# 3D Acoustic Mapping in Automotive Wind Tunnel: Algorithm and Problem Analysis on Simulated Data
## 4 Virtual Experiment
### Simulation of Microphone Signals
#### 4.2.1 Source Simulation and Synthesis of Acoustic Pressure at Microphones  
The simulated sources are \(S=6\) monopoles positioned as green/black diamonds in Figure 1. Two sources represent the aerodynamic noise generated by side mirrors, while the other four sources represent the trailing edge tire noise. All sources are driven with white noise, properly filtered to reproduce the typical frequency content of aerodynamic and tire noise. The filter settings are bandpass between 600 and 2000 Hz for aerodynamic noise (side mirrors sources), and bandpass between 1.3 and 3 kHz for tire noise. The sources are correlated in pairs because they are driven with the same signal: the two on left tires, the two on right tires, and the two on side mirrors. Resulting source spectra are depicted in Figure 2. Three one-third octave bands are selected for the analysis with acoustic mapping: 800 Hz, 1.6 kHz, and 2.5 kHz. In the first and in the last band, tire and aerodynamic noise are prevailing, respectively, while in the middle band all noise sources have the same level.  
Figure 1: Position of simulated sources (green/black diamonds) with respect to the car model. Black dots represent microphone locations of the two arrays. (**a**) Front view with superimposed the calculation volume (the bold black parallelepiped). (**b**) Rear view.  
Source signals are propagated considering free-field propagation in a uniform flow. The speed of sound is set at 343.8 m/s. Simulated microphone signals are generated at a sampling rate of 32,768 samples/s, and contributions of each source are summed together at microphone locations. The duration of the signals is 10 s.  
Uncorrelated noise on each microphone (i.e., spatially white noise) is not representative of the actual WT test conditions. Externally to the test section, radiating real sources are present. They have a well-defined spatial distribution that is also frequency-dependent. To obtain realistic simulations, real recordings of the WT background noise are used. Time signals were acquired in the real Pininfarina WT without any model in the test section at flow speed of 28 m/s, using the same array configuration used for the simulations. These signals have been used as background noise (BGN), in the synthesis of simulated signals. The simulated total pressure \(p_{tot,m}(t)\) on each microphone is obtained as follows:  
\[p_{tot,m}(t)=p_{sig,m}(t)+G\cdot p_{bgn,m}(t)\qquad m=1,\ldots,M \tag{18}\]  
where \(p_{sig,m}(t)\) is the contribution of all simulated sources on each microphone and \(p_{bgn,m}(t)\) is the real WT noise recorded by each _m-th_ microphone. The desired Signal-to-Noise Ratio (SNR) is obtained by setting the proper gain \(G\) and has been calculated using microphone auto-spectra, averaged over all microphones, respectively, of simulated source signals and real WT noise signals. Once the band of interest is selected, the overall band power, \(P_{sig}\) and \(P_{bgn}\), is estimatedand \(G\) is calculated as  
\[G=\sqrt{\frac{P_{sig}}{P_{bgn}}}10^{(-\text{SNR}_{dB}/20)} \tag{19}\]  
where \(\text{SNR}_{dB}\) is the target SNR, expressed in dB. In this way, data produced have the desired overall SNR for the band of interest (not for each single spectral line).