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Article(id=1244280828348449638, tenantId=1146029695717560320, journalId=1243978990336127019, issueId=1244280827157263057, articleNumber=null, orderNo=null, doi=10.7520/1001-4888-24-141, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1726070400000, receivedDateStr=2024-09-12, revisedDate=1733155200000, revisedDateStr=2024-12-03, acceptedDate=null, acceptedDateStr=null, onlineDate=1774589267097, onlineDateStr=2026-03-27, pubDate=1753977600000, pubDateStr=2025-08-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774589267097, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774589267097, creator=13701087609, updateTime=1774589267097, updator=13701087609, issue=Issue{id=1244280827157263057, tenantId=1146029695717560320, journalId=1243978990336127019, year='2025', volume='40', issue='4', pageStart='387', pageEnd='538', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1774589266813, creator=13701087609, updateTime=1774589721933, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244282736148595306, tenantId=1146029695717560320, journalId=1243978990336127019, issueId=1244280827157263057, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244282736148595307, tenantId=1146029695717560320, journalId=1243978990336127019, issueId=1244280827157263057, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=409, endPage=432, ext={EN=ArticleExt(id=1244280828524610408, articleId=1244280828348449638, tenantId=1146029695717560320, journalId=1243978990336127019, language=EN, title=A Study on the 2D digital image correlation displacement measurement method based on transfer learning, columnId=null, journalTitle=Journal of Experimental Mechanics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Digital Image Correlation (DIC) is a non-contact optical measurement technique that uses speckle patterns as deformation carriers to measure surface displacement and deformation fields of objects. It has been widely applied in key industrial fields such as aerospace, mechanical engineering, and power engineering. In general, specialized software is required for Digital Image Correlation (DIC) measurement and analysis. In particular, in the measurement of fatigue and dynamic problems, it is essential to address challenges arising from big data processing, such as long computation times and low efficiency. With the development of artificial intelligence technology, deep learning provides new opportunities for DIC method. However, a huge dataset is required for the construction of DIC deep learning network, which not only increases the cost of data collection but also takes a long computation time. To solve the above problems, this paper proposes a DIC-2D displacement measurement method based on migration learning, which is based on U-Net network including a multi-level feature extractor, an attention mechanism and a depth-separable convolution. In the pre-training process of the network, simulated scattering images are used as the training dataset to form the pre-trained network；On this basis, multiple transfer learning fine-tuning strategies are used to optimize the network parameters using a small number of real speckle images with different mean intensity gradients to establish the migration network, and real speckle images are used for verification. The analysis results show that the network trained by the global fine-tuning strategy exhibits higher accuracy and better robustness in the training of different mean intensity gradient speckle images. The DIC migration learning method proposed in this paper can significantly reduce the training time and cost for data acquisition.

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数字图像相关（DIC）是一种非接触式光学测量技术，该技术以散斑为变形载体进行物体表面位移和变形场测量，目前已被广泛应用在航空航天、机械工程、动力工程等重要工业领域。DIC测试与分析中需要专用软件，特别是在疲劳和动态测量中，涉及大数据的分析与处理，会造成计算时间长和效率低等问题。随着人工智能技术的发展，深度学习为DIC方法提供了新的发展机遇。然而，在DIC深度学习网络构建中，需要庞大的数据集进行网络构建，这不仅增加了数据采集成本还需耗费较长的计算时间。为解决上述问题，本文提出了一种基于迁移学习的DIC-2D位移测量方法。该方法将多级特征提取器、注意力机制与深度可分离卷积层融合到U-Net网络中，在网络的预训练过程中，使用模拟散斑图像作为训练数据集，形成预训练网络；在此基础上，采用多种迁移学习微调策略，利用少量具有不同平均灰度梯度的真实散斑图像进一步优化网络参数，形成迁移后的网络，并采用真实散斑图像进行验证实验。分析表明，在不同平均灰度梯度散斑图像的训练中，全局微调策略训练的网络表现出较高的精度和较好的鲁棒性；本文所提出的DIC迁移学习方法可显著减少训练时间和数据采集成本。

