# Vehicle Interior Noise Prediction Based on Elman Neural Network
## 1 Introduction
[21] used the response surface method to establish a connection between the gear lead crown and involute modifications of the 3 rd-gear pair to the transmission radiation noise. By optimizing the response surface, the transmission measurement noise at the measuring point was reduced by 2 dB to 4 dB (A). Given the large finite element model of the vehicle, the finite element calculation process consumes a large amount of resources. To reduce the amount of calculation, the abovementioned NVH optimization study based on the finite element model applies the response surface methodology and other approximate models instead of undergoing the calculation process. However, the establishment of the response surface approximation model has high requirements for the designed experimental points. If these experimental points are not properly selected, then the accuracy of the response surface will be greatly reduced. Neural networks can approximate any nonlinear process [22] and have been recently applied in predicting and optimizing automobile noise given their high prediction accuracy [23; 24; 25]. [PERSON] et al. [26] proposed a finite element neural network model to simulate the acoustic behavior of the auditory system. [PERSON] et al. [27] demonstrated the feasibility for the neural network to optimize noise in a vehicle through the error of the neural network prediction and boundary element calculation values. [PERSON] et al. [28] used a BP neural network model to predict the acoustic response characteristics of commercial cabs. [PERSON] et al. [29] proposed a GA-BP-based electric vehicle sound quality prediction model, which offers many advantages in accuracy and generalizability. The neural network compensates for the shortcomings of the traditional response surface prediction model that is overly dependent on experimental points. Therefore, the neural network is selected in this article as the basic model for vehicle interior noise prediction. Although some achievements have been reported in the use of neural networks to predict vehicle noise, the accuracy of this approach needs to be improved, and the appropriate neural network algorithm needs to be identified. [PERSON] et al. [30] used the Elman neural network to accurately predict short-term temperature changes in a digester. [PERSON] et al. [31] used the same network to predict the battery capacity of electric vehicles in real time. [PERSON] et al. [32] used three neural networks to predict active COVID-19 cases in Jordan. In these applications, the Elman model demonstrated its high predictive ability and a significantly better prediction accuracy compared with NARX and feed forward networks. [PERSON] et al. [33] predicted indoor temperature using the Elman neural network algorithm and found that this algorithm has a simple structure, small storage space, and high prediction accuracy. [PERSON] et al. [34] designed an Elman neural network predictive controller to solve the nonlinearity of the electro-hydraulic compound steering system of heavy commercial vehicles. Inspired by these achievements, this article uses the Elman neural network to predict the noise inside a vehicle and compares its prediction accuracy with that of other neural network algorithms. The structural noise in a vehicle is mainly radiated from body panel vibration. In this paper, all panels surrounding the acoustic cavity in a vehicle are treated as design variables, and an optimal combination of variables that meets the specified conditions is selected. The B-pillar inner panel, side wall, roof, and other panels are coupled with the interior acoustic cavity given their significant impact on interior noise. The changes in the thickness of some panels due to NVH optimization can greatly affect the side impact performance [35; 36; 37]. In the abovementioned research, when optimizing structural parameters such as the thickness of body panels, only the characteristics of the lightweight body and body-in-white modal are considered.