表面轮廓滤波技术滤波一致性问题的研究

In surface metrology, there are two sets of the profile filtering techniques included in the international standards for the mean line.They recommend respectively the Gaussian filter and the spline filter to determine the mean line as the reference line for surface assessment. However, the filtering characteristics of these international standards are different, it brings difficulty to the comparision between the assessment results and standards implementation. In order to overcome this new problem, the new spline filters and the corresponding algorithms are constructed with the development on the fundamental theory of the spline filters,to make their filtering characteristics approximate that of the Gaussian filter, and to achieve the unity of two sets of the standards. Under the guidance of the center limit theorem about the spline filter, the new spline filters with the convergnce characteristic are constructed, and the central limit theorem is proved, then the spline filters can be used in series to approximate the Gaussian filtering characteristic. The robust weight functions are introduced to improve the robust spline filters, which can achieve the same filtering characteristics with the robust Gaussian filter. Hence, the unity of the Gaussian filters and the spline filters are realized. This research is to resolve the existing problem during the implementation of the Geometry product specification standards(GPS), and to provide some suggestions for the development of the profile filtering standards.

在表面计量学领域，以轮廓中线制为基础的轮廓滤波技术已经形成两套国际标准体系，它们分别推荐使用高斯滤波器和样条滤波器提取滤波中线作为轮廓评定基准线。但这两套现行标准的滤波特性不一致，给表面评定结果比对及标准传递带来困难。针对这一新的问题，本研究拟从样条滤波器基础理论入手，研究和构造新型样条滤波器算法，使其滤波特性逼近于高斯滤波器，进而实现两套标准评定结果的统一。提出基于样条滤波器的中心极限定理实现逼近高斯滤波器的思路，构造具有收敛特性的新型样条滤波器、验证其中心极限定理并创新性地将样条滤波器级联使用,以逼近高斯滤波器的滤波特性、引入抗差权函数构造稳健型样条滤波器并达成与稳健高斯滤波器一致的滤波结果，最终实现样条滤波体系与高斯滤波体系的统一。本研究着力解决几何产品技术规范（GPS）标准传递与使用中存在的实际问题，并为表面滤波标准的制定和改进提供一些参考和建议。

在表面计量学领域，以轮廓中线制和区域中面制为基础的表面形貌滤波技术已经形成两套国际标准体系，它们分别推荐使用高斯滤波器和样条滤波器提取轮廓中线或区域中面作为表面评定基准。然而，在二维轮廓评定中，两套现行标准的滤波特性并不一致，已然影响表面评定结果比对以及标准传递；在三维区域评定中，扩展所得三维样条滤波器的滤波特性又呈现各向异性，势必导致基准中面扭曲失真。针对这些问题，本研究从样条滤波器基础理论入手，研究和构造新型样条滤波器，使其滤波特性逼近于高斯滤波器，理想地实现了两套标准评定结果的统一，同时也解决了三维样条滤波器各向异性问题。其中，分别给出两种逼近方法，一种是基于中心极限定理的级联方法，另一种是构造高阶逼近样条滤波器。两种样条滤波器与高斯滤波器的传输特性偏差均小于1%。此外，本研究对样条滤波器的边界条件也进行了分析，并筛选出最优边界条件替代传统边界条件；在以上线性滤波方法的基础上，引入抗差权函数实现了对应的稳健型样条滤波器。. 本研究解决了几何产品技术规范（GPS）标准传递与使用中存在的实际问题，给已有的二维轮廓滤波标准改进提供一些参考和建议，也借此推动三维区域滤波标准的制定。