑相关方法测量物体位移,通过物体变形前后的散斑图,对相关性位移和导数进行迭代,找到相关系数的极值,进而算出散斑位移场,得到物体的位移量。直至1990年,中国科学技术大学的Han et al.(1990)才将DIC应用到SHPB试验中,并测得了不同时刻下碳钢和铝合金受冲击荷载产生的应变场,图4所示为SHPB结合DIC的测量示意图。从此,DIC技术在SHPB试验中的应用越来越广泛。
3.1 应变和位移的测量
借助DIC技术,通过对材料表面图像的精确分析、比对和匹配运算,能够准确获取位移和应变的相关信息。范亚夫等(2015)通过DIC技术真实记录了铝合金在SHPB动态拉伸下裂纹的起裂、扩展和失稳过程,克服了传统应变片不能测量位移的缺点。Pandya et al.(2019)在SHPB试验中分别使用应变片和 2D-DIC 技术测量5种生物复合材料在不同加载率下的应变—时间历史,发现2种测量方式的测量结果接近,其中冲击荷载为103.42 kPa的测量结果如图5所示。邢灏喆等(2021)利用SHPB结合3D-DIC技术对粗粒、中等和细粒径(CG、MG、FG)3种砂岩进行压缩试验,由图6(a)可以看出,粗粒径砂岩应变局部化现象明显,最终局部裂纹汇合成一条主裂纹,图6(b)和图6(c)反映了中等粒径和细粒径砂岩的应变局部化特征,均从试件的受力端开始,最后裂纹贯通到试件的另一端,可以看出粒径对裂纹扩展的显著影响。杨仁树等(2020)观测了不同冲击速度下红砂岩、灰砂岩和花岗岩3种岩石表面拉伸应变场和剪切应变场的动态演化规律。Gilat et al.(2018)对纤维复合材料的缺口试样受剪切作用的实时应变场进行了分析。叶晓盛(2020)利用2D-DIC技术分析了碳纤维和树脂的动态拉伸过程以及失效模式。
式中:为应力(Pa);为材料的密度(kg/m3);为传播波的速度(m/s);为测得的应变。借此方法,Pandya et al.(2019)测量了一种生物复合材料的动态应力—应变曲线,测试结果可靠;Dave et al.(2018)分析了3种类型的生物复合材料在3种应变率下的应力—应变特征,也证明了DIC测试数据的可靠性,其中应变率为950 s-1条件下的测量结果如图7所示。
此外,需特别注意测量过程中应力平衡条件。内部力在材料静态下是平衡的,但在动态加载中,非平衡力引起应力分布差异,例如在材料的某个区域,非平衡力可能会导致局部应力增加或减小,而在其他区域则产生相反的效果,从而导致DIC计算的应力结果不准确。然而,由于软材料波速和波阻抗较低、透射信号微弱、应力平衡时间长、透射和反射波的起点选取困难,很难评估材料两端力的平衡状况。为此,谢倍欣等(2014)使用DIC获取入射杆和透射杆两端的应变,将杆两端的应变通过一维应力波理论换算成应力,能够有效评估试件两端的应力平衡状态,测量原理如图8所示。但有的软材料在动态测试时间尺度内很难达到应力平衡(Meyland et al.,2023)。为了解决该问题,学者们使用了很多方法,例如采用波阻抗低的铝杆(Pang et al.,2019)、镁杆(Shergold et al.,2006)和聚合物杆(Jamie et al.,2019)等降低软材料和杆之间阻抗失配,通过增加垫片来调整波形(宋力等,2004),在加载设备上施加与非平衡力相反的静态力或者补偿力来抵消非平衡力(王永刚等,2003)。
增量相关可以较好地解决大变形问题,其原理是增大图像采集频率,将大变形视为多个小变形的累积以实现对大变形的测量和分析,原理如图10所示。然而,每次小变形的累积计算均存在误差,以子区偏移误差为主要因素,插值误差为次要因素。子区偏移指每次图像更新后子区所发生的变化,其误差主要受参考图像更新次数的影响;插值误差是指在进行数据插值过程中引入的误差。为此,Pan et al.(2012)定义了一个种子点在原始参考图像中,在变形图像中进行搜索,并判断相关系数是否到达预设阈值来限制参考图像的更新次数,从而减小子区偏移误差。Wang et al.(2018)提出了一种精确且简单的增量式DVC方法,更新后参考体图像中的参考子体被自动转换到最近的整数体像素位置,避免亚像素插值中复杂的数据计算。
4.2 形函数