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谢惠民（1965－），男，博士，教授。主要研究领域：实验固体力学。Email：;
贾亚雷（1973－），男，博士，教授。主要研究领域：智能制造工程。Email：;
刘战伟（1973－），男，博士，教授。主要研究领域：光测实验力学与材料的动态力学性能。Email：
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Experimental Mechanics, 2022, 62(4):639-654., articleTitle=DIC challenge 2.0: Developing images and guidelines for evaluating accuracy and resolution of 2D analyses: Focus on the metrological efficiency indicator, refAbstract=null)], funds=[Fund(id=1244340266396663830, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, awardId=12327801; 12032013, language=CN, fundingSource=国家自然科学基金项目(12327801; 12032013), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1244340257173390140, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, xref=1., ext=[AuthorCompanyExt(id=1244340257181778749, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, companyId=1244340257173390140, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.School of Aeronautics and Astronautics, North China Institute of Aerospace 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caption=Transfer learning-based DIC-2D displacement measurement method：(a) network pre-training stage；(b) the fine-tuning stage of the real speckle image with a mean intensity gradient of approximately 50；(c) the fine-tuning stage of the real speckle image with a mean intensity gradient of approximately 30, figureFileSmall=OfnLwJ17V7srk2Lr8ctsbg==, figureFileBig=uIZ6PxNlDSP4sXeLt5r3yA==, tableContent=null), ArticleFig(id=1244340262093308871, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图1, caption=基于迁移学习的DIC-2D位移测量方法：（a）网络预训练阶段；（b）平均灰度梯度约为50的真实散斑图像微调阶段；（c）平均灰度梯度约为30的真实散斑图像微调阶段, figureFileSmall=OfnLwJ17V7srk2Lr8ctsbg==, figureFileBig=uIZ6PxNlDSP4sXeLt5r3yA==, tableContent=null), ArticleFig(id=1244340262193972170, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.2, caption=Displacement field prediction network structure, 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tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.4, caption=Attention module：(a) hybrid attention module；(b) the channel attention module；(c) the spatial attention module, figureFileSmall=hXnnSXAbd+fLKoDiEZwUMw==, figureFileBig=bAB3vCj26iXsSuOR1E9Qxg==, tableContent=null), ArticleFig(id=1244340262613402580, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图4, caption=注意力模块：（a）混合注意力模块；（b）通道注意力模块；（c）空间注意力模块[26], figureFileSmall=hXnnSXAbd+fLKoDiEZwUMw==, figureFileBig=bAB3vCj26iXsSuOR1E9Qxg==, tableContent=null), ArticleFig(id=1244340262676317142, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.5, caption=Random displacement samples generated using 8 pixel×8 pixel spaced control points in the simulated speckle dataset (the values in the figure are in pixel), figureFileSmall=j0IMGxRzoSG7zwztkIwa7Q==, figureFileBig=sxTP+tFv9nSiPRsd7dOKeQ==, tableContent=null), ArticleFig(id=1244340262751814616, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图5, caption=模拟散斑数据集中使用8 pixel×8 pixel间隔控制点生成的随机位移样本（图中数值以pixel为单位）, figureFileSmall=j0IMGxRzoSG7zwztkIwa7Q==, figureFileBig=sxTP+tFv9nSiPRsd7dOKeQ==, tableContent=null), ArticleFig(id=1244340262827312090, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.6, caption=Smooth displacement samples generated using 256 pixel×256 pixel spaced control points in the simulated speckle dataset (the values in the figure are in pixel), figureFileSmall=QiP5aYMxnLltpVZ6YiXnPg==, figureFileBig=g5r2VFc/EpE8+v+2uzlrTQ==, tableContent=null), ArticleFig(id=1244340262919586780, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图6, caption=模拟散斑数据集中使用256 pixel×256 pixel间隔控制点生成的平滑位移样本（图中数值以pixel为单位）, figureFileSmall=QiP5aYMxnLltpVZ6YiXnPg==, figureFileBig=g5r2VFc/EpE8+v+2uzlrTQ==, tableContent=null), ArticleFig(id=1244340262986695646, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.7, caption=Schematic diagram of the smartphone-based speckle image acquisition system, figureFileSmall=CJQH2M5sUljlOJYIID3UUg==, figureFileBig=vLrXyBl8Q+2ZAO/BHcBajg==, tableContent=null), ArticleFig(id=1244340263078970336, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图7, caption=基于智能手机的散斑图像采集系统示意图, figureFileSmall=CJQH2M5sUljlOJYIID3UUg==, figureFileBig=vLrXyBl8Q+2ZAO/BHcBajg==, tableContent=null), ArticleFig(id=1244340263154467810, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.8, caption=Two samples from the real speckle dataset，consisting of reference and deformed images with different mean intensity gradients of real speckle，along with the corresponding displacement fields (the values in the figure are in pixel), figureFileSmall=WK2xZM2AIQOr5TdIoL477A==, figureFileBig=9BSXYhInhvDRG4SOebhocg==, tableContent=null), ArticleFig(id=1244340263234159588, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图8, caption=真实散斑数据集中的2个样本，具有不同平均灰度梯度真实散斑的参考图片和变形图片，以及相应的位移场（图中数值以pixel为单位）, figureFileSmall=WK2xZM2AIQOr5TdIoL477A==, figureFileBig=9BSXYhInhvDRG4SOebhocg==, tableContent=null), ArticleFig(id=1244340263297074150, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.9, caption=Layer-wise incremental fine-tuning strategy, figureFileSmall=Ito0bMBlKaGbLiFzkk0tNQ==, figureFileBig=2C6IoKW9kAPpKRA7lwfWoA==, tableContent=null), ArticleFig(id=1244340263393543144, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图9, caption=逐层累加微调策略, figureFileSmall=Ito0bMBlKaGbLiFzkk0tNQ==, figureFileBig=2C6IoKW9kAPpKRA7lwfWoA==, tableContent=null), ArticleFig(id=1244340263481623530, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.10, caption=Loss variation curves of different fine-tuning strategies on the real speckle dataset with a mean intensity gradient of approximately 50，including the changes in loss values on the training and validation sets, figureFileSmall=a0PwrNC52jB9MF0WGRWLoA==, figureFileBig=lgYpqtd7i5VYDFiPN+zJUw==, tableContent=null), ArticleFig(id=1244340263540343788, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图10, caption=不同微调策略在平均灰度梯度约为50的真实散斑数据集上的损失变化曲线，包括训练集和验证集上的损失值变化, figureFileSmall=a0PwrNC52jB9MF0WGRWLoA==, figureFileBig=lgYpqtd7i5VYDFiPN+zJUw==, tableContent=null), ArticleFig(id=1244340263603258350, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.11, caption=Loss variation curves of different fine-tuning strategies on the real speckle dataset with a mean intensity gradient of approximately 30，including the changes in loss values on the training and validation sets, figureFileSmall=Ki3GMdNUsxTlKVNoScLUdA==, figureFileBig=vqOvGccoPETkH4935ql6Sw==, tableContent=null), ArticleFig(id=1244340263666172912, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图11, caption=不同微调策略在平均灰度梯度约为30的真实散斑数据集上的损失变化曲线，包括训练集和验证集上的损失值变化, figureFileSmall=Ki3GMdNUsxTlKVNoScLUdA==, figureFileBig=vqOvGccoPETkH4935ql6Sw==, tableContent=null), ArticleFig(id=1244340263741670386, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.12, caption=Prediction results of different displacement measurement methods on a real speckle image with a mean intensity gradient of 48.8553 (the values in the figure are in pixel), figureFileSmall=uto7zi1RggDAAwdVc1rz9Q==, figureFileBig=dOYuofWgvWi4xgBVX7pfiw==, tableContent=null), ArticleFig(id=1244340263808779252, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图12, caption=不同位移测量方法在平均灰度梯度为48.8553的真实散斑图像上的预测结果（图中数值以pixel为单位）, figureFileSmall=uto7zi1RggDAAwdVc1rz9Q==, figureFileBig=dOYuofWgvWi4xgBVX7pfiw==, tableContent=null), ArticleFig(id=1244340263892665334, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.13, caption=Prediction results of different displacement measurement methods on a real speckle image with a mean intensity gradient of 27.5461 (the values in the figure are in pixel), figureFileSmall=99A9ARVL00ivAXJW40Nyrg==, figureFileBig=7TROzXilL8Mrq2PK4MSQZQ==, tableContent=null), ArticleFig(id=1244340263980745720, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图13, caption=不同位移测量方法在平均灰度梯度为27.5461的真实散斑图像上的预测结果（图中数值以pixel为单位）, figureFileSmall=99A9ARVL00ivAXJW40Nyrg==, figureFileBig=7TROzXilL8Mrq2PK4MSQZQ==, tableContent=null), ArticleFig(id=1244340264060437497, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.14, caption=A real speckle image and a star-shaped displacement field image with a mean intensity gradient of 21.7933：(a) reference image：(b) star-shaped displacement field (the values in the figure are in pixel), figureFileSmall=VsL2Kmr7yKfMGjXQlffdrw==, figureFileBig=CBCrqj3NlQtwFKsBcOWnNA==, tableContent=null), ArticleFig(id=1244340264127546362, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图14, caption=平均灰度梯度为21.7933的真实散斑图像及星形位移场图像：（a）参考图像；（b）星形位移场（图中数值以pixel为单位）, figureFileSmall=VsL2Kmr7yKfMGjXQlffdrw==, figureFileBig=CBCrqj3NlQtwFKsBcOWnNA==, tableContent=null), ArticleFig(id=1244340264190460923, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.15, caption=A real speckle image and a star-shaped displacement field image with a mean intensity gradient of 12.5188：(a) reference image；(b) star-shaped displacement field (the values in the figure are in pixel), figureFileSmall=vkjybqJMNxQ50DnOjh7O8Q==, figureFileBig=E/CBszywuA8dxQsA8hZShw==, tableContent=null), ArticleFig(id=1244340264261764092, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图15, caption=平均灰度梯度为12.5188的真实散斑图像及星形位移场图像：（a）参考图像；（b）星形位移场（图中数值以pixel为单位）, figureFileSmall=vkjybqJMNxQ50DnOjh7O8Q==, figureFileBig=E/CBszywuA8dxQsA8hZShw==, tableContent=null), ArticleFig(id=1244340264345650173, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.16, caption=Displacement fields and corresponding error distributions predicted by different displacement measurement methods based on a real speckle image with a mean intensity gradient of 21.7933 (the values in the figure are in pixel), figureFileSmall=jAhiEefNcEvblAFwqtXO8A==, figureFileBig=/ORyn08XDLXr4QYbLsOzHw==, tableContent=null), ArticleFig(id=1244340264425341950, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图16, caption=使用不同位移测量方法基于平均灰度梯度为21.7933的真实散斑图像预测的位移场及其相应的误差分布（图中数值以pixel为单位）, figureFileSmall=jAhiEefNcEvblAFwqtXO8A==, figureFileBig=/ORyn08XDLXr4QYbLsOzHw==, tableContent=null), ArticleFig(id=1244340264492450815, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.17, caption=Displacement fields and corresponding error distributions predicted by different displacement measurement methods based on a real speckle image with a mean intensity gradient of 12.5188 (the values in the figure are in pixel), figureFileSmall=E/zezOaMLU0V9pkE0feBZw==, figureFileBig=z5ad/lw7jImouyPfqGJ7WA==, tableContent=null), ArticleFig(id=1244340264551171072, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图17, caption=使用不同位移测量方法基于平均灰度梯度为12.5188的真实散斑图像预测的位移场及其相应的误差分布（图中数值以pixel为单位）, figureFileSmall=E/zezOaMLU0V9pkE0feBZw==, figureFileBig=z5ad/lw7jImouyPfqGJ7WA==, tableContent=null), ArticleFig(id=1244340264635056128, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.18, caption=Performance and error analysis of different displacement measurement methods in predicting star-shaped displacements on a real speckle image with a mean intensity gradient of 21.7933 (the values in the figure are in pixel), figureFileSmall=Yps7j+yeTKZE7O/vVB6Ryg==, figureFileBig=crwLvcUzF4L9FwsNZnkQFQ==, tableContent=null), ArticleFig(id=1244340264710553601, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图18, caption=不同位移测量方法预测基于平均灰度梯度为21.7933的真实散斑图像中星形位移的性能和误差分析（图中数值以pixel为单位）, figureFileSmall=Yps7j+yeTKZE7O/vVB6Ryg==, figureFileBig=crwLvcUzF4L9FwsNZnkQFQ==, tableContent=null), ArticleFig(id=1244340264777662466, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Fig.19, caption=Performance and error analysis of different displacement measurement methods in predicting star-shaped displacements on a real speckle image with a mean intensity gradient of 12.5188 (the unit in the figure are in pixel), figureFileSmall=AZR9xjd3PkzR/jfP0w/3oA==, figureFileBig=8bItmWHOgvWninli2Ets2A==, tableContent=null), ArticleFig(id=1244340264857354243, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=图19, caption=不同位移测量方法预测基于平均灰度梯度为12.5188的真实散斑图像中星形位移的性能和误差分析（图中数值以pixel为单位）, figureFileSmall=AZR9xjd3PkzR/jfP0w/3oA==, figureFileBig=8bItmWHOgvWninli2Ets2A==, tableContent=null), ArticleFig(id=1244340264928657412, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Tab.1, caption=

