基于高斯过程模型的高动态三维表面智能采样与重构方法研究

Sampling and reconstruction are the foundation of modern digital measurement science and technology. With the increasing number of dynamic and high-dynamic surface products, the low-efficiency problem of Nyquist uniform sampling and reconstruction method has been urgently raised. To this end, based on the latest non-uniform sampling theory and Gaussian process reconstruction models, with the aid of the modern artificial intelligence computing methods, a high-efficiency intelligent sampling and reconstruction method adaptive to the dynamic distribution of information is proposed. To achieve the above objective, we will carry out the following researches on a high-flexibility Gaussian process model design, model reconstruction computation and its accurate uncertainty estimation and analysis based on which intelligent sampling is programed, and the performance optimization and verification based on simulation and measuring experiments. In particular, fast reconstruction algorithms of Gaussian process model for millions of data and their accurate uncertainty spectrum estimation and pattern analysis methods will be focused. The proposed method will break through the efficiency constraints of the traditional Nyquist uniform sampling theory, and defeat other adaptive sampling methods on the problems of flexibility, accuracy and computational efficiency. It will provide a new and powerful solution for efficient inspection of dynamic and high dynamic surface products and materials and promote a new progress of computational metrology science.

采样与重构是现代数字化测量科学技术的基础。随着越来越多动态乃至高动态表面产品的出现，奈圭斯特均匀采样与重构的测量低效性成为亟待解决的问题。为此，申请人基于最新的非均匀采样理论，依托高斯过程统计构造模型，并结合现代人工智能计算方法，提出一种适应信息动态化分布的高效智能采样与重构方法，用于高动态三维表面检测。为实现以上目标，本项目将依次开展高灵活度高斯过程模型设计，面向智能采样的模型快速重构及其重构精准度分析，以及基于仿真与实验的方法优化验证等研究工作，并着重解决面向百万级测量数据的高斯过程模型快速重构计算，及重构不确定度谱的精准估计与模式分析等关键科学问题。本项目方法将突破奈圭斯特均匀采样理论的低效性约束，在灵活度、精准度及计算效率上超越现有其他方法，为高动态表面产品与材料的高效检测提供新的有力解决方案，是计算计量科学发展的新促进力。

几何结构是决定机械功能特性的首要因素。机械结构的功能特性表征要求对其宏观、微观三维形状与形貌实施密集扫描，这导致基于点接触测头离散采样的表面三坐标测量通常效率低下。为适应高速采样测量的工程需求，本项目研究使用自然界信号的基础单元——高斯基函数与其有限支撑近似形式——B样条，对高动态范围复杂三维曲面形状进行几何建模，并基于不确定度分析与非均匀采样理论引导实现自适应的稀疏采样设计与高精度三维重建。这包括1）研究了高灵活度的参数化曲面模型设计方法，明确了高斯过程与平移不变B样条函数的近似关系，基于适合分析AST样条理论对B样条在三维流形曲面上进行了非张量积拓展，实现了对任意复杂三维曲面的高效近似；2）研发了任意复杂三维曲面的参数化样条曲面快速重建算法与不确定度估计算法，分别提出了基于不确定度引导的自由节点B样条建模自适应采样方法与基于非均匀采样理论的T-patch智能采样算法，实现了任意复杂曲面在样条空间中的高精度重建；及3）结合光学共焦位移传感器与三坐标测量机，开展了智能采样与重建测量实验与蒙特卡洛仿真，成功应用于航空叶片自由曲面与功能性结构表面的高分辨力快速测量中。. 项目形成了一套基于高斯过程与B样条的高动态范围复杂三维曲面的自适应采样与高精度重建方法；在IJPEM-GT，Precision Engineering，Optics Express等国际知名期刊发表相关学术论文13篇；授权国家发明专利3项；培养博士生1名、硕士生6名。