## 5 Conclusions  
1. The finite element analysis for the electromagnetic-thermal field is carried out to obtain the distribution of the temperature and current density, which provides a theoretical basis for the numerical calculation of electromagnetic track launch.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Technical Indicators** & **Values** \\ \hline Range of speed measurement & 20–3000 m/s \\ Relative error of measurement & no greator than 0.1\% \\ Temperature of environment & \(-10\)–50 \({}^{\circ}\)C \\ Power supply & AC220 V 50/6 Hz \\ Power & 0.5 A 220 V mean power 60 W \\ \hline \hline \end{tabular}
\end{table}
Table 6: The technical indicators of the light curtain.  
Figure 19: Electromagnetic track launcher experiment platform.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Value/(m/s)** & **Relative Error/(\%)** \\ \hline Experimental test value (\(v_{\mathrm{e}}\)) & 2295.45 \(\pm\) 2.95 & - \\ Calculated value by Ls-dyna (\(v_{\mathrm{s}}\)) & 2428.41 & 5.79 \(\pm\) 0.13 (\(e_{\mathrm{rs}}\)) \\ Predicted value of improved model (\(v_{\mathrm{m}}\)) & 2322.53 & 1.18 \(\pm\) 0.13 (\(e_{\mathrm{m}}\)) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Error comparison between \(v_{\mathrm{e}}\) with \(v_{\mathrm{s}}\) and \(v_{\mathrm{m}}\).  
2. This paper mainly studies the armature velocity and inductance gradient variation rules of the electromagnetic track launcher under the influence of a dynamic conductivity. When the track conductivity is fixed, the armature velocity and inductance gradient increase gradually with the armature conductivity. When the armature conductivity is fixed, the armature velocity and inductance gradient decrease gradually with the track conductivity.
3. According to variation rules of the armature velocity and inductance gradient, the improved electromagnetic-thermal coupling model of the electromagnetic track launcher considering dynamic conductivity is established. The proposed PSO-GA hybrid algorithm is used to identify the parameters of the established model. Moreover, another ten sets of finite element calculated values are taken and compared with the predicted values of the improved model, whose relative error is controlled to within 3%. The validity of the improved model is verified.
4. An experimental platform is built to further verify the improved model. Compared with the available finite element calculation, the proposed model in this paper has a smaller error, which is closer to the experimental test value, which is reduced by 4.61% Thus, it can provide a certain theoretical basis for the study of the dynamic parameters of electromagnetic track launch.  
Conceptualization, R.Y. and J.J.; methodology, R.Y. and J.J.; software, J.J. and K.A.; validation, J.J.; formal analysis, R.Y. and J.J.; investigation, R.Y., J.J. and K.A.; resources, R.Y. and K.A.; data curation, R.Y. and J.J.; writing--original draft preparation, R.Y. and J.J.; writing--review and editing, R.Y. and J.J.; visualization, J.J.; supervision, Q.Y. and R.Y.; project administration, Q.Y. and R.Y.; funding acquisition, Q.Y. and R.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Major Research Program of the National Natural Science Foundation of China, grant number 92066206, S&T Program of Hebei, grant number 215676146H, and S&T Program of Hebei, grant number 225676163 GH.  
Not applicable.  
All data, models generated or used during the study appear in the submitted article.  
The authors declare no conflict of interest.