Network framework table

, figureFileSmall=null, figureFileBig=null, tableContent=
层名称卷积核大小/pixel步长/pixel输出特征图大小/pixel
多级特征提取块7×7，3×3，3×3，3×31，1，1，1256×256
最大池化2×22128×128
深度可分离卷积3×31128×128
卷积3×31128×128
最大池化2×2264×64
深度可分离卷积3×3164×64
卷积3×3164×64
最大池化2×2232×32
深度可分离卷积3×3132×32
卷积3×3132×32
最大池化2×2216×16
深度可分离卷积3×3116×16
卷积3×3116×16
CBAM(Convolutional Block Attention Module)
混合注意力		－－16×16
反卷积2×2232×32
双卷积3×3，3×31，132×32
反卷积2×2264×64
双卷积3×3，3×3164×64
反卷积2×22128×128
双卷积3×3，3×31，1128×128
反卷积2×22256×256
双卷积3×3，3×31，1256×256
卷积1×11256×256
), ArticleFig(id=1244340265004154885, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=表1, caption=

网络架构表

, figureFileSmall=null, figureFileBig=null, tableContent=
层名称卷积核大小/pixel步长/pixel输出特征图大小/pixel
多级特征提取块7×7，3×3，3×3，3×31，1，1，1256×256
最大池化2×22128×128
深度可分离卷积3×31128×128
卷积3×31128×128
最大池化2×2264×64
深度可分离卷积3×3164×64
卷积3×3164×64
最大池化2×2232×32
深度可分离卷积3×3132×32
卷积3×3132×32
最大池化2×2216×16
深度可分离卷积3×3116×16
卷积3×3116×16
CBAM(Convolutional Block Attention Module)
混合注意力		－－16×16
反卷积2×2232×32
双卷积3×3，3×31，132×32
反卷积2×2264×64
双卷积3×3，3×3164×64
反卷积2×22128×128
双卷积3×3，3×31，1128×128
反卷积2×22256×256
双卷积3×3，3×31，1256×256
卷积1×11256×256
), ArticleFig(id=1244340265075458054, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Tab.2, caption=

Comparative analysis of model performance

, figureFileSmall=null, figureFileBig=null, tableContent=
训练方法参数数量(×106)训练时间/h推理时间/ms eMAE/pixel eRMSE/pixel
完整模型6.437714.602311.07280.01510.0224
移除所有模块模型6.185212.901710.62120.02470.0366
移除CBAM模块模型6.372114.610311.12340.01730.0281
移除深度可分离卷积模型6.257915.732411.67720.01800.0263
移除多级特征提取器模型6.430712.615810.12170.01780.0262
), ArticleFig(id=1244340265150955527, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=表2, caption=

不同模型的对比结果

, figureFileSmall=null, figureFileBig=null, tableContent=
训练方法参数数量(×106)训练时间/h推理时间/ms eMAE/pixel eRMSE/pixel
完整模型6.437714.602311.07280.01510.0224
移除所有模块模型6.185212.901710.62120.02470.0366
移除CBAM模块模型6.372114.610311.12340.01730.0281
移除深度可分离卷积模型6.257915.732411.67720.01800.0263
移除多级特征提取器模型6.430712.615810.12170.01780.0262
), ArticleFig(id=1244340265230647304, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Tab.3, caption=

Parameters of different datasets

, figureFileSmall=null, figureFileBig=null, tableContent=
模拟散斑数据集平均灰度梯度约为50的真实散斑数据集平均灰度梯度约为30的真实散斑数据集
训练样本数量/个20000100100
图像大小/pixel256×256256×256256×256
位移范围/pixel[－2，2][－2，2][－2，2]
训练轮次200200200
优化算法AdamAdamAdam
初始学习率0.010.010.01
), ArticleFig(id=1244340265293561865, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=表3, caption=

不同数据集的参数

, figureFileSmall=null, figureFileBig=null, tableContent=
模拟散斑数据集平均灰度梯度约为50的真实散斑数据集平均灰度梯度约为30的真实散斑数据集
训练样本数量/个20000100100
图像大小/pixel256×256256×256256×256
位移范围/pixel[－2，2][－2，2][－2，2]
训练轮次200200200
优化算法AdamAdamAdam
初始学习率0.010.010.01
), ArticleFig(id=1244340265360670730, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Tab.4, caption=

The error results of displacement u prediction using different training methods on the real speckle image test set with a mean intensity gradient of approximately 50 (values in the table are in pixel)

, figureFileSmall=null, figureFileBig=null, tableContent=
训练方法 u
预训练0.06270.01800.03610.09640.02400.0505
无迁移学习0.22250.07110.15570.36360.09220.2235
全局微调0.14500.01610.07340.18380.02070.1019
微调block10.11270.03940.07460.14370.05140.0988
微调block1＋block20.08750.02130.05330.26410.02810.0806
微调block1＋block2＋block30.08800.02590.06080.23220.03380.0896
微调block1＋block2＋block3＋block40.08010.02820.05720.23020.03630.0841
微调block1＋block2＋block3＋block4＋block50.09270.02630.06080.22220.03410.0894
微调block1＋block2＋block3＋block4＋block5＋CBAM0.08390.02700.05480.15870.03570.0771
微调block100.07300.02230.04210.10620.02880.0571
微调block9＋block100.12820.02150.07040.16300.02840.0960
微调block8＋block9＋block100.14000.01750.07270.17750.02330.0983
微调block7＋block8＋block9＋block100.14320.01730.07290.18090.02270.0997
微调block6＋block7＋block8＋block9＋block100.14320.01740.07360.18080.02270.1003
微调CBAM＋block6＋block7＋block8＋block9＋block100.14390.01710.07510.18200.02240.1023
), ArticleFig(id=1244340265448751115, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=CN, label=表4, caption=

不同训练方法在平均灰度梯度约为50的真实散斑图像测试集上预测位移u的误差结果(表中数值以pixel为单位)

, figureFileSmall=null, figureFileBig=null, tableContent=
训练方法 u
预训练0.06270.01800.03610.09640.02400.0505
无迁移学习0.22250.07110.15570.36360.09220.2235
全局微调0.14500.01610.07340.18380.02070.1019
微调block10.11270.03940.07460.14370.05140.0988
微调block1＋block20.08750.02130.05330.26410.02810.0806
微调block1＋block2＋block30.08800.02590.06080.23220.03380.0896
微调block1＋block2＋block3＋block40.08010.02820.05720.23020.03630.0841
微调block1＋block2＋block3＋block4＋block50.09270.02630.06080.22220.03410.0894
微调block1＋block2＋block3＋block4＋block5＋CBAM0.08390.02700.05480.15870.03570.0771
微调block100.07300.02230.04210.10620.02880.0571
微调block9＋block100.12820.02150.07040.16300.02840.0960
微调block8＋block9＋block100.14000.01750.07270.17750.02330.0983
微调block7＋block8＋block9＋block100.14320.01730.07290.18090.02270.0997
微调block6＋block7＋block8＋block9＋block100.14320.01740.07360.18080.02270.1003
微调CBAM＋block6＋block7＋block8＋block9＋block100.14390.01710.07510.18200.02240.1023
), ArticleFig(id=1244340265520054284, tenantId=1146029695717560320, journalId=1243978990336127019, articleId=1244280828348449638, language=EN, label=Tab.5, caption=

The error results of displacement v prediction using different training methods on the real speckle image test set with a mean intensity gradient of approximately 50 (values in the table are in pixel)

, figureFileSmall=null, figureFileBig=null, tableContent=
训练方法 v
预训练0.08220.01840.03770.17220.02310.0563
无迁移学习0.35270.05380.14050.52600.07540.1941
全局微调0.14610.01580.07530.18610.02000.1070
微调block10.15300.03520.07640.22890.04700.1039
微调block1＋block20.11560.02560.05270.19610.03320.0749
微调block1＋block2＋block30.11230.02350.06480.19900.03000.0891
微调block1＋block2＋block3＋block40.10970.02600.05910.19680.03260.0822
微调block1＋block2＋block3＋block4＋block50.11300.02370.06340.20060.03010.0876
微调block1＋block2＋block3＋block4＋block5＋CBAM0.11080.02530.05590.19870.03160.0783
微调block100.08950.02210.04220.18240.02800.0608
微调block9＋block100.11870.01950.07020.19040.02590.0988
微调block8＋block9＋block100.13990.01750.07320.18620.02210.1023
微调block7＋block8＋block9＋block100.14400.01700.07490.18480.02150.1057
微调block6＋block7＋block8＋block9＋block100.14360.01780.07550.18370.02230.1060
微调CBAM＋block6＋block7＋block8＋block9＋block100.14460.14460.07650.18680.02260.1079
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不同训练方法在平均灰度梯度约为50的真实散斑图像测试集上预测位移v的误差结果(表中数值以pixel为单位)

