# Interior Sound Quality Prediction of Pure Electric Vehicles Based on Transfer Path Synthesis
## 3 Measurements
### Transfer Function Measurements
#### 3.1.2 Structure-Borne Noise Transfer Function Measurements  
Structure-borne noises in PEVs originate from the suspension and mount systems. Structure-borne noise is transmitted as vibrations excited in the X, Y, and Z directions from each noise source. The vibrational excitations generated by the electric drive system are attenuated by the mount system, and an exciting force is imparted to the vehicle body. In the driving state of the vehicle, the road excitation is transmitted from the tires to the suspension system, which attenuates the excitation and transmits it to the body, where it is expressed as an exciting force. The exciting force generated by the powertrain system and the road is then transmitted through the body to the wall plate, which produces vibration and radiation noise. The excitation force of the structure-borne noise source was calculated by the inverse-matrix method. The inverse-matrix method is appropriate for multi-load identification. For the linear system formed by the noise path in the vehicle, numerous load forces and transfer functions with responses form a matrix relationship, as shown in formula:  
\[\left[ \begin{array}{c}P_{1}\\ \vdots\\ P_{n}\end{array} \right]=\left[ \begin{array}{ccc}H_{11}&\cdots&H_{1m}\\ \vdots&\ddots&\vdots\\ H_{n1}&\cdots&H_{nm}\end{array} \right]\left[ \begin{array}{c}F_{1}\\ \vdots\\ F_{n}\end{array} \right], \tag{8}\]  
In the formula, matrix [P] represents response matrix; matrix [H] represents path transfer function matrix; matrix [F] represents excitation force matrix [14]. This calculation requires the transfer functions of reference points near the excitation point. The reference points should be as close as possible to the excitation source, and their number should be \(2n\), where \(n\) is the number of excitation points. The vibro-acoustic characteristics of the vehicle body reflect the excitation force transferred from the body to the noise inside the vehicle. Structure-borne noise transfer function measurement equipment is shown in Table 2. For the transfer function measurements, the prototype vehicle was suspended in the free state using a gas spring (see Figure 8). When measuring the transfer function of the mount system, the electric drive system was not completely disassembled, but all mounts of the frame and body were disassembled, and the electric drive system was lifted by hanging (with most of the weight not added to the frame). When measuring the transfer function of the suspension system, the electric drive system and sub-frame were not detached, but all connection points between the front and rear suspensions and the body were disconnected. Figure 7: Measured spectra of the noise transfer functions of the tires. The microphone was arranged at the target point in the vehicle. The position of the target point was unchanged from that of the airborne noise transfer function measurements. The connection points between the suspension and mount system and the body in the X, Y, and Z directions were excited by a miniature exciter. The sound pressure was recorded at the target points, and the response acceleration was measured at all reference points. For the acceleration measurements, three-direction acceleration sensors were arranged at each reference point near the excitation point. At the large number of measurement and reference points, multiple measurements were collected. To ensure the accuracy of the subsequent load identification, the number of degrees of freedom of the reference point for each measurement was guaranteed to exceed twice the number of degrees of freedom of the excitation point. Figure 9 shows the positions of the exciter and acceleration sensor at the reference point.