DIC方法常用的形函数类型包括零阶、一阶和二阶形函数,它们可以提供不同的精度和适应性,不同阶数的形函数对比如图11所示。若变形阶数超过形函数的阶数,会发生形状函数欠匹配问题,因此选择高阶形函数可以较好地解决大变形中欠匹配的问题,例如Lu et al.(2000)通过二阶形函数准确地测量二阶位移梯度,相比一阶形函数测量精度更高。然而,传统的二阶形函数具有数值不稳定性,为此Gao et al.(2015)和Bai et al.(2017)将传统的二阶形函数进行优化后得到可逆的二阶形函数,提高了测量的稳定性。在材料的整个变形过程中,有时会涉及小变形区域,对该区域采用高阶形函数是过度匹配的,同时可能会在一定程度上影响DIC算法的收敛性并增加计算负担(Xu et al.,2015),因此对于不同的采样点,选择合适的子集大小显得尤为重要。Liang et al.(2015)和Li et al.(2017)以像素到中心点的距离作为每个像素的灰度强度分配权重,进而权衡不同采样点子集大小。此外还有学者针对子集大小的自适应匹配问题提出很多方法,例如Yuan et al.(2023)引入巴特沃斯函数作为加权窗口,通过该窗口可以连续调整子集大小,并提出了变形偏差函数,通过DIC中仿射和二阶形函数的计算偏差来评估子集中仿射形函数的匹配程度。通过求给定子集大小范围内变形偏差函数的峰值来确定每个采样点的最佳子集大小。
4.3 初值估计方法
尽管增量相关技术和形函数能够有效测量一定范围内的大变形,但当变形程度过大时,会导致无法为每个采样点找到合适的初值。为此,在子像素插值算法方面,学者们提出了各种基于插值的子像素精度方法,包括基于像素互相关的插值方法(Zhang et al.,2012)、基于光流的插值方法(Sun et al.,2010)以及高阶多项式插值方法,这些方法能够提高位移估计精度,尤其在处理复杂形变的场景时更有效。在形变模型方面,学者们提出了基于网格的非线性变形模型(赵勇等,2008),以更准确地建模和评估各种形变;在多尺度策略方面,用于DIC初值估计的多尺度方法能够在不同粒度的图像金字塔中进行匹配和优化(Wang et al.,2020),先在较粗尺度上估计初始位移场,再逐步细化到较细尺度,从而提高了算法的稳健性和精度。
4.4 深度学习
除了上述增量相关、形函数和初值估计方面的优化,近年来深度学习的方法也逐渐应用于DIC测量领域(刘小勇等,2018;Yang et al.,2022;萧红等,2023),但目前仍处于探索优化阶段。通过学习图像的特征,提取更具判别性的特征,这些特征可以帮助解决DIC中的匹配困难问题;然后学习复杂的形变模型,如非线性模型,以更好地描述大变形场景中的形变;对DIC的数据集进行训练,并使用数据增强技术来模拟大变形场景,再引入各种形变和扭曲,进一步扩展训练数据集的多样性,提高深度学习模型对于大变形场景的泛化能力;最后通过训练生成器和判别器的对抗过程,生成更真实的变形图像。
(1)提升图像采集与处理速度。针对高应变率下的动态力学行为测量,DIC技术需要进一步提高图像采集和处理速度,以确保实时、准确地捕捉试样的变形过程。这包括采用更高帧率的高速相机和优化图像处理算法等。其中,图像处理中的去噪算法既能有效去除噪声又能保留图像中的重要细节和结构信息,对于高应变率下的力学行为,去噪算法需要特别关注时间分辨率和空间分辨率的平衡。例如,时空域双边滤波去噪(张涛等,2019),通过结合时空域的像素距离和强度差异进行加权平均来减少噪声,同时保留图像和视频帧的边缘细节,在快速变化的场景中,时空域双边滤波可以减少由于噪声引起的伪影,提供更清晰的图像;三维非局部均值滤波去噪(Antonio,2022),利用视频序列中相似块之间的加权平均和相似性去除噪声,同时保留时空细节和纹理,适用于处理复杂的噪声模式,特别是在快速变形和运动的场景中;总变差(Total Variation,TV)去噪(Zohre et al.,2018),通过最小化总变差,去除噪声的同时保留图像和视频中的边缘和运动细节,在高噪声水平下,总变差去噪能够有效地抑制噪声,提高图像质量。
AntonioP,2022.A 3D space-time Non-Local Mean Filter (NLMF) for land changes retrieval with synthetic aperture radar images[J].Remote Sensing,14(23):5933-5933.