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训练方法 v
预训练0.08220.01840.03770.17220.02310.0563
无迁移学习0.35270.05380.14050.52600.07540.1941
全局微调0.14610.01580.07530.18610.02000.1070
微调block10.15300.03520.07640.22890.04700.1039
微调block1＋block20.11560.02560.05270.19610.03320.0749
微调block1＋block2＋block30.11230.02350.06480.19900.03000.0891
微调block1＋block2＋block3＋block40.10970.02600.05910.19680.03260.0822
微调block1＋block2＋block3＋block4＋block50.11300.02370.06340.20060.03010.0876
微调block1＋block2＋block3＋block4＋block5＋CBAM0.11080.02530.05590.19870.03160.0783
微调block100.08950.02210.04220.18240.02800.0608
微调block9＋block100.11870.01950.07020.19040.02590.0988
微调block8＋block9＋block100.13990.01750.07320.18620.02210.1023
微调block7＋block8＋block9＋block100.14400.01700.07490.18480.02150.1057
微调block6＋block7＋block8＋block9＋block100.14360.01780.07550.18370.02230.1060
微调CBAM＋block6＋block7＋block8＋block9＋block100.14460.14460.07650.18680.02260.1079
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The error results of displacement u prediction using different training methods on the real speckle image test set with a mean intensity gradient of approximately 30 (values in the table are in pixel)

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训练方法 u
预训练0.99180.02280.32151.18470.02980.4045
无迁移学习0.21110.05070.10700.35100.06260.1505
全局微调0.10440.02060.05350.20970.02670.0828
微调block10.33770.04860.17980.45720.06150.2593
微调block1＋block20.27450.02670.14340.35990.03390.1972
微调block1＋block2＋block30.24710.03110.13210.32340.03990.1809
微调block1＋block2＋block3＋block40.22470.03570.12320.29280.04520.1702
微调block1＋block2＋block3＋block4＋block50.25360.03250.13390.33070.04140.1832
微调block1＋block2＋block3＋block4＋block5＋CBAM0.24650.03210.13060.32060.04110.1788
微调block100.56730.02680.18020.76860.03390.2494
微调block9＋block100.37350.03840.14960.52250.04970.2131
微调block8＋block9＋block100.18840.02560.08260.27580.03310.1264
微调block7＋block8＋block9＋block100.12120.02480.06500.23120.03230.1005
微调block6＋block7＋block8＋block9＋block100.12030.02430.06470.22950.03160.0999
微调CBAM＋block6＋block7＋block8＋block9＋block100.11670.02260.06080.22730.02940.0936
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不同训练方法在平均灰度梯度约为30的真实散斑图像测试集上预测位移u的误差结果(表中数值以pixel为单位)

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训练方法 u
预训练0.99180.02280.32151.18470.02980.4045
无迁移学习0.21110.05070.10700.35100.06260.1505
全局微调0.10440.02060.05350.20970.02670.0828
微调block10.33770.04860.17980.45720.06150.2593
微调block1＋block20.27450.02670.14340.35990.03390.1972
微调block1＋block2＋block30.24710.03110.13210.32340.03990.1809
微调block1＋block2＋block3＋block40.22470.03570.12320.29280.04520.1702
微调block1＋block2＋block3＋block4＋block50.25360.03250.13390.33070.04140.1832
微调block1＋block2＋block3＋block4＋block5＋CBAM0.24650.03210.13060.32060.04110.1788
微调block100.56730.02680.18020.76860.03390.2494
微调block9＋block100.37350.03840.14960.52250.04970.2131
微调block8＋block9＋block100.18840.02560.08260.27580.03310.1264
微调block7＋block8＋block9＋block100.12120.02480.06500.23120.03230.1005
微调block6＋block7＋block8＋block9＋block100.12030.02430.06470.22950.03160.0999
微调CBAM＋block6＋block7＋block8＋block9＋block100.11670.02260.06080.22730.02940.0936
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The error results of displacement v prediction using different training methods on the real speckle image test set with a mean intensity gradient of approximately 30 (values in the table are in pixel)

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训练方法 v
预训练0.97640.02770.32041.16870.03770.4005
无迁移学习0.24170.07120.13970.37370.09850.2095
全局微调0.08710.01910.05370.14260.02540.0822
微调block10.36960.03630.18020.49480.04890.2517
微调block1＋block20.29430.02720.14870.37900.03480.2022
微调block1＋block2＋block30.23170.03470.12370.29980.04490.1693
微调block1＋block2＋block3＋block40.19760.03520.11110.25840.04700.1546
微调block1＋block2＋block3＋block4＋block50.24390.03410.12790.31530.04420.1750
微调block1＋block2＋block3＋block4＋block5＋CBAM0.23110.03250.12250.29980.04280.1679
微调block100.57720.02820.19540.77870.03720.2675
微调block9＋block100.42770.04510.15710.59640.05760.2191
微调block8＋block9＋block100.19230.03090.08310.27640.04030.1251
微调block7＋block8＋block9＋block100.11720.02490.06370.16940.03360.0970
微调block6＋block7＋block8＋block9＋block100.12090.02580.06420.17610.03500.0976
微调CBAM＋block6＋block7＋block8＋block9＋block100.10330.02370.05990.15390.03160.0910
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不同训练方法在平均灰度梯度约为30的真实散斑图像测试集上预测位移v的误差结果(表中数值以pixel为单位)

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训练方法 v
预训练0.97640.02770.32041.16870.03770.4005
无迁移学习0.24170.07120.13970.37370.09850.2095
全局微调0.08710.01910.05370.14260.02540.0822
微调block10.36960.03630.18020.49480.04890.2517
微调block1＋block20.29430.02720.14870.37900.03480.2022
微调block1＋block2＋block30.23170.03470.12370.29980.04490.1693
微调block1＋block2＋block3＋block40.19760.03520.11110.25840.04700.1546
微调block1＋block2＋block3＋block4＋block50.24390.03410.12790.31530.04420.1750
微调block1＋block2＋block3＋block4＋block5＋CBAM0.23110.03250.12250.29980.04280.1679
微调block100.57720.02820.19540.77870.03720.2675
微调block9＋block100.42770.04510.15710.59640.05760.2191
微调block8＋block9＋block100.19230.03090.08310.27640.04030.1251
微调block7＋block8＋block9＋block100.11720.02490.06370.16940.03360.0970
微调block6＋block7＋block8＋block9＋block100.12090.02580.06420.17610.03500.0976
微调CBAM＋block6＋block7＋block8＋block9＋block100.10330.02370.05990.15390.03160.0910
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Performance comparison of different fine-tuning strategies on real speckle images with a mean intensity gradient of approximately 50

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训练方法参数数量(×106)训练时间/min推理时间/ms
预训练6.441437.1711.17
无迁移学习6.445.8312.50
全局微调6.445.7810.97
微调block10.015.1010.90
微调block1＋block20.055.1911.24
微调block1＋block2＋block30.205.2111.10
微调block1＋block2＋block3＋block40.835.2211.44
微调block1＋block2＋block3＋block4＋block53.325.6211.10
微调block1＋block2＋block3＋block4＋block5＋CBAM3.395.2511.10
微调block100.014.9711.44
微调block9＋block100.045.2711.70
微调block8＋block9＋block100.184.8211.50
微调block7＋block8＋block9＋block100.754.9111.50
微调block6＋block7＋block8＋block9＋block103.055.3411.77
微调CBAM＋block6＋block7＋block8＋block9＋block103.114.9911.24
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不同微调策略在平均灰度梯度约50的真实散斑图像上的性能比较

