## 1 Introduction
[11] applied a similar analysis method to investigate the cause of booming noise arising from the chassis pitch mode induced by the engine's rotational component, which was attributed to excessive suspension energy through the fifth torsional mode of the drivetrain, and conducted research to address this issue. [PERSON] et al. [12] developed predictive models for noise improvement by combining the chassis and interior acoustic models. These models were based on simulated road profiles from which sound pressure data were extracted and validated using experimental data. Several studies have focused on enhancing the quality of booming noise [13; 14; 15]. In recent years, as electric vehicles have gained increasing popularity, extensive research efforts have been directed towards minimizing the noise generated by these vehicles. These studies specifically focused on addressing the noise associated with the powertrains of electric vehicles. [PERSON] et al. [16] conducted experiments to validate structural optimization techniques for both the rotor and stator of an eight-pole 48-slot permanent magnet synchronous motor commonly used in electric vehicles. Their objective was to reduce the zeroth-order spatial electromagnetic force generated by a motor. They meticulously analyzed the origins of this force and attempted to reduce it. [PERSON] et al. [17] identified vibration issues stemming from the distortion in the air-gap magnetic field of a BLDC motor. This distortion was attributed to the dynamic eccentricity within the rotor, which is a phenomenon arising from the electromechanical coupling specific to electric vehicles. [PERSON] et al. [18] employed various techniques, including order analysis, ODS analysis, and TPA to determine whether the secondary component of the drivetrain of an electric vehicle was the primary source of vibration. They analyzed the coupling between the powertrain and rear axle, which induced vibrations, leading to overall resonance in the drivetrain. These vibrations were subsequently transmitted to the chassis through the mounts and V-rods. [PERSON] et al. [19] developed a comprehensive finite-element analysis model that encompasses the entire drivetrain. The accuracy of their model was validated using experimental data. They proposed an analytical approach to predict the noise levels induced by electromechanical couplings, with particular emphasis on the significance of the rotor properties. Sensitivity analysis during their modeling process proved to be instrumental. [PERSON] et al. [20] created an analysis model for electric powertrain systems operating under varying speed conditions, with a specific focus on NVH analysis. They improved the reliability of their model by incorporating experimental results related to the natural modes of the stator. The validity of this model was established by comparing the vibration and noise signals between the experimental and analytical outcomes. Furthermore, bearing force analysis using multibody dynamics simulations confirmed that the noise components induced by the stator teeth predominated, with minimal impact from the torque ripple. Ultimately, they predicted noise levels by measuring the sound pressure arising from the vibrations within the powertrain housing. [PERSON] et al. [21] employed a conventional powertrain from a pure electric vehicle to perform dynamic simulations of vibration and noise. They developed a powertrain model that accounted for gear meshing stiffness, transmission errors, bearing factors, and shell flexibility. Subsequently, they simulated the dynamic response of powertrain vibration and sound radiation. The results of their simulations indicated a reduction in housing surface vibration amplitude of 0.2 to 0.6 m/s\({}^{2}\), and a decrease in far-field noise levels of 3 to 5 dB. [PERSON] et al. [22] conducted research to mitigate the noise of a two-speed automatic transmission for pure electric vehicles. They proposed a scheme to reduce noise by optimizing the gearbox housing.