【作者】 苏勇；

【导师】 张青川；

【作者基本信息】 中国科学技术大学 ， 固体力学， 2016， 博士

【摘要】 数字图像相关方法作为一种非接触、非干涉的全场光学测量技术,业已广泛应用于实验力学领域形貌、运动和变形的测量,并由于其简单实用性获得越来越广泛的关注。数字图像相关方法如今非常成熟,己涌现出诸多界面友好、功能强大的商业软件。由于数字图像相关方法是基于跟踪测量试件表面的纹理特征,故而散斑图案对数字图像相关方法至关重要。遗憾的是,当前实验采用的散斑仍缺乏统一的制作规范,不同学者采用的散斑不同,不同商业公司推荐的散斑也不同,一线实验人员莫衷一是、难以抉择甚至无法判定哪种散斑效果更好。该现象的产生原因在于完备散斑标准的缺失。因为最优化的散斑应对应着最小化的计算误差,所以完备的散斑质量评价标准的提出应基于对数字图像相关计算误差的深入理解。虽然经过了十几年的研究,对数字图像相关中插值误差导致的系统误差的深层物理机制仍然不明,理论分析遇到相当大的阻力,插值偏差的简单有效的估计算法仍不存在,插值偏差是提出完备散斑质量评价标准的瓶颈。对于同样是系统误差的噪声引入偏差,现有的评价算法也存在诸多不足,根本无法适用于当前广泛采用的B样条、O-MOMS等高精度的广义型插值算法。本人博士期间工作的目标在于攻克插值偏差问题,提出适用于广义型插值算法的噪声引入偏差估计公式,综合考虑随机误差和系统误差提出一种完备的散斑质量评价标准。本文取得的主要成果如下：(1)在插值偏差方面,推导了连续和离散信号插值偏差的解析表达式,揭示了插值偏差的深层物理本质,提出插值偏差核的概念,表明插值偏差由插值偏差核与图像功率谱乘积的积分决定,提出了一种简单、快速、有效的插值偏差估计算法。在数字图像相关领域首次引入随机积分法,将插值偏差降低1个数量级。(2)在噪声引入偏差方面,提出了更广义、更简洁、更优美的噪声引入偏差理论体系,提出一种简单有效的噪声引入偏差估计算法,直观解释了噪声引入偏差的产生原因。(3)在随机误差方面,推导了非均匀噪声情况下数字图像相关随机误差的解析表达式,并通过真实实验进行了验证。(4)在散斑质量评价方面,综合插值偏差、噪声引入偏差和随机误差的理论结果,推导了数字图像相关总误差的解析表达形式,提出了完备的散斑质量评价标准。更多还原

【Abstract】 Digital image correlation (DIC) is a non-contact and non-interference full-field optical metrology, which is widely used in shape, motion, and deformation measurement in experimental mechanics community and receives growing attention for its simplicity and practicality. This technique has been thoroughly developed and many powerful and user-friendly commercial DIC systems are available in the market.The DIC method is based on the texture of the specimen; thus, the quality of the speckle patterns have a critical influence on the measurement performance of DIC. However, there is no unified standard for the produce of speckle patterns. Different scholars use different speckle patterns; different company recommend different speckle patterns; for practitioners, it is difficult to choose which pattern to use, and it is even difficult to justify which pattern is better. This phenomenon is due to the lack of valid assessment of speckle patterns. The assessment of speckle patterns demands thoroughly knowledge of errors in DIC for the optimized speckle patterns has the smallest errors. Nevertheless, after a decade’s study, the inherent nature of interpolation bias, a sys-tematic error of DIC, is still unexplained; significant difficulties occur in the study of interpolation bias; there is no method to estimate the interpolation bias efficiently; in-terpolation bias have been the bottleneck problem of speckle assessment. Besides, for noise-induced bias, which is a systematic error of DIC as well, existing methods fail to estimate the noise-induced bias for high accuracy generalized interpolation methods such as B-spline,O-MOMS.The aim of this dissertation is to solve the problem of interpolation bias, present a formula of noise-induced bias for generalized interpolation, and present a valid speckle pattern assessment. The major achievements of this dissertation are as follows. (1) In the context of interpolation bias, analytical formulae of interpolation bias for both con-tinuous and discrete signals are derived; a concept called interpolation bias kernel is presented, and it is shown that the interpolation bias is determined by the integral of the product of interpolation bias kernel and image power spectrum; a simple, fast, and effective method to estimate the interpolation bias is proposed. The stochastic integral method is introduced to DIC community and a significant decrease of the interpolation bias is achieved. (2) In the context of noise-induced bias, a more general, briefer, and more elegant theoretical framework for noise-induced bias is presented, a simple yet effective method is proposed to estimate the noise-induced bias, and the cause of noise-induced bias is explained intuitively. (3) In the context of random errors, a formula of random errors under non-uniform noise is derived and verified. (4) In the context of speckle patterns assessment, a formula of total errors is derived; valid speckle assess-ment parameters are presented by considering the interpolation bias, the noise-induced bias, and the random errors in total.更多还原