# An Improved Self-Born Weighted Least Square Method for Cylindicity Error Evaluation
## 6 Conclusions  
Since there are cases of gross errors in cylindricity error evaluation, this paper proposes the ISWLS method to evaluate the cylindricity error. The algorithm was compared with the standard PSO, standard GA, and LS methods for error assessment. The ability of the algorithm to resist gross errors was verified by inserting gross error points, and the correctness of the algorithm was verified using literature data. The experimental results show that:  
(1) The method in this paper differs from SWLS and conventional global optimization algorithms in that it does not require setting parameters such as independent group order, population size, and crossover variation, and the operation steps are simple. As a result, the algorithm is relatively simple. (2) By randomly inserting three gross error points, it was demonstrated that the cylindrical axis parameters calculated by the ISWLS method are stable when the data contain gross error points. The variation of cylindricity error is within 0.08 mm. The  
Figure 9: Statistics chart of true error value when inserting gross error point. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & \multicolumn{2}{c}{**Value [mm]**} \\ \hline best estimate & \multicolumn{2}{c}{0.1338} \\ \hline
95\% probability inclusion interval & \multicolumn{2}{c}{[0.1294, 0.1381]} \\ \hline Project & \(d_{low}\) & \(d_{high}\) & MCM verifies GUM results (\(\delta\leq\) 0.0005) \\ \hline MCM Verification GUM & 0.0002 & 0.0001 & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 9: MCM method evaluation results of the first set of data. variation is smaller compared with the results without inserting gross error points, so the algorithm is able to resist gross errors. (3) In several experimental evaluations, compared with the particle swarm algorithm and genetic algorithm, the method in this paper took relatively less time and had faster computing power than the LS. In the experiment of inserting three gross error points, the LS method was most affected by the gross error points, and the standard PSO method and the standard GA method had less error increase in the cylindricity error value after the insertion of the second error point due to the advantage of the algorithm. The ISWLS method and the SWLS method have 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. (4) The LS method, SWLS method, ISWLS, standard PSO method, and standard GA method were used to evaluate the model without inserting gross error points. Compared with other optimization algorithms, ISWLS has higher accuracy and stable arithmetic results with strong robustness. The results of the uncertainty evaluation experiments show that the GUM method results were verified by the MCM method, and thus the error uncertainty evaluation results are reliable. The ISWLS method has the robustness of the cylindrical error evaluation results. The algorithm can be extended to error evaluation. Methodology, Y.Y. ; Formal analysis, Y.Y. ; Resources, K.Z. ; Data curation, Y.Y. ; Writing--original draft, Y.Y. ; Writing--review & editing, K.Z. ; Supervision, K.Z. ; Project administration, K.Z. ; Funding acquisition, Y.Y. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The study was funded by author Y.Y. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: No data was made public. The authors would like to thank the Managing Editor and the anonymous reviewers for their pertinent comments on this paper. The authors declare no conflict of interest. References  
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