新一代产品几何规范（GPS）不确定度理论及应用研究
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摘要
新一代GPS标准体系是适应经济全球化要求的,面向数字化设计、制造与检验的标准与计量信息系统。不确定度理论是新一代GPS标准体系的重要基础理论,它不再局限于测量不确定度,还包括总体不确定度、相关不确定度、依从不确定度、规范不确定度、方法不确定度和执行不确定度等一系列新的概念。国际上新一代GPS不确定度理论的研究近几年才刚刚起步,相关的国际标准和应用指南也尚在酝酿之中。本文对这一理论及其应用技术进行了分析和研究,为工件的合格性判定提供了更为合理的判定原则,为工件在规范和认证过程中不确定度的传递计算提供了行之有效的方法,进而为中国参与相关国际标准的制订提供理论支持。主要研究内容与创新如下:
针对ISO 14253-1给出的测量不确定度的判定原则在实际应用过程中存在的问题,本文提出了新一代GPS不确定度的判定原则,包括针对单个GPS规范的依从不确定度的判定原则和针对工件的总体不确定度的判定原则;所提出的判定原则不仅考虑了测量不确定度对于工件认证结果的影响,而且考虑了规范不确定度和相关不确定度对于工件认证结果的影响。与单纯的测量不确定度的判定原则相比,新一代GPS不确定度的判定原则的判定结果更为合理,而且与新一代GPS标准体系的基本要求相一致。
提出了GPS标准链依从不确定度的计算框架。在对GPS标准链进行建模的基础上,分别给出了缺省状态下和特殊状态下依从不确定度的计算流程:在缺省状态下,依从不确定度应该根据执行不确定度和规范不确定度对于规范操作链影响的具体情况,经过规范操作链的传递计算得到;在特殊状态下,应该根据执行不确定度、方法不确定度和规范不确定度对于认证操作链影响的具体情况,经过认证操作链的传递计算得到。
针对滤波操作,提出了线性轮廓滤波器的不确定度传递的计算方法。根据线性轮廓滤波器方程,由未滤轮廓的协方差矩阵推导出了滤过轮廓的协方差矩阵,从而由未滤轮廓的不确定度得到了滤过轮廓的不确定度。给出了典型的线性轮廓滤波器——高斯滤波器的两个测量实例,实验结果表明经过滤波操作后滤过轮廓的不确定度是有所变化的,这一传递规律对于GPS标准链依从不确定度的计算非常重要。
针对拟合操作,提出了平面度和直线度最小二乘拟合的不确定度的计算方法。根据平面度和直线度最小二乘拟合的基本原理,推导出了平面度和直线度最小二乘拟合的不确定度的计算公式,并且对坐标测量中平面度和直线度最小二乘拟合的不确定度计算进行了实验分析,实验表明这种方法为平面度和直线度的坐标测量结果提供了不确定度指标,从而保证了测量结果的完整性,提高了认证的有效性。
The improved GPS system is an information system of standard and metrology, which adapts to the economic globalization and faces the digital designing, manufacturing and measuring. The uncertainty theory is an important component of the improved GPS system, which not only is destined for measurement uncertainty, but also includes such new concepts as total uncertainty, correlation uncertainty, compliance uncertainty, specification uncertainty, method uncertainty and implementation uncertainty. The study of the improved GPS uncertainty theory starts just now, and there are no relative international standards and guides for application. This theory and its application techniques are researched systematically in this paper. The more rational decision rules for conformance comparison of workpieces and the calculation method for uncertainty propagation of GPS standard-chain are supplied. Furthermore, the study will help China to attend the establishment of relative international standards. The main researches and creative points are as follows:
After discussing the shortages of the decision rules based on measurement uncertainty given by ISO 14253-1, the decision rules based on improved GPS uncertainty are put forward, which include the decision rules based on compliance uncertainty for a given GPS specification and the decision rules based on total uncertainty for a given workpiece. In the decision rules presented in this paper, specification uncertainty and correlation uncertainty are taken into account besides measurement uncertainty. Therefore, the decision rules based on improved GPS uncertainty are more rational than the decision rules based on measurement uncertainty because they are accordant with the basic principle of the improved GPS system.