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训练方法参数数量(×106)训练时间/min推理时间/ms
预训练6.441437.1711.17
无迁移学习6.445.8312.50
全局微调6.445.7810.97
微调block10.015.1010.90
微调block1＋block20.055.1911.24
微调block1＋block2＋block30.205.2111.10
微调block1＋block2＋block3＋block40.835.2211.44
微调block1＋block2＋block3＋block4＋block53.325.6211.10
微调block1＋block2＋block3＋block4＋block5＋CBAM3.395.2511.10
微调block100.014.9711.44
微调block9＋block100.045.2711.70
微调block8＋block9＋block100.184.8211.50
微调block7＋block8＋block9＋block100.754.9111.50
微调block6＋block7＋block8＋block9＋block103.055.3411.77
微调CBAM＋block6＋block7＋block8＋block9＋block103.114.9911.24
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Performance comparison of different fine-tuning strategies on real speckle images with a mean intensity gradient of approximately 30

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训练方法参数数量(×106)训练时间/min推理时间/ms
预训练6.441437.1711.19
无迁移学习6.446.1413.30
全局微调6.445.8711.37
微调block10.015.1311.04
微调block1＋block20.055.2010.57
微调block1＋block2＋block30.205.2410.64
微调block1＋block2＋block3＋block40.835.3011.10
微调block1＋block2＋block3＋block4＋block53.325.2911.17
微调block1＋block2＋block3＋block4＋block5＋CBAM3.395.2911.10
微调block100.015.0910.97
微调block9＋block100.044.7710.90
微调block8＋block9＋block100.184.8611.17
微调block7＋block8＋block9＋block100.754.9710.97
微调block6＋block7＋block8＋block9＋block103.054.9811.24
微调CBAM＋block6＋block7＋block8＋block9＋block103.115.0311.24
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不同微调策略在平均灰度梯度约30的真实散斑图像上的性能比较

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训练方法参数数量(×106)训练时间/min推理时间/ms
预训练6.441437.1711.19
无迁移学习6.446.1413.30
全局微调6.445.8711.37
微调block10.015.1311.04
微调block1＋block20.055.2010.57
微调block1＋block2＋block30.205.2410.64
微调block1＋block2＋block3＋block40.835.3011.10
微调block1＋block2＋block3＋block4＋block53.325.2911.17
微调block1＋block2＋block3＋block4＋block5＋CBAM3.395.2911.10
微调block100.015.0910.97
微调block9＋block100.044.7710.90
微调block8＋block9＋block100.184.8611.17
微调block7＋block8＋block9＋block100.754.9710.97
微调block6＋block7＋block8＋block9＋block103.054.9811.24
微调CBAM＋block6＋block7＋block8＋block9＋block103.115.0311.24
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基于迁移学习的二维数字图像相关位移测量方法研究
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胡佳梁 1 , 张展飞 2, 3 , 马晓桐 4 , 李祥 1 , 谢惠民 2, 3 , 贾亚雷 1 , 刘战伟 4
实验力学 | 2025,40(4): 409-432
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实验力学 | 2025, 40(4): 409-432
基于迁移学习的二维数字图像相关位移测量方法研究
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胡佳梁1, 张展飞2, 3, 马晓桐4, 李祥1, 谢惠民2, 3 , 贾亚雷1 , 刘战伟4
作者信息
  • 1.北华航天工业学院航空宇航学院，河北廊坊 065000
  • 2.清华大学航天航空学院，北京 100084
  • 3.清华大学柔性电子技术国家级重点实验室，北京 100084
  • 4.北京理工大学宇航学院，北京 100081

通讯作者:

谢惠民（1965－），男，博士，教授。主要研究领域：实验固体力学。Email：;
贾亚雷（1973－），男，博士，教授。主要研究领域：智能制造工程。Email：;
刘战伟（1973－），男，博士，教授。主要研究领域：光测实验力学与材料的动态力学性能。Email：
A Study on the 2D digital image correlation displacement measurement method based on transfer learning
Jialiang HU1, Zhanfei ZHANG2, 3, Xiaotong MA4, Xiang LI1, Huimin XIE2, 3 , Yalei JIA1 , Zhanwei LIU4
Affiliations
  • 1.School of Aeronautics and Astronautics, North China Institute of Aerospace Engineering, Langfang 065000, Hebei, China
  • 2.School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
  • 3.State Key Laboratory of Flexible Electronics Technology, Tsinghua University, Beijing 100084, China
  • 4.School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
出版时间: 2025-08-01 doi: 10.7520/1001-4888-24-141
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摘要
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数字图像相关（DIC）是一种非接触式光学测量技术，该技术以散斑为变形载体进行物体表面位移和变形场测量，目前已被广泛应用在航空航天、机械工程、动力工程等重要工业领域。DIC测试与分析中需要专用软件，特别是在疲劳和动态测量中，涉及大数据的分析与处理，会造成计算时间长和效率低等问题。随着人工智能技术的发展，深度学习为DIC方法提供了新的发展机遇。然而，在DIC深度学习网络构建中，需要庞大的数据集进行网络构建，这不仅增加了数据采集成本还需耗费较长的计算时间。为解决上述问题，本文提出了一种基于迁移学习的DIC-2D位移测量方法。该方法将多级特征提取器、注意力机制与深度可分离卷积层融合到U-Net网络中，在网络的预训练过程中，使用模拟散斑图像作为训练数据集，形成预训练网络；在此基础上，采用多种迁移学习微调策略，利用少量具有不同平均灰度梯度的真实散斑图像进一步优化网络参数，形成迁移后的网络，并采用真实散斑图像进行验证实验。分析表明，在不同平均灰度梯度散斑图像的训练中，全局微调策略训练的网络表现出较高的精度和较好的鲁棒性；本文所提出的DIC迁移学习方法可显著减少训练时间和数据采集成本。

数字图像相关  /  二维位移测量  /  深度学习  /  迁移学习  /  微调策略

Digital Image Correlation (DIC) is a non-contact optical measurement technique that uses speckle patterns as deformation carriers to measure surface displacement and deformation fields of objects. It has been widely applied in key industrial fields such as aerospace, mechanical engineering, and power engineering. In general, specialized software is required for Digital Image Correlation (DIC) measurement and analysis. In particular, in the measurement of fatigue and dynamic problems, it is essential to address challenges arising from big data processing, such as long computation times and low efficiency. With the development of artificial intelligence technology, deep learning provides new opportunities for DIC method. However, a huge dataset is required for the construction of DIC deep learning network, which not only increases the cost of data collection but also takes a long computation time. To solve the above problems, this paper proposes a DIC-2D displacement measurement method based on migration learning, which is based on U-Net network including a multi-level feature extractor, an attention mechanism and a depth-separable convolution. In the pre-training process of the network, simulated scattering images are used as the training dataset to form the pre-trained network；On this basis, multiple transfer learning fine-tuning strategies are used to optimize the network parameters using a small number of real speckle images with different mean intensity gradients to establish the migration network, and real speckle images are used for verification. The analysis results show that the network trained by the global fine-tuning strategy exhibits higher accuracy and better robustness in the training of different mean intensity gradient speckle images. The DIC migration learning method proposed in this paper can significantly reduce the training time and cost for data acquisition.

