Learning and Predicting Shape Deviations of Smooth and Non-Smooth 3D Geometries Through Mathematical Decomposition of Additive Manufacturing
Learning and Predicting Shape Deviations of Smooth and Non-Smooth 3D Geometries Through Mathematical Decomposition of Additive Manufacturing
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DOI：
10.1109/tase.2022.3174228
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发表时间：
2023-07
影响因子：
5.6
通讯作者：
Yuanxiang Wang;C. Ruiz;Qiang Huang
中科院分区：
文献类型：
--
作者：
Yuanxiang Wang;C. Ruiz;Qiang Huang
在增材制造（AM）中，最终产品的几何形状经常变形或扭曲。三维（3D）形状与其预期设计的偏差可以表示为$\mathbb {R}^{3}$空间中的2D表面，这构成了用于学习和预测几何质量的复杂数据集。偏差表面的图案随形状几何结构、尺寸/体积、材料和AM工艺而变化。我们之前的工作已经建立了一个工程上知情的卷积框架，可以从使用相同材料和过程构建的一小组训练产品中学习形状偏差。它通过卷积公式和一类光滑3D形状（如圆顶或圆柱体）的尺寸因子结合了逐层形状形成过程的特征。这项研究将这种制造感知学习框架扩展到更大的一类产品，包括光滑和非光滑表面（多面体形状）。在统一模型下学习异构偏差曲面数据的核心思想是建立光滑基面偏差轮廓与非光滑多面体偏差轮廓之间的关联。该协会的特点是一个新的3D饼干切割功能，认为多面体形状是从光滑的基础形状雕刻出来的。从本质上讲，构建非光滑形状的AM过程在数学上被分解为两个步骤：使用卷积学习框架增材制造光滑的基础形状，然后使用饼干切割器函数减去额外的材料。建议的形状偏差数据的联合学习框架通过采用顺序模型估计过程来反映这种分解。模型学习过程首先建立卷积模型以捕获逐层制造和尺寸的影响，然后估计3D饼干切割函数以实现光滑和非光滑形状之间的几何差异。提出了一种新的高斯过程模型来考虑三维形状内相邻区域之间以及不同形状之间的空间相关性。该案例研究表明了AM中复杂3D形状偏差的规定性学习的可行性和前景，并扩展到更广泛的工程表面数据。从业人员注意事项-工程过程（如3D打印）以3D点云的形式生成复杂的形状数据。3D形状的鉴定和验证涉及对受产品几何形状和工艺物理影响的异构形状偏差数据进行建模和学习。这项研究开发了一种工程信息，小样本机器学习方法，在统一的建模框架中学习和预测光滑和非光滑3D形状的偏差。非光滑三维形状的制造在数学上被分解为光滑基础形状的形成和形状差异的实现。过程知识和形状几何都被捕获在学习框架中。它为增材制造及其他领域的形状工程提供了一种新的数据分析工具。
In additive manufacturing (AM), final product geometries are often deformed or distorted. The deviations of three-dimensional (3D) shapes from their intended designs can be represented as 2D surfaces in a $\mathbb {R}^{3}$ space, which constitutes a complicated set of data for learning and predicting geometric quality. Patterns of deviation surfaces vary with shape geometries, sizes/volumes, materials, and AM processes. Our previous work has established an engineering-informed convolution framework to learn shape deviation from a small set of training products built with the same material and process. It incorporates the characteristics of the layer-wise shape forming process through a convolution formulation and the size factor for a category of smooth 3D shapes such as domes or cylinders. This study extends this fabrication-aware learning framework to a larger class of products including both smooth and non-smooth surfaces (polyhedral shapes). The key idea of learning heterogeneous deviation surface data under a unified model is to establish the association between the deviation profiles of smooth base shapes and those of non-smooth polyhedral shapes. The association, which is characterized by a novel 3D cookie-cutter function, views polyhedral shapes as being carved out from smooth base shapes. In essence, the AM process of building non-smooth shapes is mathematically decomposed into two steps: additively fabricate smooth base shapes using a convolution learning framework, and then subtract extra materials using a cookie-cutter function. The proposed joint learning framework of shape deviation data reflects this decomposition by adopting a sequential model estimation procedure. The model learning procedure first establishes the convolution model to capture the effects of layer-wise fabrication and sizes, and then estimates the 3D cookie-cutter function to realize geometric differences between smooth and non-smooth shapes. A new Gaussian process model is proposed to consider the spatial correlation among neighboring regions within a 3D shape and across different shapes. The case study demonstrates the feasibility and prospects of prescriptive learning of complex 3D shape deviations in AM and extension to broader engineering surface data. Note to Practitioners—Engineering processes such as 3D printing generate complex shape data in the form of 3D point clouds. Qualification and verification of 3D shapes involves modeling and learning of heterogeneous shape deviation data that are affected by both product geometries and process physics. This study develops an engineering-informed, small-sample machine learning methodology to learn and predict deviations of smooth and non-smooth 3D shapes in a unified modeling framework. The fabrication of a non-smooth 3D shape is mathematically decomposed into the smooth base shape formation and shape difference realization. Both process knowledge and shape geometries are captured in the learning framework. It provides a new data analytical tool for shape engineering in additive manufacturing and beyond.