The calculation framework for compliance uncertainty of GPS standard-chain is proposed. Based on the modeling of GPS standard-chain, the calculation flow for compliance uncertainty of GPS standard-chain is given respectively either in a default state or in a special state. In the default state, the compliance uncertainty should be calculated by the propagation of implementation uncertainty and specification uncertainty though the specification operator. However, in the special state, the compliance uncertainty should be obtained by the propagation of implementation uncertainty, specification uncertainty and method uncertainty though the verification operator.
Aiming at the filtration operation, the calculation method for uncertainty propagation of linear profile filter is put forward. According to the filter equation of linear profile filter, the covariance matrix of filtered profile can be derived from the covariance matrix of unfiltered profile, so the uncertainty of filtered profile can be deduced from the unfiltered profile by the algorithm. Furthermore, two measurement examples of Gaussian filter are given, and the experimental results indicate that the uncertainty is variational after filtration operation. The variation of uncertainty is very important to the calculation of compliance uncertainty.
Aiming at the association operation, the calculation method for the uncertainty of flatness and spatial straightness least-square verification is proposed. According to the basic principle of flatness and spatial straightness least-square verification, the calculation equation for the uncertainty of flatness and spatial straightness in three-dimensional measurement is deduced. The experimental results indicate that the method not only assures the integrity of the verification result, but also improves the veracity of verification by providing the index of uncertainty.
针对ISO 14253-1给出的测量不确定度的判定原则在实际应用过程中存在的问题,本文提出了新一代GPS不确定度的判定原则,包括针对单个GPS规范的依从不确定度的判定原则和针对工件的总体不确定度的判定原则;所提出的判定原则不仅考虑了测量不确定度对于工件认证结果的影响,而且考虑了规范不确定度和相关不确定度对于工件认证结果的影响。与单纯的测量不确定度的判定原则相比,新一代GPS不确定度的判定原则的判定结果更为合理,而且与新一代GPS标准体系的基本要求相一致。
提出了GPS标准链依从不确定度的计算框架。在对GPS标准链进行建模的基础上,分别给出了缺省状态下和特殊状态下依从不确定度的计算流程:在缺省状态下,依从不确定度应该根据执行不确定度和规范不确定度对于规范操作链影响的具体情况,经过规范操作链的传递计算得到;在特殊状态下,应该根据执行不确定度、方法不确定度和规范不确定度对于认证操作链影响的具体情况,经过认证操作链的传递计算得到。
针对滤波操作,提出了线性轮廓滤波器的不确定度传递的计算方法。根据线性轮廓滤波器方程,由未滤轮廓的协方差矩阵推导出了滤过轮廓的协方差矩阵,从而由未滤轮廓的不确定度得到了滤过轮廓的不确定度。给出了典型的线性轮廓滤波器——高斯滤波器的两个测量实例,实验结果表明经过滤波操作后滤过轮廓的不确定度是有所变化的,这一传递规律对于GPS标准链依从不确定度的计算非常重要。
针对拟合操作,提出了平面度和直线度最小二乘拟合的不确定度的计算方法。根据平面度和直线度最小二乘拟合的基本原理,推导出了平面度和直线度最小二乘拟合的不确定度的计算公式,并且对坐标测量中平面度和直线度最小二乘拟合的不确定度计算进行了实验分析,实验表明这种方法为平面度和直线度的坐标测量结果提供了不确定度指标,从而保证了测量结果的完整性,提高了认证的有效性。
The improved GPS system is an information system of standard and metrology, which adapts to the economic globalization and faces the digital designing, manufacturing and measuring. The uncertainty theory is an important component of the improved GPS system, which not only is destined for measurement uncertainty, but also includes such new concepts as total uncertainty, correlation uncertainty, compliance uncertainty, specification uncertainty, method uncertainty and implementation uncertainty. The study of the improved GPS uncertainty theory starts just now, and there are no relative international standards and guides for application. This theory and its application techniques are researched systematically in this paper. The more rational decision rules for conformance comparison of workpieces and the calculation method for uncertainty propagation of GPS standard-chain are supplied. Furthermore, the study will help China to attend the establishment of relative international standards. The main researches and creative points are as follows:
After discussing the shortages of the decision rules based on measurement uncertainty given by ISO 14253-1, the decision rules based on improved GPS uncertainty are put forward, which include the decision rules based on compliance uncertainty for a given GPS specification and the decision rules based on total uncertainty for a given workpiece. In the decision rules presented in this paper, specification uncertainty and correlation uncertainty are taken into account besides measurement uncertainty. Therefore, the decision rules based on improved GPS uncertainty are more rational than the decision rules based on measurement uncertainty because they are accordant with the basic principle of the improved GPS system.
