# Vehicle Interior Noise Prediction Based on Elman Neural Network
## 6 Analysis of Prediction Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Prediction Object** & **MSE** & **RMSE** & **MAE** & **MAPE** \\ \hline Body mass & \(1.964\times 10^{-3}\) & \(4.432\times 10^{-2}\) & \(3.486\times 10^{-2}\) & \(9.547\times 10^{-2}\) \\ First-order torsion modal & \(3.258\times 10^{-5}\) & \(5.708\times 10^{-3}\) & \(4.457\times 10^{-3}\) & \(1.156\times 10^{-4}\) \\ First-order bending modal & \(1.064\times 10^{-4}\) & \(1.031\times 10^{-2}\) & \(8.252\times 10^{-3}\) & \(1.529\times 10^{-4}\) \\ P4 maximum intrusion & \(2.181\times 10^{-4}\) & \(1.477\times 10^{-2}\) & \(9.530\times 10^{-3}\) & \(1.903\times 10^{-4}\) \\ P5 maximum intrusion & \(1.944\times 10^{-4}\) & \(1.394\times 10^{-2}\) & \(5.361\times 10^{-3}\) & \(1.772\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Elman neural network algorithm prediction error. Tables 4 and 5 show that the Elman neural network had the smallest prediction error for the maximum sound pressure level of the target point in a vehicle and significantly outperforms the other three neural network algorithms in terms of MSE, RMSE, MAE, and MAPE. The Elman neural network algorithm predicted the mass of the vehicle body, the first-order global modal of the body-in-white, and the maximum intrusion of the B-pillar P4 and P5 points. This algorithm generated small prediction errors that met the prediction accuracy requirements. The enumeration method was applied to enumerate all feasible solutions in the solution set space, and the solution set space was initially discretized. Taking processing accuracy into account, the step length of each input variable in the solution space was set to 0.1, which was equivalent to 1,071,815 feasible solutions. The Elman neural network was then used to predict the maximum sound pressure level at the target point, body mass, first-order modal of the body-in-white, and maximum intrusion of B-pillar P4 and P5 points corresponding to all feasible solutions. By taking the minimum maximum sound pressure level of the target point in a vehicle as the goal, both the body mass and the first-order global modal of the body-in-white did not decrease, whereas the maximum intrusions of the B-pillar P4 and P5 points, as the constraint conditions, were less than 60 mm and 70 mm, respectively. The optimal solution in the feasible solution set was then filtered as:  
\[\left\{ \begin{array}{c}\min f(X_{i})\\ h_{1}(X_{i})\geq 38.60\\ h_{2}(X_{i})\geq 54.05\\ m(X_{i})\leq 365.3\\ r_{4}(X_{i})\leq 60\\ r_{5}(X_{i})\leq 70\end{array} \right. \tag{22}\]  
where \(X_{i}\) is a feasible solution, and \(f(X_{i})\), \(h(X_{i})\), \(m(X_{i})\), \(r_{4}(X_{i})\), and \(r_{5}(X_{i})\) are the maximum sound pressure levels of the target node, the first-order global modal of the body-in-white, the maximum intrusion amount at point P4, and the maximum intrusion amount at point P5 as obtained by the feasible solution, respectively. The prediction results were filtered, and the optimal solution conditions that met the constraints were obtained as [1.1,1.2,0.9,1.5,1.5,0.9,2.1,0.9]. To verify the quality of the optimal solution predicted by the Elman neural network algorithm, the thickness of the optimal solution was assigned to the properties of the finite element model, which in turn was submitted to Optistruct and LS-DYNA for the simulation calculation. The noise transfer function curve of the target point in a vehicle and the five-point invasion curve of the B-pillar inner panel are shown in Figures 17 and 18. The maximum sound pressure level of the target point in a vehicle was reduced by 5.92 dB. Compare Figure 18 and Figure 7, the maximum intrusions of points P4 and P5 on the B-pillar inner panel were reduced by 31.1 mm and 33.71 mm, respectively. The comparison between Elman neural network prediction and finite element calculation is shown in Table 6.