Novel GPS-Based Robust Gaussian Filtering For Surface Texture

It is very necessary to conduct the research on the characterization technique of surfacetopography based-on the novel GPS (Geometrical Product Specification and Verification)system, such as theoretical study, applied transition and standard development. In thisdissertation surface Gaussian filtering is developed, put in practice and combined with RobustStatistics. It not only broadens the applied fields of robust theory but also provides theeffective characterization technique for surface topography. The relevant achievement can beconsidered to further apply in the international and national surface standard draft. The mainresearches and creative points are as follow:Based on the novel GPS system and the filtering masteroplan of relevant internationalstandards, Gaussian Filtering for a Closed Profile (GFC) is proposed and analyzed. As a linearfiltering, GFC possesses the good performance to the closed surface signal obeying to thenormal distribution. However, it will be influenced by such factors as information loss fromboundary effect, marginal distortion from local form tolerance and reference distortion fromoutlier signal, when it is used to deal with the open profile.To overcome the above drawback, Gaussian Filtering for an Open Profile (GFO) is putforward and the corresponding measures are took to improve the computational efficiency.The active weight function is adopted and the non-parameter fitting is used to distract theform signal in GFO. The influence of boundary effect and local form tolerance is removed inthe course of filtering. However, filtering reference is increased in the margin of measuredsignal due to the increase of weight function. The zero stretch of boundary can avoid theboundary effect but its overall performance is worse than GFO. The involvement ofpolynomial fitting in the convolution operation makes computation complicated and difficult.Therefore, the pre-processing of cubic B-spline fitting is given to improve GFO.The influence of outlier signal on GFO is analyzed. Based on the figure comparison andparameter evaluation of concave outlier signals, the simulated and real surface profiles arestudied respectively. The results show that the filtering reference from GFO distorts in theneighborhood of outlier. The distortion extent is concerned with the window width ofGaussian weight function, sampling length and geometrical size of outlier, etc. If there are afew homotypic scratches near to one another involved in the measured signal, the distortionwill be accumulated and widened. If heterotypic scratches are involved, the distortion will bemore complex.Robust Statistics is introduced to enhance the resistance property of GFO. In combinationwith the characteristics of surface topography, a new robust Gaussian filtering algorithm(RGF) is proposed to obtain robustly the surface reference. 2D and 3D characterizationmodels are developed to perform the robust processing of GFO.Different robust weight functions are analyzed and compared in robust statistical and filteringproperty. On the base of the results, a novel Auto-Developed Robust Weight Function (ADRF)is brought forward, which possesses a more robust scale parameter and higher computationefficiency, avoids effectively the masking and swamping problem of outlier. The case studyproves that ADRF Gaussian filtering have the merits of GFO in the normal conditions andfurther enhances the robust ability of GFO in the outlier conditions.