# Prediction Research on Irregularly Cavited Components Volume Based on Gray Correlation and PSO-SVM
## 6 Conclusions  
This research studies the regression method of GRA-PSO-SVM used to model and predict the volume of irregularly cavitied components. The volume of irregularly cavitied components was affected by a variety of influencing factors. Through the grey-correlation analysis of the influencing factors, this experiment selected eight main influencing factors on the volume of irregularly cavitied components, and sorted them according to the degree of influence on the volume of irregularly cavitied components, in descending order. A volume-prediction model of irregularly cavitied components with the strong search ability of PSO and the good generalization performance of a support-vector machine, was then established. The simulation results showed that, compared to the conventional SVM, the GRA-PSO-SVM showed its strength by generating more accurate and stable results, with R\({}^{2}\) as high as 0.9704, MSE of 0.0046 and MAE of 0.035. The volume change can be well predicted, and this prediction model provides a new idea for accurately predicting the volume of irregularly cavitied components. In the follow-up research, we will continue to search for factors that may affect the volume-prediction model of irregularly cavitied components through a large number of experiments, and further optimize the algorithm to improve the detection accuracy and reliability.  
Conceptualization, Y.J., X.Z.; methodology, X.Z.; software, X.Z., W.Z.; validation, W.Z.; formal analysis, X.Z., W.Z.; investigation, X.Z.; resources, Y.J., X.Z.; data curation, X.Z.; writing--original draft preparation, X.Z.; writing--review and editing, X.Z.; visualization, X.Z., W.Z.; supervision, Y.J., X.Z.; project administration, Y.J.; funding acquisition, Y.J. All authors have read and agreed to the published version of the manuscript.  
The authors would like to acknowledge support from the following projects: Liaoning Province Higher Education Innovative Talents Program Support Project (Grant No. XLYC1902095), Shenyang Young and Middle-aged Science and Technology Innovation Talent Support Program (Grant No. RC200386), Liaoning Province Basic Research Projects of Higher Education Institutions (Grant No. LG202107, IJKZ0239). the construction plan of scientific research and innovation team of Shenyang Ligong University (Grant No. SYLU202101), the comprehensive reform project of graduate education of Shenyang Ligong University (Grant No. 2021 DSTD004,2021 PYPT006).  
We exclude these statements because the study did not require ethical approval.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **Actual** & \multicolumn{2}{c}{**GRA-PSO-SVM**} & \multicolumn{2}{c}{**Traditional SVM**} \\ \cline{3-6}  & **Value** & **Predicted Value** & **Relative Error** & **Predicted Value** & **Relative Error** \\ \cline{3-6}  & **mL** & **mL** & **\%** & **mL** & **\%** \\ \hline
1 & 2350 & 2347.96 & 0.09 & 2340.35 & 0.41 \\
2 & 2360 & 2357.30 & 0.11 & 2383.65 & 1.00 \\
3 & 2370 & 2372.97 & 0.13 & 2387.32 & 0.73 \\
4 & 2380 & 2386.38 & 0.27 & 2398.27 & 0.77 \\
5 & 2390 & 2398.12 & 0.34 & 2401.93 & 0.50 \\
6 & 2400 & 2404.05 & 0.17 & 2415.23 & 0.63 \\
7 & 2450 & 2445.67 & 0.18 & 2440.98 & 0.37 \\
8 & 2550 & 2556.65 & 0.26 & 2571.69 & 0.85 \\
9 & 2600 & 2610.02 & 0.39 & 2584.54 & 0.59 \\
10 & 2650 & 2642.97 & 0.27 & 2667.28 & 0.65 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation results from three models.