# Interior Sound Quality Prediction of Pure Electric Vehicles Based on Transfer Path Synthesis
## 2 Materials and Methods
### Psychoacoustic Parameters of SQ  
Sound pressure is the most basic physical quantity to quantitatively describe sound waves, where parameters, such as sound pressure, sound intensity, and sound power, among others, are typically considered when describing the physical characteristics of noise. However, these parameters cannot reflect the subjective feelings of a person; hence, objective psychoacoustic parameters have been developed on the basis of considering the auditory characteristics of the human ear as well as fully reflecting subjective feelings [1]. Psychoacoustic parameters have been identified as objective physical quantities that describe the degree of difference in subjective feelings caused by different sound signals and which can eliminate the unstable factors of subjective evaluations. At present, the more commonly used parameters are loudness, sharpness, and roughness [22]. After we obtained the synthesized sound in the vehicle, we could objectively analyze the SQ of the synthesized sound in each transmission path according to the process in Figure 3.  
Figure 2: Schematic of the interior sound synthesis model of the PEV. Loudness is the degree of subjective perception of the human ear to sound intensity. It is a psychoacoustics parameter that can reflect auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud, and it fully takes into account the masking characteristics of the human ear to the sound spectrum. Generally, the larger the loudness value of sound, the more annoying the subjective perception is, and the worse the SQ; however, loudness is not a decisive criterion for evaluating SQ. The unit of loudness is \"sone,\" and the loudness of a 40 dB pure tone at 1 kHz is defined as 1 sone [23]. [PERSON]'s loudness model introduced the critical band rate and specific loudness. The total loudness, N, can be obtained by integrating the specific loudness in the Bark scale, as shown in Equation (2):  
\[N=\int_{0}^{24\;Bark}N^{\prime}(z)dz, \tag{4}\]  
where \(N^{\prime}(z)\) is the specific loudness in units of \"Bark\". [PERSON] proposed using the Bark scale as a spectrum division, similar to the third octave band [22]. Sharpness reflects the frequency characteristics of the sound. Sharpness describes the proportion of high-frequency components in sound, directly reflecting the harshness of the sound. The unit of sharpness is \"acum,\" and the sharpness of 60-dB narrowband noise with a central frequency of 1 kHz and a bandwidth of 160 Hz is defined as 1 acum. The level of noise sharpness is affected by several parameters, such as the central frequency, bandwidth, SPL, and the spectral envelope. Among them, the central frequency and spectrum envelope are identified the most important. In general, the greater the proportion of high-frequency components in the spectral components of sound, the greater the sharpness [24]. [PERSON]'s model is usually used to calculate sharpness, the mathematical formulation of which is based on [PERSON]'s loudness model as follows:  
\[S=k\frac{\int_{0}^{24\;Bark}N^{\prime}(z)\cdot z\cdot g(z)dz}{N}, \tag{5}\]  
Figure 3: Flowchart for calculating the objective psychoacoustic evaluation parameters of SQ. where \(S\) is the total sharpness value, \(N\) is the total loudness value, \(N^{\prime}(z)\) represents the specific loudness in the \(z\) Bark, \(k\) is the weighting coefficient, and \(g(z)\) is the weight coefficient of sound signal in different Bark. The roughness is a psychoacoustic parameter reflecting the degree, amplitude, and frequency distribution of the modulation, along with other characteristics of sound signals. As a sound-evaluation index, the roughness is applicable to modulation frequencies below 200 Hz, and is especially used at modulation frequencies near 70 Hz. In music psychology, smooth and rough sounds are perceived as harmonious and discordant, respectively. The unit of roughness is asper. A 60 dB sound with a 1 kHz tone which is 100% amplitude-modulated at 70 Hz has a roughness of 1 asper.