# Prediction of Tooth Profile Deviation for WEDM Rigid Gears Based on ISSA-LSSVM
## 5 Conclusions  
In this study, a novel profile deviation prediction model (ISSA-LSSVM) is proposed for accurately predicting the profile error of WEDM rigid gears. The model is utilized to analyze the impact of WEDM process parameters on the profile error of rigid gears and to enable intelligent adjustment of the profile error. The key findings are outlined below: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & \(\mathbf{R^{2}}\) & \(RMSE\) & \(MAPE\) \\ \hline PSO-LSSVM & 0.9307 & 0.0056 & 0.0327 \\ GWO-LSSVM & 0.9205 & 0.0071 & 0.0357 \\ SSA-LSSVM & 0.9439 & 0.0038 & 0.0226 \\ ISSA-LSSVM & 0.9828 & 0.0029 & 0.0156 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of the evaluation indicators for the four models. Figure 7: Prediction results and errors for each model. (**a**) PSO-LSSVM model; (**b**) GWO-LSSVM model; (**c**) SSA-LSSVM model; (**d**) ISSA-LSSVM model. * The standard SSA is improved by introducing Tent chaotic mapping, adaptive adjustment strategy, dynamic inertia weights, and grey wolf hierarchy strategy, which significantly improve the effectiveness and robustness of the algorithm. The improved ISSA is verified to have better convergence speed and global optimization capability than PSO, GWO, and SSA by four different types of benchmark test functions. * The prediction results and errors of the ISSA-LSSVM tooth profile deviation prediction model were compared with those of the PSO-LSSVM, GWO-LSSVM, and SSA-LSSVM prediction models on different datasets. The results show that the ISSA-LSSVM prediction model has a higher prediction accuracy and faster convergence speed (ISSA-LSSVM model: \(R^{2}=0.9828\), \(RMSE=0.0029\), \(MAPE=0.0156\)). * The developed ISSA-LSSVM model exhibits superior prediction capability and can provide reliable theoretical guidance for predicting the tooth profile deviation of rigid gears. This research provides an innovative and reliable model for predicting tooth profile deviation in WEDM rigid gears. Despite the promising results, this study has several limitations that should be addressed in future research. Firstly, the dataset used for model training and validation is relatively small and specific to certain types of rigid gears and WEDM conditions. To enhance the generalizability of the proposed ISSA-LSSVM model, it is essential to collect and utilize more diverse and extensive datasets. Secondly, while the ISSA optimization strategy has been shown to be effective, the influence of different parameter settings on the model's performance needs further exploration. Additionally, the current model's applicability to other types of gears and machining methods remains uncertain and warrants further investigation. Future research could focus on several key areas to further improve and validate the proposed ISSA-LSSVM model. One important direction is the collection and analysis of more diverse and extensive datasets to ensure the model's robustness and generalizability across different types of rigid gears and machining conditions. Additionally, exploring the combination of the LSSVM with other advanced optimization algorithms could potentially enhance the model's prediction accuracy and stability. Furthermore, developing new models or improving existing ones to handle more complex prediction tasks and larger datasets will be crucial for advancing the state of the art in gear profile deviation prediction. Conceptualization, Y.W. and Z.W. ; methodology, Y.W. and Z.W. ; software, Z.W. ; validation, Z.W. ; formal analysis, Y.W., Z.W., G.W. and H.X. ; investigation, Z.W., G.W. and H.X. ; resources, Y.W. and Z.W. ; data curation, Z.W., G.W. and H.X. ; writing--original draft preparation, Z.W. ; writing--review and editing, Y.W. ; visualization, Y.W. and Z.W. ; supervision, Y.W. ; project administration, Y.W. ; funding acquisition, Y.W. All authors have read and agreed to the published version of the manuscript. This research was funded by the Natural Science Foundation of Gansu Province, grant number 22 JR5 RA268. Not applicable.