A new method for predicting the acoustic transfer function inside vehicles using physics-informed neural networks

The acquisition of acoustic transfer functions (ATFs) inside vehicles is generally achieved through experimental measurement methods. However, the ATF measured by experimental measurement methods is discrete in space and frequency, which means that it is difficult to obtain the ATF continuous in space and frequency using experimental measurement methods. This is unfavorable for active control of the sound field inside vehicles. Firstly, an analytical model of the ATF between any two points in space based on the general form of the Helmholtz equation is derived, and the physical constraints of the ATF between any two points inside vehicles is clarified. Then, a calculation model of the ATF inside vehicles based on physics-informed neural network (PINN) is established. Finally, a calculation model of the ATF in the real car is established through transfer learning. Under the same conditions, the proposed PINN model for ATF prediction (ATF-PINN) converges faster and has smaller steady-state losses than the neural network model without physical information. The root mean square error (RMSE) and mean absolute error (MAE) of the ATF-PINN are reduced by more than 50% compared to the neural network model without physical information, and the coefficient of certainty (R-square) is increased by 27%. The prediction accuracy of the interior ATF by ATF-PINN is improved to over 94%. The trained ATF-PINN is used to calculate the ATF between any two new spatial points in the real car. The experimental results indicate that, the predicted ATFs of the proposed method are in good agreement with the experimental measurement values.