digital image correlation  /  2D displacement measurement  /  deep learning  /  transfer learning  /  optimization strategy
胡佳梁, 张展飞, 马晓桐, 李祥, 谢惠民, 贾亚雷, 刘战伟. 基于迁移学习的二维数字图像相关位移测量方法研究. 实验力学, 2025 , 40 (4) : 409 -432 . DOI: 10.7520/1001-4888-24-141
Jialiang HU, Zhanfei ZHANG, Xiaotong MA, Xiang LI, Huimin XIE, Yalei JIA, Zhanwei LIU. A Study on the 2D digital image correlation displacement measurement method based on transfer learning[J]. Journal of Experimental Mechanics, 2025 , 40 (4) : 409 -432 . DOI: 10.7520/1001-4888-24-141
正文
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0 引言
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数字图像相关（DIC）作为一种非接触式的变形测量方法，在学术界和工业界都得到了广泛应用[1－4]。尽管传统DIC方法在提高计算精度方面取得了显著进展[5－9]，但随着应用场景从静态测量到动态测量的推广，需要解决大数据的处理问题，如何提高计算效率，降低计算时间和成本仍是备受关注的问题。为解决上述问题，研究人员已将深度学习技术引入DIC领域。MIN等[10]将神经网络引入DIC方法，提出了基于三维卷积神经网络的端到端学习方法，利用真实实验数据生成的数据集进行训练，有效地减少了计算时间。在U-Net[11]结构下，BOUKHTACHE等[12－13]提出了StrainNet方法，该方法使用8×8的像素区域和线性插值方法对位移场进行处理，生成散斑数据集1.0，并进一步通过改变像素区域的大小和对散斑图像施加噪声生成散斑数据集2.0，通过2种散斑数据集的训练实现了亚像素的位移预测。黄举等[14]提出一种基于卷积神经网络的数字散斑图像位移场的测量方法，通过多种变形模式的模拟散斑图像对网络进行训练，提高了网络对多种变形位移场的测量能力。YANG等[15]提出了基于深度学习的数字图像相关方法（Deep DIC），通过2个独立的卷积神经网络，实现了位移和应变场端到端的预测。LAN等[16]提出了基于卷积神经网络的U-DICNet方法，通过设计特定的网络架构，结合细化的卷积层和更少的下采样等策略，简化了网络的测量过程并提高了计算效率。WANG等[17]结合高阶Hermite元素的方法创建了具有丰富变形特征的散斑数据集，使网络在训练过程中能够学习到更加全面的变形特征，提高了网络对复杂变形的处理能力。CHENG等[18]将应变-位移关系引入神经网络，提出了DIC-PCNN方法，通过在损失函数中同时考虑位移和应变误差，优化了网络训练过程，提高了位移和应变场的预测精度。DUAN等[19]基于子集的局部DIC方法提出了卷积神经网络的DIC方法，采用金字塔结构和二阶形状函数来提高处理复杂变形场的能力，使其在无需迭代计算的情况下实现了位移场测量。此外，一些学者提出了适应于大变形的深度学习DIC方法，有效扩展了深度学习DIC方法的测量范围和精度[20－22]。
随着深度学习DIC方法的发展，降低计算成本已成为相关研究中备受关注的问题。从文献调研来看，目前主要有2种策略。第一种是无监督学习策略，例如，WANG等[23]提出基于无监督卷积神经网络的二维位移测量DIC方法，引入散斑图像扭曲模型，减少了对训练数据进行标注所需的时间。ZHU等[24]提出一种基于无监督学习的非线性优化DIC方法，该方法利用单对图像进行训练，通过引入形函数和特定的损失函数，仅使用一对参考图像和变形图像即可实现位移测量，提高了数据利用效率并降低了计算成本。第二种是采用迁移学习策略，MA等[25]提出的基于CNN的全视场亚像素位移测量方法，利用2个串联的CNN模型对变形前后的散斑图像进行处理，并引入迁移学习，利用已有的预训练模型在新任务中进行微调，减少了对大量新任务训练数据的需求。相关工作已成功将迁移学习应用于DIC位移测量中，但迁移学习中的微调策略仍有待进一步讨论和验证。为此，本文开展基于迁移学习的数字图像相关的2D位移测量方法研究。
本文的内容安排如下：首先，介绍基于迁移学习的DIC方法及网络结构的设计方案；其次，给出了模拟与真实散斑数据集的生成方法及迁移学习的微调策略；随后，开展网络性能的消融实验研究，并分析迁移学习微调策略的实际效果；最后，给出全文的结论。
1 方法研究
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基于迁移学习的二维数字图像相关（DIC-2D）位移测量方法如图1所示（图中u为沿x轴的水平位移分量；v为沿y轴的垂直位移分量），该方法由图1（a）网络预训练和图1（b）、图1（c）迁移学习2个阶段组成。在网络预训练阶段，通过Simplex Noise[26]算法生成了不同类型的随机分布模拟散斑图像；利用编码器-解码器网络对模拟散斑图像进行处理，生成预测位移场（即二维正交位移分量），通过反向传播逐步调整网络权重和偏置参数，形成预训练网络。在迁移学习阶段，考虑到模拟数据与真实数据在噪声、畸变等方面的差异，采集了不同的平均灰度梯度真实散斑图像用于微调预训练的神经网络；结合微调策略进一步优化网络的参数，从而提升网络的泛化能力。
1.1 网络架构
本文提出的位移场预测网络基于U-Net结构[11]，采用对称的编码器-解码器设计，并在U-Net结构的基础上加入多级特征提取块[23]、混合注意力机制[27]和深度可分离卷积层[28]搭建用于位移场测量的神经网络，整体网络结构如图2所示。其中编码器用于逐步提取散斑图像的特征，而解码器则恢复相关特征并进行高精度的位移预测。具体网络架构参数见表1。在表1中，像素（pixel）被定义为数字图像中长度的最小单位，pixel的实际物理尺寸取决于所使用的相机或成像系统的分辨率。在后续的计算和分析中，若未涉及实际的物理测量，则单位均以pixel为标准。
在位移场预测网络的编码器部分，如图2所示，采用多级特征提取块[23]用于初步提取不同尺度和深度的位移特征，该模块如图3所示。多级特征提取块与深度可分离卷积层的结合能够使网络在降低计算量的同时，有效提取并融合图像特征。每个编码层由一个深度可分离卷积层和一个标准卷积层组成。深度可分离卷积层通过将标准卷积操作分解为深度卷积和逐点卷积，分别执行空间特征提取和通道特征映射的功能，可在降低计算复杂度的同时，减少参数数量。而标准卷积层则进一步通过卷积操作加强通道间的特征融合，学习更复杂的非线性特征表达。该种组合方式可有效平衡计算效率与特征表达能力，使网络实现高效计算。
对图2中的解码器部分，设计了多层反卷积和双卷积层的组合结构，同时在每层中引入跳跃连接。在该组合结构中反卷积层对特征图进行上采样，即通过增加图像的空间分辨率来恢复图像的尺寸，双卷积层由2个连续的卷积层组成，每个卷积操作后均施加激活函数和归一化处理，以提高网络的非线性表达能力和训练稳定性。此外，双卷积结构通过2次卷积操作进一步增强跳跃连接中的高分辨率特征，使不同的图像特征能够更好地融合。
为增强网络对关键特征的提取与感知能力，在编码器和解码器之间引入了通道注意力和空间注意力机制的混合注意力模块[27]，如图4（a）所示。通道注意力模块（图4（b））通过调整各通道的权重来增强重要特征，而空间注意力模块（图4（c））则通过加权空间位置来突出关键区域。CBAM模块将通道注意力和空间注意力机制相结合，对特征图进行双重加权调整，增强了特征图在通道和空间2个维度上的关键信息表达。
1.2 数据集的生成
1.2.1 模拟散斑数据集的生成
为了实现基于迁移学习的DIC-2D位移测量方法，本文构建了模拟散斑数据集和涵盖不同平均灰度梯度的真实散斑数据集，其中模拟散斑数据集用于预训练深度学习模型。为此，在ORTEU等[29]的研究基础上，结合Simplex Noise[26]算法生成模拟散斑图案。在每个像素位置（u，v），通过计算其n×n邻域内多个采样点的噪声值并取平均值来平滑噪声纹理，改进散斑图的质量。噪声平均值N的公式如下[28]：
式中：n为采样区域内像素点的数量；fnoise为Simplex Noise函数；ui、vj为邻域采样点的坐标。ui、vj的具体公式如下[29]：
式中：u、v为当前处理的像素位置；f为调整采样点分布的因子，用来控制采样点之间的间距，较大的f值会使采样点更分散，反之则更集中；δu和δv为随机偏移量，用来增加采样点的随机性，在本文采用的δu和δv的像素为[－0.5，0.5]。
为进一步调整噪声值并增强特征对比度，采用Sigmoid函数[30]对累积的噪声值进行非线性映射，公式如下：