[2]
BaiR X, JiangH, LeiZ K,et al,2017.A novel 2nd-order shape function based digital image correlation method for large deformation measurements[J].Optics and Lasers in Engineering,90:48-58.
[3]
ChenZhenning,2018.Optimizations and Applications of Digital Speckle Patterns[D].Nanjing:Southeast University.
[4]
DaiX, JiangF L, LiuJ,et al,2020.Strain anisotropy models for refined diffraction line profile analysis in cubic metals[J].Transactions of Nonferrous Metals Society of China,30(8):2090-2106.
[5]
DaveM J, PandyaT S, DamianS,et al,2018.Dynamic characterization of biocomposites under high strain rate compression loading with split Hopkinson pressure bar and digital image correlation technique[J].International Wood Products Journal,9(3):115-121.
[6]
DongRuilan, PengZhihang, XiangYang,et al,2023.Research progress in composition and preparation process of alumina fiber reinforced alumina ceramic matrix composites[J].Journal of Materials Engineering,51(10):27-41.
[7]
FanYafu, WeiYanpeng, XueYuejun,et al,2015.On the application of digital image correlation testing technology in Hopkinson bar loading[J].Journal of Experimental Mechanics,30(5):590-598.
[8]
FuHua, PengJinhua, LiJunling,et al,2014.A new measurement method applied to Hopkinson bar experiment[J].Chinese Journal of High Pressure Physics,28(4):423-428.
[9]
GaoY, ChengT, SuY,et al,2015.High-efficiency and high-accuracy digital image correlation for three-dimensional measurement[J].Optics and Lasers in Engineering,65:73-80.
[10]
GilatA, SchmidtT E, WalkerA L,2009.Full field strain measurement in compression and tensile split Hopkinson bar ex-periments[J].Experimental Mechanics,49(2):291-302.
[11]
GilatA, SeidtJ D,2018.Compression,tension and shear testing of fibrous composite with the split Hopkinson bar technique[J].The European Physical Journal Conferences,183:02006.
[12]
GuoXian, LiXiaomao, PengYingcheng,et al,2015.Design and application of internal-stress sensor of concrete[J].Instrument Technique and Sensor,52(1):20-21,37.
[13]
HanHongliang, WangLizhong, ZhangZhen,et al,2022.Application of digital image correlation method in thin plate deformation measurement[J].Machine Tool and Hydraulics,50(16):13-17.
[14]
HanL, WuX P, HuS S,1990.Pulsed holographic and speckle interferometry using Hopkinson loading technique to investigate the dynamical deformation on plates[C]//19th International Congress on High-speed Photography and Photonics,16-21 September,1990.Cambridge:International Society for Optics and Photonics.
[15]
HuangS, ShuD, HuC,et al,2016.Effect of strain rate and deformation temperature on strain hardening and softening behavior of pure copper[J].Transactions of Nonferrous Metals Society of China,26(4):1044-1054.
[16]
JamieK, LeslieE L, StevenM,2019.Dynamic Behavior of Materials,Volume1[M].Scotland:Springer,Cham.
