## 5 Experimental Results  
A honing surface with an obvious deformity was used in the experiments as shown in Figure 10(a). The data were sampled at 4-um interval, and 3854 data points were obtained. In order to evaluate the surface roughness accurately, the polynomial fitting method was used to remove the large shape components of the surface. The same cut-off wavelength (0.8 mm) was used in all filtering processes. The results of the robust Gaussian regression filter were used as a reference. As shown in Figure 10(b), the waviness curve after using approximating spline was distorted at a large deep valley, resulting in a large distortion of the roughness. After different robust processing, the waviness profile of the filter output was smooth and natural, and the influence of abnormal features was suppressed. It can be seen that robust processing can obtain more realistic and reliable filtering values even in the case of surface profiles with large outliers, such as deep valleys or high peaks. The profile processed by the robust Gaussian regression filter was used as the reference data. A robust second-order Gaussian regression filter with a cut-off wavelength of 0.8 mm was used to perform the filtering operation. The evaluation length was set to be the same as the total length of the profile. Figure 12 shows the similarity between the waviness profile processed by different robust approximating spline filters and robust Gaussian regression filter. It can be seen that for most of the profiles, the profiles processed by the Tukey, ADRF, and Andrews are in good agreement with the reference curve, while those of the WLAV, Hampel, and Huber show significant differences. The typical roughness parameters values of using different filtering methods are presented in Table 6. First, the amplitude parameters were investigated. \(Ra\) (the arithmetical mean deviation of the profile) is the most commonly used 2D roughness parameter. After robust treatment, \(Rp\) (the maximum peak height of the profile) and \(Rv\) (the maximum valley depth of the profile) increased. \(Rt\) is the total height of the profile and equal to the sum of \(Rp\) and \(Rv\). Meanwhile, \(Rq\) (the root mean square deviation of the profile) and \(Rku\) (the kurtosis of the profile) also increased accordingly. \(Rsk\) (the skewness of the profile) showed a negative decreased trend. The results show that compared to the unrobust approximating spline filter, the robust processing can effectively suppress the influence and propagation of the malformed characteristic signal and reduce the distortion of the median line of the filter. The roughness profile retains the characteristics of the deep valley and high peak well. Therefore, robust filtering can more truly reflect the low-frequency waviness and high-frequency roughness components and is more conducive to the evaluation of surface morphology. The roughness parameters processed by Huber and Hampel methods differed greatly from the robust Gaussian processing values. Furthermore, the spacing parameter \(Rsm\) (mean width of the profile elements) increased after robust treatment as well. The results show that the robust processing can more truly reflect the density of the peak and valley of the surface profile compared to the unrobust approximating spline filter. The results were further verified, and the roughness parameters of Tukey, ADRF, and Andrews were further analyzed as shown in Figure 12. The relative errors between the roughness parameters obtained by Tukey, ADRF, and Andrews and the reference data are given in Table 7. The relative errors of \(Rp\) parameters between Tukey, ADRF, and Andrews methods and the robust Gaussian regression filter were 11.3%,3.85%, and 19.6%, respectively; the relative errors of \(Rv\) parameters were 0.63%, 0.21%, and 0.58%, respectively; lastly, the relative errors of \(Rt\) parameters were 2.58%, 1.17%, and 4.74%, respectively.