式中：x为本算法的平均噪声值；a为控制Sigmoid函数陡峭程度的参数；b为控制Sigmoid函数中心偏移的参数；Tsigmoid为经过Sigmoid函数变换后的输出值；e为自然对数的底数。
根据式（1）~（4），可以计算得到噪声平均值N（u，v）为
处理后的噪声值需要映射到实际图像的灰度值范围，以表示图像在像素位置（u，v）处的最终灰度值，灰度值I（u，v）的公式如下：
式中：Imax和Imin为灰度值范围的最大值和最小值，通常为0到255之间的值。此外，为了使生成的模拟散斑图更贴近真实实验场景，对生成的模拟散斑图采用了高斯模糊和自适应直方图均衡化处理，处理后的模拟散斑图如图5（a）、图6（a）所示。
本文采用不同间隔的控制点生成随机位移和平滑位移2种位移场，首先，在图像的水平方向和垂直方向生成规则间隔的控制点，确保控制点覆盖图像边缘，如果图像边缘处的控制点未覆盖边缘，则额外添加1个控制点覆盖边缘。然后，为每个控制点生成随机的水平和垂直位移，取值为（－2~＋2）pixel，并使用3次插值的方法在控制点之间生成位移场。最后，通过YANG等[15]提出使用网格插值的方法来生成256 pixel×256 pixel大小的变形图像。图5（b）和图6（b）展示了变形后的散斑图像，图5（c）（d）（8 pixel×8 pixel间隔控制点）和图6（c）（d）（256 pixel×256 pixel间隔控制点）展示了随机位移和平滑位移2种位移场。
1.2.2 真实散斑数据集的生成
为验证迁移学习对不同散斑图像的适应性，本文基于文献[31]的思想搭建了如图7所示的实验装置，用于散斑图像的采集和数据构建。实验中，选择白色打印纸作为基底材料，在其表面喷涂哑光黑漆（金门子JMZ-202）制作散斑载体；随后，使用智能手机拍摄所制作的散斑图像。实验中采集了2种真实散斑图像，分别为平均灰度梯度约为50的散斑图像和平均灰度梯度约为30的散斑图像，其对应图像如图8（a）和图8（e）所示[32]。采用控制点在散斑图像上施加随机位移，并通过网格插值方法生成变形后的散斑图像，如图8（b）（f）所示。利用1.2.1节的方法对采集的真实散斑图像进行处理，生成真实散斑数据集。在图8（c）（d）和图8（g）（h）中，均使用了256 pixel×256 pixel间隔的控制点。
1.3 微调策略
在基于U-Net网络的位移场预测任务中，编码器通过连续的下采样操作逐步压缩空间分辨率并扩展特征通道，实现从局部细节到全局结构的特征提取；解码器则通过上采样逐步恢复空间信息，用于重建高精度的位移场。编码器和解码器协同作用，共同决定了位移预测的准确性。因此，U-Net网络仅通过冻结浅层参数，并调整深层参数可能无法充分发挥网络的特征学习能力，微调策略需要根据不同优化需求进行调整[33]，为此本文采用图9所示的逐层微调策略，并设计了13种微调方案，图中的每个block（基本模块）表示网络结构中的1个基本模块，包含特征提取与下采样或上采样等操作，分别对应U-Net编码器或解码器中的1个处理阶段。对编码器，图9（a）展示了6种不同的微调方法，涵盖了从单层到多层的微调过程；对解码器，图9（b）展示了6种微调方法，以及逐步微调解码器的各个层次；图9（c）所示为全局微调方法，该方法可对整个网络（包括编码器、解码器及注意力机制）进行微调。
为统一符号，本文以e表示误差（error），并通过下标区分其具体形式。该误差用于衡量预测位移值和真实位移值之间的差异，并在微调过程中用于优化参数以进一步提升网络性能。在本文的训练任务中，采用均方误差eMSE作为损失函数[15]，具体公式如下：
式中：n为图像中有效像素点的数量；yg为真实的位移值；yp为模型预测出的位移值；eMSE为模型预测结果和实际结果之间的偏差。
2 实验验证
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2.1 基于消融实验的模型结构选择
消融实验对网络结构的选择至关重要，为了探究模型中不同模块对预测结果的影响，设计并实施了消融实验。实验选取深度可分离卷积、CBAM注意力机制、多级特征提取器作为研究对象，分别测试了以下5种模型配置：1）完整模型。2）移除深度可分离卷积，仅保留标准卷积的模型。3）移除CBAM模块的模型。4）移除多级特征提取器的模型。5）移除上述所有模块，仅保留基本U-Net架构的最小模型。各个模型都使用同一个数据集进行200个轮次的训练，采用均方误差作为损失函数。以均方根误差（eRMSE）和平均绝对误差（eMAE）作为性能指标，评估不同模块配置对位移预测精度的影响。
表2展示了不同模型的对比结果，由表可以看出，包含所有模块的完整模型表现最佳，具有最低的eMAE和eRMSE，同时在参数数量、训练时间和推理时间之间实现了良好的平衡。当移除深度可分离卷积模块时，参数数量和训练时间显著增加，性能下降明显，说明该模块在降低计算复杂度和提升特征提取效率方面具有重要作用。移除多级特征提取器可以减少训练时间，但会导致精度下降，移除CBAM模块对模型效率影响较小，但eMAE和eRMSE有所增加，这表明多级特征提取器和注意力机制在提升特征选择方面可起到重要作用。完全移除所有模块的模型虽然训练时间缩短至12.9017 h，但eMAE和eRMSE显著增加，进一步表明了模块的协同作用是实现最佳性能的关键。
2.2 数据集和模型训练过程
为了提升网络模型在真实数据上的表现，需要通过模拟散斑数据集对神经网络进行初始训练，使网络学习到位移的基本特征。为此，利用1.2.1节的方法生成模拟散斑训练数据，首先在预训练阶段，生成20000个模拟散斑样本用于训练，5000个模拟散斑样本用于验证，每个图像的大小均为256 pixel×256 pixel。在完成预训练后，将模型迁移到真实散斑数据集上进行微调，真实散斑数据集通过第1.2.2节所述方法构建，分别生成了140个平均灰度梯度约为50的真实散斑样本和140个平均灰度梯度约为30的真实散斑样本，对每个散斑图像样本的位移预测任务，分别使用100个样本用于训练，25个样本用于验证，15个样本用于测试。
本文的预训练与迁移学习训练均基于PyTorch框架在NVIDIA GeForce RTX 3080 Ti平台完成。为了保证实验过程的一致性，全部训练都使用自适应梯度Adam优化器，并将初始学习率设置为0.01，若在20个周期内损失值趋于平稳，则将学习率降低为原来的10%，以加速收敛并防止过拟合。批量大小设置为16，对每个微调模型进行200个轮次的训练，在表3中列出了训练过程中所需数据集的大小、位移范围和数据种类，图10和图11展示了不同微调策略在2种数据集（平均灰度梯度分别约为50和30的真实散斑数据集）上的训练与验证损失变化曲线。由图10和图11可以看出，全局微调方法与其他微调策略相比，表现出了更快的收敛速度和更好的效果，且损失值波动较小。而未使用迁移学习的方法，则表现出较慢的收敛速度和较高的损失值，这进一步验证了利用预训练知识进行迁移学习在提高模型性能和加速训练过程中的重要性。
2.3 对不同平均灰度梯度真实散斑图像的性能验证
为了提升网络在真实散斑图像中的性能表现，采用迁移学习技术对预训练网络进行了微调，在本节实验中，验证了网络在2类不同平均灰度梯度真实散斑图像上的预测效果。使用1.2.2节中的方法收集不同的散斑图像，分别是平均灰度梯度约为50的散斑图像和平均灰度梯度约为30的散斑图像。微调过程中，采用了1.3节中的逐层累加微调策略，使用平均绝对误差和均方根误差作为训练结果的评估指标，并在此基础上选取误差值最小的策略作为最佳微调方案。eMAE和eRMSE的公式如下：
式中：eMAE为预测值与真实值之间的平均绝对误差；eRMSE为预测值与真实值之间的均方根误差。
表4和表5展示了平均灰度梯度约为50的真实散斑图像测试集的评估结果，包括（最大平均绝对误差）、（最小平均绝对误差）、（最大均方根误差）、（最小均方根误差）、（平均绝对误差平均值）、（均方根误差平均值），这些指标可用于评估网络在最差和最佳情况下的预测表现。表6和表7展示了平均灰度梯度约为30的真实散斑图像测试集的评估结果。基于和、和计算结果的对比，可以了解网络在不同平均灰度梯度真实散斑图像下的预测波动范围。
通过比较表4和表5及表6和表7的预测结果可以看出，在平均灰度梯度约50的真实散斑图像上，全局微调方法表现出色，具有最小的和。预训练模型的效果同样较好，表现出最小的平均误差，说明在无迁移学习的情况下，预训练模型本身具有良好的性能。而仅对网络部分层进行微调的方法，eMAE和eRMSE相较于预训练模型和全局微调方法都明显上升，说明部分层微调方法的适应性较差。相比之下，在平均灰度梯度约30的真实散斑图像上的结果表明，尽管全局微调方法的eMAE和eRMSE最小，但与平均灰度梯度约50的真实散斑图像相比误差明显增大。而无迁移学习方法在2类散斑图像中的误差均最大，表明迁移学习可明显提升该模型的适应能力。此外，全局微调的迁移学习方法具有巨大的潜力。表8和表9展示了不同平均灰度梯度真实散斑图像上各种微调策略（包括预训练方法）所需的参数数量、训练时间和单样本推理时间的性能比较。从2个表的比较结果来看，预训练方法所需的训练时间较长，而使用迁移学习方法后训练时间明显降低，且2种方法的推理时间相当，说明使用迁移学习可以显著提高训练效率且能减少计算资源的消耗。