[17]
KajbergJ, WikmanB,2007.Viscoplastic parameter estimation by high strain-rate experiments and inverse modelling—Speckle measurements and high-speed photography[J].International Journal of Solids and Structures,44(1):145-164.
[18]
LiB J, WangQ B, DuanD P,et al,2017.Modified digital image correlation for balancing the influence of subset size choice[J].Optical Engineering,56(5):054104.
[19]
LiangZ L, YinB, MoJ Q,et al,2015.A new method to deal with the effect of subset size for digital image correlation[J].Optik- International Journal for Light and Electron Optic,126(24):4940-4945.
[20]
LiuXiaoyong, GongYan, LiRongli,et al,2018.Non-iterative gray-gradient algorithm based on BP artificial neural network in image correlation[J].Machine Tool and Hydraulics,46(1):7-11.
[21]
LuH, CaryP D,2000.Deformation measurements by digital image correlation:Implementation of a second-order displacement gradient[J].Experimental Mechanics,40(4):393-400.
[22]
LuoXin, XuJinyu, SuHaoyang,et al,2014.Strength properties of highly fluidized geopolymer concrete under impact loading[J].Journal of Building Materials,17(1):72-77.
[23]
MeylandM J, EriksenR N W, NielsenJ H,2023.A modified split-Hopkinson pressure bar setup enabling stereo digital image correlation measurements for flexural testing[J].International Journal of Impact Engineering,173:104480.
[24]
NieMingming, XuZhifeng, WangYing,et al,2023.Effects of matrix on fiber damage of continuous Al2O3f/Al composite[J].Special Casting and Nonferrous Alloys,43(10):1414-1420.
[25]
PanB, WuD F, XiaY,2012.Incremental calculation for large deformation measurement using reliability-guided digital image correlation[J].Optics and Lasers in Engineering,50(4):586-592.
[26]
PandyaS T, DaveJ M, StreetJ,et al,2019.High strain rate response of bio-composites using split Hopkinson pressure bar and digital image correlation technique[J].International Wood Products Journal,10(1):22-30.
[27]
PangS, TaoW, LiangY,et al,2019.A modified method of pulse-shaper technique applied in SHPB[J].Composites Part B:Engineering,165(15):215-221.
[28]
PetersW, RansonW,1982.Digital imaging techniques in experimental stress analysis[J].Optical Engineering,21(3):427-431.
[29]
RavichandranG, SubhashG,1995.A micromechanical model for high strain rate behavior of ceramics[J].International Journal of Solids and Structures,32(17/18):2627-2646.
[30]
SheHuan, ShiLei, DongAnping,2024.Dispersion,interface structure and mechanical properties of Titanium based graphene composites[J].Materials Reports,38(5):238-245.
[31]
ShergoldO A, FleckN A, RadfordD,2006.The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates[J].International Journal of Impact Engineering,32(9):1384-1402.
[32]
SongLi, HuShisheng,2004.A modified SHPB device for material testing[J].Journal of Experimental Mechanics,4(19):448-452.
[33]
SongLi, HuShisheng,2006.A new technique for testing soft material using a modified Hopkinson pressure bar[J].Engineering Mechanics,23(5):32-36.
[34]
SunD Q, RothS, BlackM J,2010.Secrets of optical flow estimation and their principles[C]// 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.San Francisco:IEEE.
[35]
SunXuan, WangYaping, WangBohuai,2019.Research and application on digital image correlation deformation measurement system[J].Machinery Design and Manufacture,57(3):149-152.
[36]
TangZhengzong,2012.Research on the Theory and Application of Digital Image Correlation Methods[D].Xi’an:Xi’an Jiaotong University.
[37]
ThaiT Q, RueschJ, GradlP R,et al,2022.Speckle pattern inversion in high temperature DIC measurement[J].Experimental Techniques,46:239-247.
[38]
WangB, PanB,2018.Incremental digital volume correlation method with nearest subvolume offset:An accurate and simple approach for large deformation measurement[J].Advances in Engineering Software,116:80-88.
[39]
WangL P, BiS L, LiH,et al,2020.Fast initial value estimation in digital image correlation for large rotation measurement[J].Optics and Lasers in Engineering,127:105838.