The calculation framework for compliance uncertainty of GPS standard-chain is proposed. Based on the modeling of GPS standard-chain, the calculation flow for compliance uncertainty of GPS standard-chain is given respectively either in a default state or in a special state. In the default state, the compliance uncertainty should be calculated by the propagation of implementation uncertainty and specification uncertainty though the specification operator. However, in the special state, the compliance uncertainty should be obtained by the propagation of implementation uncertainty, specification uncertainty and method uncertainty though the verification operator.
Aiming at the filtration operation, the calculation method for uncertainty propagation of linear profile filter is put forward. According to the filter equation of linear profile filter, the covariance matrix of filtered profile can be derived from the covariance matrix of unfiltered profile, so the uncertainty of filtered profile can be deduced from the unfiltered profile by the algorithm. Furthermore, two measurement examples of Gaussian filter are given, and the experimental results indicate that the uncertainty is variational after filtration operation. The variation of uncertainty is very important to the calculation of compliance uncertainty.
Aiming at the association operation, the calculation method for the uncertainty of flatness and spatial straightness least-square verification is proposed. According to the basic principle of flatness and spatial straightness least-square verification, the calculation equation for the uncertainty of flatness and spatial straightness in three-dimensional measurement is deduced. The experimental results indicate that the method not only assures the integrity of the verification result, but also improves the veracity of verification by providing the index of uncertainty.
引文
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[97] ISO/DTS 16610-21: Geometrical product specification (GPS) – Filtration – Part 21: Linear profile filters: Gaussian filters, 2003
[98] ISO/DTS 16610-22: Geometrical product specification (GPS) – Filtration – Part 22: Linear profile filters: Spline filters, 2003
[99] ISO/DTS 16610-26: Geometrical product specification (GPS) – Filtration – Part 26: Linear profile filters: Filtration on nominally orthogonal grid planar data sets, 2003
[100] ISO/DTS 16610-27: Geometrical product specification (GPS) – Filtration – Part 27: Linear profile filters: Filtration on nominally orthogonal grid cylindrical data sets, 2003
[101] ISO/DTS 16610-29: Geometrical product specification (GPS) – Filtration – Part 29: Linear profile filters: Spline wavelets, 2003
[102] ISO/DTS 16610-60: Geometrical product specification (GPS) – Filtration – Part 60: Linear areal filters: Basic concepts, 2003
[103] ISO/DTS 16610-30: Geometrical product specification (GPS) – Filtration – Part 30: Robust profile filters: Basic concepts, 2003
[104] ISO/DTS 16610-31: Geometrical product specification (GPS) – Filtration – Part 31: Robust profile filters: Gaussian regression filters, 2003
[105] ISO/DTS 16610-32: Geometrical product specification (GPS) – Filtration – Part 32: Robust profile filters: Spline filters, 2003
[106] ISO/DTS 16610-40: Geometrical product specification (GPS) – Filtration – Part 40: Morphological profile filters: Basic concepts, 2003
[107] ISO/DTS 16610-41: Geometrical product specification (GPS) – Filtration – Part 41:Morphological profile filters: Disk and horizontal line segment filters, 2003
[108] ISO/DTS 16610-42: Geometrical product specification (GPS) – Filtration – Part 42: Morphological profile filters: Motif filters, 2003
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