## 5 Experimental Results
Generally speaking, the filtering effect of the ADRF method on the deep valley and high peak was more similar to that of the robust Gaussian regression filter. The relative errors of \(Rq\) parameters were 0.80%, 0.57%, and 0.34%, while the relative errors of profile kurtosis \(Rku\) parameters were 12.9%, 0.76%, and 1.40%. Thus, the results of the Tukey, ADRF, and Andrews methods in reflecting peak-valley symmetry are close to that of the robust Gaussian regression filter. The relative errors of \(Rsm\) parameters were 2.64%, 0.28%, and 6.10%. ADRF was closer to the robust Gaussian regression filter in reflecting peak-valley symmetry. Another important factor for filter is the iteration time. The numbers of iterations of the [PERSON] and Andrews methods were \(k=3\) (0.027 s) and \(k=4\) (0.024 s) respectively, and the calculation efficiencies of these methods were relatively low. The number of iterations of the ADRF method was \(k=2\) (0.017 s), but it achieved high computational efficiency. The experimental results show that the ADRF method has good filtering performance for honing profile. The evaluation result of the surface roughness is also close to that of using the robust Gaussian regression filter. Through a large number of experiments, it is found that the ADRF method is neutral when it is applied to the profile with regular form and Gaussian distribution. It shows good robustness when ADRF method is applied to the surface profile with outliers such as scratches and grooves, which further verifies the applicability of ADRF method in surface roughness extraction. Figure 11: (**a**) Honing profile and (**b**) waviness profile after using the robust filter. Figure 12: The output waviness profile of the robust Gaussian regression filter and robust approximating spline filter (**a**) Tukey, (**b**) ADRF, (**c**) WLAV, (**d**) Hampel, (**e**) Andrews, (**f**) Huber. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Not Robust** & **[PERSON]** & **ADRF** & **WLAV** & **Hampel** & **Andrews** & **Huber** & **Robust Gaussian** \\ \hline _Ra_ (\(\mu\)m) & 1.0945 & 1.1652 & 1.1618 & 1.1422 & 1.0763 & 1.1590 & 1.1325 & 1.1518 \\ _Rq_ (\(\mu\)m) & 1.5434 & 1.6665 & 1.6626 & 1.6375 & 1.6650 & 1.6588 & 1.6210 & 1.6532 \\ _Rp_ (\(\mu\)m) & 2.7425 & 3.2163 & 3.4880 & 3.2760 & 2.5425 & 2.9162 & 3.1268 & 3.6277 \\ _Rv_ (\(\mu\)m) & 9.0952 & 10.2168 & 10.1310 & 9.9840 & 10.4705 & 10.2113 & 9.9364 & 10.1526 \\ _Rt_ (\(\mu\)m) & 11.8377 & 13.4331 & 13.6191 & 13.2601 & 13.0130 & 13.1275 & 13.0632 & 13.7802 \\ _Rku_ & _7.2788_ & 8.8127 & 8.6766 & 8.7273 & 10.2548 & 8.9193 & 8.7533 & 8.8800 \\ _Rsk_ & \(-1.7914\) & \(-2.0305\) & \(-1.9900\) & \(-1.9887\) & \(-2.5561\) & \(-2.0567\) & \(-2.0004\) & \(-2.0167\) \\ \(Rsm\) (mm) & 0.3310 & 0.3509 & 0.3594 & 0.3508 & 0.5251 & 0.3384 & 0.3344 & 0.3604 \\ \(k\) & & 3 & 2 & 17 & 4 & 4 & 4 & 3 \\ time & 0.008 s & 0.027 s & 0.017 s & 0.054 s & 0.028 s & 0.024 s & 0.022 s & 0.276 s \\ \hline \end{tabular}
\end{table} 
Table 6: Comparison of roughness parameter values of using different filtering methods. The constructed ADRF robust approximating spline filter was then applied to areal filtering. The step surface obtained by the Talysurf CCI measurement system is presented in Figure 13. The existing surface shape was deleted, and the surface details were retained. The waviness surface and rough surface obtained by the approximating spline filtering without robust treatment is presented in Figure 14. According to the output results, there was an obvious distortion in the step area, and a false peak phenomenon occurred in the vicinity of the deep valley. Therefore, the presence of steps will seriously affect the accurate evaluation of roughness. The waviness profiles of the RGRF and ADRF outputs are almost the same, and both suppress the influence of the step as shown in Figures 15a and 16a. It can be seen that the robust filtering not only produced small distortion in the step region and around it but also had small deformation at the boundary.