# An Improved Self-Born Weighted Least Square Method for Cylindicity Error Evaluation
## 5 Experimental Verification and Literature Verification
### Experimental Verification
#### 5.1.3 Comparison and Evaluation of Algorithms after Inserting Gross Error Points  
The ISWLS algorithm differed from other algorithms in terms of its ability to resist gross differences. The standard PSO, standard GA, SWLS, and ISWLS methods were used to compare the error ratings according to the number of insertion gross error point. The comparison results are shown in Table 4 and Figure 8.  
As can be seen from Table 4, when one gross error point was inserted, the cylindricity error of the ISWLS method was 0.1475 mm, the cylindricity error of the SWLS method was 0.1681 mm, and the cylindricity errors of the standard PSO method, standard GA method, and LS method were 1.0698 mm, 1.4444 mm, and 1.1775 mm respectively, which showed that the five algorithms were gradually affected by gross errors. ISWLS had a better ability to resist gross error than SWLS. SWLS had a better ability to resist gross error than other algorithms. When two gross error points were inserted, the cylindricity error of the ISWLS method was 0.1875 mm, and the cylindricity error of the SWLS method was 0.2130 mm. The cylindricity errors of the standard PSO method, standard GA method, and LS method were 10.2447 mm, 9.2046 mm, and 10.6446 mm, respectively. When the number of gross error points increased, the five algorithms were affected by the number of  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Evaluation Method** & \begin{tabular}{c} **1 Gross Error Point** \\ **[mm]** \\ \end{tabular} & \
\begin{tabular}{c} **2 Gross Error Points** \\ **[mm]** \\ \end{tabular} &
\begin{tabular}{c} **3 Gross Error Points** \\ **[mm]** \\ \end{tabular} \\ \hline LS & 1.1775 & 10.6446 & 19.0610 \\ SWLS & 0.1681 & 0.2130 & 0.2911 \\ ISWLS & 0.1475 & 0.1875 & 0.2038 \\ PSO & 1.0698 & 10.2447 & 10.8566 \\ GA & 1.4444 & 9.2046 & 9.4694 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Error evaluation results of different algorithms when inserting gross error points (mm).  
Figure 8: Influence of gross error on the results of different algorithms.  
gross error increases. As the number of gross error points increased, ISWLS outperformed SWLS, PSO, GA, and LS in resisting gross errors, and their ability to resist gross errors gradually declined. When three gross error points were inserted, the cylindricity error of the ISWLS method was 0.2038 mm, that of the SWLS method was 0.2911 mm, and that of the standard PSO method, standard GA method, and LS method were 10.8566 mm, 9.4694 mm and 19.0610 mm, respectively. The ISWLS method had less error change than the SWLS method, and its ability to resist gross error was significantly better than that of standard PSO and standard GA methods, while the cylindricity error of the LS method increased significantly with the increase of gross error points, and the ability to resist gross error declined significantly.  
As can be seen from Figure 8, with the increase in inserting gross error points, the LS method was most affected by the gross error points, and the cylindricity error value increased gradually. The standard PSO and standard GA methods had a significant decrease in the error elevation of the cylindricity error value after the insertion of the 2 nd error point due to the reason of the gross error point location and the advantage of the algorithm. The ISWLS method and the SWLS method had a certain resistance to gross errors. Compared with other algorithms, the cylindricity error assessment results did not increase significantly after inserting gross error points, the changes were relatively flat, and the ISWLS method was more resistant to gross errors than the SWLS method.