# 3D Acoustic Mapping in Automotive Wind Tunnel: Algorithm and Problem Analysis on Simulated Data
## 5 Results of Parametric Study
### Influence of Background Noise Level  
The simulations produced for this last parametric study are useful to study the effect of spatially structured BGN. In fact, uncorrelated noise on each microphone is not representative of actual WT conditions, as some radiating real sources are present out of the test section. Indeed, machinery and environment produce BGN with well-defined spatial distribution. Three different SNRs are tested: 20, 10, and 0 dB. Figure 15 depicts maps in the best and worst condition, i.e., 20 dB and 0 dB of SNR, respectively. The map with the lowest level of BGN is almost identical to the noise-free condition, while the spatial distribution of BGN is clearly visible when the SNR is 0 dB. One interesting fact is that the main sources are  
Figure 14: Computation time versus grid resolution.  
Figure 13: Source power ratio \(W_{s}\). Ideal source power ratio is 0. (a) Grid step of 25 mm. (b) Grid step of 50 mm. (c) Grid step of 100 mm.  
always visible, while the lowest level sources tend to disappear from the maps, especially at low frequency. This effect is mainly given by two causes. First, source components require much more regularization, and therefore they are heavily underestimated. Second, the source components are mixed (or completely covered) by the background noise. It is also very interesting to observe the spatial distribution of disperse sources. Looking at Figure 15, it is evident how those grid points are concentrated at the trailing edges of the calculation box, from where the noise actually originates, being mainly generated by the suction fan of the wind tunnel. This is very interesting, not only because it is physically sound, but because it allows the implementation of map enhancement strategies, from a simple spatial masking to more sophisticated corrections.  
Figure 16 shows that the non-dimensional distance error \(D_{s}\) is maintained at a reasonable amount even with the highest level of BGN. However, it seems to have a counterin  
Figure 15: Maps of test cases with WT background noise. (**a**) 800 Hz and Signal-to-Noise Ratio (SNR) 20 dB. (**b**) 800 Hz and SNR 0 dB. (**c**) 1600 Hz and SNR 20 dB. (**d**) 1600 Hz and SNR 0 dB. (**e**) 2500 Hz and SNR 20 dB. (**f**) 2500 Hz and SNR 0 dB. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)  
tuitive behavior, as it returns worst performance with the middle noise level for 800 Hz and 2500 Hz bands. Actually, the explanation is quite simple: in these bands, sources with different levels are present. When the noise level is low (SNR of 20 dB), all sources are correctly detected. When the noise level increases (SNR of 10 dB), all sources are still identified but the noise heavily spoils the location of weaker sources on the map, and this produces a bad average score. With the highest noise level, the weakest sources are not identified at all or strongly regularized, thus returning a better score. Instead, power concentration \(W_{\%}\) produces the expected result, as a lot of energy outside the zones of interest arises because of BGN.  
Source quantification is still good, especially for the main sources, as evidenced in Figure 17. In fact, only the weakest sources are negatively affected by the BGN. This means that the source quantification of the main source is still possible even in challenging testing conditions with a high level of noise.  
Figure 16: Scores of maps for different SNRs. (**a**) Non-dimensional distance error \(D_{s}\). Average value obtained from identified sources only. Transparent bars represent the ratio between different grid steps and \(\lambda\). (**b**) Power concentration \(W_{\%}\).  
Figure 17: Source power ratio \(W_{s}\). Ideal source power ratio is 0. (**a**) SNR of 20 dB. (**b**) SNR of 10 dB. (**c**) SNR of 0 dB.