# Optimization Study of Driver Crash Injuries Considering the Body NWH Performance
## 6 Analysis of Elman Forecast Results
employed to predict the outputs corresponding to these feasible solutions, including the driver injury value, body mass, and first-order modes. The optimization problem aimed to minimize the driver's head injury value while avoiding an increase in body mass and preserving the first-order modal state of the body-in-white as constraints. The mathematical expression is as follows:  
\[\left\{ \begin{array}{l}\min f(X_{i})\\ h_{1}(X_{i})\geq 39.75\\ h_{2}(X_{i})\geq 43.34\\ m(X_{i})\leq 306.86\end{array} \right. \tag{9}\]  
This problem involved a large solution set, which is typically addressed through iterative operations. However, conventional iterative methods are prone to becoming trapped in local minima or \"dead loops\", hindering the optimization process. Genetic algorithms, which are global optimization algorithms inspired by biological evolution, excel in overcoming this drawback. Compared to traditional optimization methods, genetic algorithms offer strong convergence, reduced computation time, and high robustness. The optimization process using genetic algorithms involved generating multiple solution groups in the solution set space. The predicted values corresponding to each group of solutions were obtained through the trained Elman neural network, and only those that satisfied the constraints were retained until the population size met the requirements (Figure 12). The fitness of individuals in the population was calculated based on the difference between the initial solution for the driver's head injury value and the predicted injury value of each solution, with larger differences indicating a better fitness. This process continued iteratively as the Elman neural network performed genetic, crossover, and mutation operations on individuals for the prediction. The initial solution served as the global optimal solution at the start, and if a solution better than the current optimal solution was found, it was replaced until the iteration terminated. The optimization of the solution set space yielded optimal solutions that adhered to the constraints, resulting in values as follows: 1.7, 2, 1, 1.3, 1.5, 0.7, 0.8, 1.3, 0.6, 0.8, 1.2, 0.8. To assess the final prediction solution of the Elman neural network algorithm, these optimal plate thickness values were applied to the finite element model attributes, which were then submitted to the Optistruct and LS-DYNA solvers for simulation calculations. The optimization results are detailed in the Table 7, showcasing a reduction of 173.43 in the \(HIC_{36}\) value of the driver's head, minimal changes in the body mass, and an improved optimization of the first-order modes compared to the original data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Predictors** & **MSE** & **RMSE** & **MAE** & **MAPE** \\ \hline Body-in-white first-order & \(1.883\times 10^{-2}\) & \(1.372\times 10^{-1}\) & \(1.183\times 10^{-1}\) & \(2.985\times 10^{-1}\) \\ Torsional modes/Hz & \(2.845\times 10^{-1}\) & \(5.334\times 10^{-1}\) & \(3.941\times 10^{-1}\) & \(9.306\times 10^{-1}\) \\ Body mass/kg & \(2.424\times 10^{-5}\) & \(4.923\times 10^{-3}\) & \(3.603\times 10^{-5}\) & \(1.167\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Elman neural network algorithm prediction error. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Responsive** & **Pre-Optimization** & **Projected Value** & **Actual Value** & **Forecast Error (\%)** \\ \hline Driver’s head \(HIC_{36}\) value & 845.96 & 627.1895 & 672.53 & 6.74 \\ Body mass /kg & 306.86 & 304.921 & 306.62 & 0.55 \\ Body-in-white first-order & 39.749 & 40.209 & 39.972 & \(-0.59\) \\ Torsional modes/Hz & & & & \\ Body-in-white first-order & 43.338 & 44.504 & 44.800 & 0.66 \\ Bending modes/Hz & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison before and after optimization of each constraint response.