Some Linear Models for Estimating the Motion of Rigid Bodies with Applications to Geometric Quality Assurance
刚体运动估计的线性模型及其几何质量检验应用AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要对象是刚体几何匹配与工业质量检验，线性模型工具不足以对应所列经济计量细分。
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刚体运动估计的线性模型及其几何质量检验应用
- 研究问题
- 如何将理想零件模型与表面测量点对齐，并区分平面区域内部变异、方向偏差和尺寸差异对几何质量的影响？
- 方法与思路
- 作者在测量误差趋零时，用一阶展开将平面零件的旋转和平移估计局部化为线性模型，并改造线性模型诊断方法。
- 材料陈述的贡献
- 摘要称，刚体变换估计局部等价于线性模型拟合；残差距离平方和可分为三部分，支持针对特定几何缺陷的统计检验。
- 阅读关注点
- 应核对平面区域假设、局部线性化的有效范围、三类残差分量的定义，以及测量误差趋零与通常大样本渐近的区别。
- 阅读边界
- 依据稿件版本未注明的 OpenAlex 索引摘要；结论针对平面区域与小测量误差框架，摘要未说明曲面、较大误差或检验校准细节。
原文摘要
A geometrical method to assess the quality of a part is to sample points on the surface of the part and to bring an ideal computer representation of the part as close as possible to the sampled locations. The points are sampled with a coordinate measuring machine (CMM) that gives the coordinates, with respect to the machine's own three-dimensional system of axis, of the sampled locations. Computer-assisted design (CAD) gives the ideal representation of the part. The matching involves estimating a rotation and a translation vector characterizing the rigid body transformation needed to go from the computer model to the sampled locations. The sum of the squared residual distances between the sampled locations and the fitted computer part is a measure of the quality of the part. This article investigates the statistical properties of this method when the surface of the part is made of planar regions. Estimating the translation vector and the rotation matrix is shown to be “locally” equivalent to fitting a linear model to the localization data. Three components of the residual sum of squared distances are identified. They measure within planar region variability, the orientation conformity of the planar regions, and the size discrepancies of the regions. Diagnostics for linear models are adapted to yield statistical tests for specific geometric failures of a part. The developments use first-order asymptotic expansions of the estimators and of the sum of squared residuals for the local linear model, as the errors associated with the sampled locations go to 0.