为了更加直观展示每种微调方法在不同平均灰度梯度真实散斑图像上的预测位移结果，选取单个散斑图像样本进行位移预测，并通过Ncorr软件[34]设置不同的DIC子区方法对位移进行测量。计算平均绝对误差和均方根误差评估各方法的准确性，具体的位移预测结果、位移绝对误差、eMAE和eRMSE如图12所示（eMAEu为水平位移分量（u）的平均绝对误差；eMAEv为垂直位移分量（v）的平均绝对误差；eRMSEu为水平位移分量（u）的均方根误差；eRMSEv为垂直位移分量（v）的均方根误差）。图12中详细展示了各方法在平均灰度梯度为48.8553的真实散斑图像上的预测结果。从图12的结果可以看出，在预测位移u时无迁移学习模型的eMAE和eRMSE最大，表明缺乏迁移学习显著降低了预测精度。在位移v的预测中仅微调第一层的模型表现最差，eMAE和eRMSE均最高，说明单独微调第一层无法有效提升性能。加入CBAM的部分层，微调方法虽然在位移u和v的预测误差上有所改善，但整体预测误差不如全局微调。而传统DIC方法的误差分布图则表现出较大的不均匀性，表明该传统方法还存在局限性。相比之下，全局微调模型在位移u和v的预测上均取得了最低的误差，且效果最佳。
针对平均灰度梯度较低的真实散斑图像，选取了单个散斑图像样本进行位移预测。图13展示了不同位移测量方法在平均灰度梯度为27.5461的真实散斑图像上的预测结果。从图13的结果来看，全局微调方法依然表现最佳，误差分布最小，显示出较好的鲁棒性和适应性。预训练模型虽然误差略有增加，但仍能保持较好的预测性能。无迁移学习方法的误差最大，预测性能最差。而部分层微调方法的表现仍不如全局微调方法，其误差较大。此外，传统的DIC方法也表现出了不均匀的误差分布。通过图12和图13的实验结果，再次验证了全局微调方法在不同条件下的优越性，其预测结果展现了良好的适应性和稳定性。
2.4 星型位移场的性能验证
为了验证不同预测方法的鲁棒性和泛化能力，本文设计了“星形位移”[35]实验。这种复杂的位移模式与常规的线性或均匀位移相比，可以更全面地评估模型在处理不同类型位移时的性能和鲁棒性。图14和图15展示了使用的星形位移模式，并包含了不同平均灰度梯度的真实散斑图像，其中图像的分辨率为256 pixel×1024 pixel。在实验中，采用1.3节的微调方法，并通过设置子区大小为11 pixel×11 pixel和17 pixel×17 pixel的DIC参数来预测位移的分布和误差分布。下面将通过计算eMAE和eRMSE量化各方法的预测精度，为进一步优化模型提供依据。
图16和图17展示了每种方法在不同平均灰度梯度真实散斑图像上的星形位移预测结果及误差分布。对平均灰度梯度为21.7933的真实散斑图像，传统DIC方法在子区大小为11 pixel时表现较好，但当子区大小增至17 pixel时误差显著增大，显示出其在复杂位移模式下的局限性。相比之下，全局微调模型表现最佳，eMAE和eRMSE最小，而无迁移学习模型的误差最大，表明使用迁移学习可以提升预测精度。在部分层微调模型中，微调前几层或者后几层表现虽然有所改善，但其预测精度仍不及全局微调和预训练模型。
对平均灰度梯度为12.5188的真实散斑图像，稀疏的散斑特征使各模型的预测性能面临更大挑战。全局微调方法依然表现最佳，误差分布最小，但误差相较平均灰度梯度为21.7933的真实散斑图像误差有所增加。无迁移学习模型的误差，最大位移场存在明显偏差，表明在没有迁移学习的情况下，模型的适应能力有限。部分层微调方法在平均灰度梯度为12.5188的真实散斑图像上的效果同样不理想，微调少量层时误差显著增加，而使用注意力机制的部分层微调模型，虽然在一定程度上改善了预测精度，但整体预测误差仍高于全局微调模型。由实验结果分析可知，全局微调方法在不同平均灰度梯度散斑图像上均表现较好，体现了全局微调在提升模型适应性和鲁棒性方面的关键作用，表明该方法可为进一步优化和改进预测模型提供实验依据。
为了进一步分析不同方法预测“星形位移”在高空间频率时所发生的衰减情况，以及高频波动对结果的影响，在图18和图19中绘制了沿水平对称轴位移值等于0.5 pixel的曲线。为突出显示这一参考值，在这些曲线上叠加了一条0.5 pixel的水平线，曲线越接近这条水平线，表明预测结果越准确。此外，图18和图19还展示了按列计算得到的eMAE。为了更方便地评估预测结果，使用和来量化各方法的预测精度，用于衡量0.5 pixel参考值处的预测精度，而则提供了全局预测误差的平均值，公式如下：
式中：为预测点与参考值0.5 pixel之间的平均绝对误差；n为水平对称轴上用于计算误差的预测点数量。利用和误差指标，可以更准确地评估不同方法在高频位移模式下的预测性能。
图18和图19展示了不同平均灰度梯度真实散斑图像的预测结果，从结果中可以看到，在不同平均灰度梯度真实散斑图像条件下，全局微调方法的预测曲线均接近0.5 pixel的参考线，波动最小，表现出最佳的预测精度和稳定性，同时eMAE曲线也显示出最低的误差，进一步验证了全局微调方法的优越性。对预训练模型，在平均灰度梯度为21.7933的真实散斑图像上表现较好，预测曲线较为接近参考线，eMAE曲线较低，但在平均灰度梯度为12.5188的真实散斑图像上性能有所下降，预测曲线偏离较大，波动增强，eMAE曲线整体升高，说明其受到稀疏散斑特征的影响较大。无迁移学习方法在2类散斑上表现最差，预测曲线与参考线偏离最大，波动最显著，eMAE曲线也位于所有方法之上，显示出其在高频位移模式下的局限性。DIC方法同样在2类散斑上表现出较大波动，预测曲线偏离参考线较明显，eMAE曲线整体较高，表明其在复杂位移模式下的适应性较弱。部分层微调方法虽然相较于无迁移学习方法有所改进，但预测曲线与参考线的偏差仍较大，eMAE曲线也高于全局微调方法，进一步体现了其局限性。通过对比不同方法在高频位移模式下的预测性能和误差分布可以看出，全局微调方法的优势尤为突出，而其他方法则表现出不同程度的局限性，这些发现可为进一步优化和改进预测模型提供依据，并为模型选择合适的微调策略提供有力的支持。
3 结论
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为了解决深度学习DIC方法中的计算效率和训练成本问题，本文提出了一种基于迁移学习的二维位移测量方法。该方法基于模拟散斑数据集进行预训练，获得位移场深度学习网络；在此基础上，结合真实散斑数据集采用多种迁移学习策略，对位移场深度学习网络进行微调，提高了网络在不同散斑图像上的适应性和预测精度。
1）基于Simplex噪声函数的散斑图像生成算法，构建了低成本且易实现的模拟散斑数据集，为模型的预训练提供了多样化数据支持。结合改进的U-Net架构，建立了位移场深度学习模型，实现了亚像素级位移测量精度。
2）通过消融实验，研究了网络中不同模块对预测结果的影响。实验结果表明，完整模型表现最佳，移除任意模块都会导致网络性能下降。该结果进一步证明了各模块之间的相互作用对提升网络性能的重要性。
3）在预训练模型的基础上，采用多种迁移学习微调策略，并通过逐层的微调实验及性能评估实验，分析了不同微调策略对网络性能的影响。结果表明，全局微调策略在提升网络的适应性和预测精度方面表现最佳。
基金
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  • 国家自然科学基金项目(12327801; 12032013)
文献
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2025年第40卷第4期
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doi: 10.7520/1001-4888-24-141
  • 接收时间：2024-09-12
  • 首发时间：2026-03-27
  • 出版时间：2025-08-01
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  • 收稿日期：2024-09-12
  • 修回日期：2024-12-03
基金
国家自然科学基金项目(12327801; 12032013)
作者信息
    1.北华航天工业学院航空宇航学院，河北廊坊 065000
    2.清华大学航天航空学院，北京 100084
    3.清华大学柔性电子技术国家级重点实验室，北京 100084
    4.北京理工大学宇航学院，北京 100081

通讯作者:

谢惠民（1965－），男，博士，教授。主要研究领域：实验固体力学。Email：;
贾亚雷（1973－），男，博士，教授。主要研究领域：智能制造工程。Email：;
刘战伟（1973－），男，博士，教授。主要研究领域：光测实验力学与材料的动态力学性能。Email：
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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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