[40]
WangLili,2005.Fundamentals of Stress Waves[M].Beijing:National Defense Industry Press.
[41]
WangYonggang, ShiShaoqiu, WangLili,2003.An improved SHPB method and its application in the study of dynamic mechanical behavior of aluminum foams[J].Journal of Experimental Mechanics,18(2):257-264.
[42]
XiDaoying, ZhengYonglai,1995.Application of PVDF piezometers in dynamic stress measurement[J].Explosion and Shock Waves,15(2):174-179.
[43]
XiaoHong, LiChengnan, FengMingchi,2023.Large deformation measurement method of speckle image based on deep learning[J].Acta Optica Sinica,43(14):123-135.
[44]
XieBeixin, TangLiqun, ZhangXiaoyang,et al,2014.On the synchronized measurement of specimen’s strain and stress at both ends in SHPB test based on digital image[J].Journal of Experimental Mechanics,29(6):683-688.
[45]
XingHaozhe, WangMingyang, FanPengxian,et al,2021.Grain-size effect on dynamic behavior of sandstone based on high-speed 3D-DIC technique [J].Explosion and Shock Waves,41(11):46-57.
[46]
XuX H, SuY, CaiY L,et al,2015.Effects of various shape functions and subset size in local deformation measurements using DIC[J].Experimental Mechanics,55(8):1575-1590.
[47]
YamaguchiI,1981.A laser-speckle strain gauge[J].Journal of Physics E:Scientific Instruments,14(5):1270-1273.
[48]
YangR, YangL, ZengD,et al,2022.Deep DIC:Deep learning-based digital image correlation for end-to-end displacement and strain measurement[J].Journal of Materials Processing Technology,302:117474.
[49]
YangRenshu, LiWeiyu, LiYongliang,et al,2020.Comparative analysis on dynamic tensile mechanical properties of three kinds of rocks[J].Journal of China Coal Society,45(9):3107-3118.
[50]
YangShanwei,2018.Review of Hopkinson pressure bar technology based on optical inspection method[J].Technology Innovation and Application,(9):4-9.
[51]
YeXiaosheng,2020.Study on Dynamic Mechanical Properties of Carbon Fiber Woven Composites[D].Harbin:Harbin Institute of Technology.
[52]
YuanY, WuZ R, ZhengF,et al,2023.A pointwise optimal subset selection strategy assisted by shape functions in digital image correlation algorithm[J].Optics and Laser Technology,164:109420.
[53]
ZangXiaowei,2016.Study on the Pulse Shaping Technique and a Programming Implementation for Data Processing of the Hopkinson Bar Experiments[D].Changsha:Hunan University.
[54]
ZhangK B, GaoX B, TaoD C,et al,2012.Single image super-resolution with non-local means and steering kernel regression[J].IEEE Transactions on Image Processing,21(11):4544-4556.
[55]
ZhangTao, PanXihao, WangHao,et al,2019.De-interlacing method based on adaptive combination of time-domain and space-domain directions[J].Journal of Tianjin University(Science and Technology),52(11):1211-1218.
[56]
ZhangY B, HanX, LiangP,et al,2023.A deformation measurement method based on surface texture information of rocks and its application[J].International Journal of Mining Science and Technology,33(9):1117-1130.
[57]
ZhaoYong, LiuXinguo, PengQunsheng,2008.Shape deformation based on tetrahedral control mesh[J].Journal of Computer-Aided Design & Computer Graphic,20(9):1132-1139.
[58]
ZhouZ, MaJ, WangJ,et al,2024.Evolution characteristics of strain and displacement fields in double-hole short-delay blasting based on DIC[J].Processes,12(7):1291.
[59]
ZhuZhenghong, HuaJun, XingXiaoru,et al,2024.Study on hardening effect of metallic glass under cyclic loading[J].Chinese Journal of Solid Mechanics,45(3):401-415.
[60]
ZohreM, MehrdadL, MohsenR,2018.Combined shearlet shrinkage and total variation minimization for image denoising[J].Iranian Journal of Science and Technology,Transactions A:Science,42(1):31-37.