# 3D Acoustic Mapping in Automotive Wind Tunnel: Algorithm and Problem Analysis on Simulated Data
## 5 Results of Parametric Study
### Single Array versus Multiple Arrays with Different Levels of Masking Effect  
When a three-dimensional object radiates noise from some of its parts, the body itself is an obstacle for the propagation, and some sources of noise are not directly perceived from some directions. The measurement setup for acoustic mapping should account for this issue. The combined use of arrays looking at the same object from different points of view is important to identify all noise sources. Inverse methods allow using multiple planar arrays simultaneously without particular issues; the only drawback is the increment of computational cost. The simulated test cases analyzed in this section help us to understand the impact on acoustic maps of sources partially masked to the microphone array. As already said, realistic reproduction of scattering and transmission of the propagating waves by the model is a complex task. For this reason, the masking effect is simulated by means of simple attenuation of the pressure produced at microphone locations in NLOS condition by each source. No background noise is present in these simulations, and three levels of \(M.A.\) are tested: 6, 10, and 20 dB. The calculation is performed on a regular grid of monopoles with a 50 mm step that is all around the car model. All potential sources inside the car volume are removed from the calculation grid.  
In Table 1, \(S_{id}\) in the case of single array is reported for different bands and attenuation levels. In the case that both arrays are used, all the sources are always localized. \(M.A.\) plays a major role in the ability of identifying all the active sources adopting only the top array. This effect is much more evident at lower frequencies, first, because of the major ill-conditioning of the problem for those frequencies, and second, because the noise sources located close to tires, mainly emitting at low frequency, are almost completely masked to the top array. Figure 4 reports the mean source position error \(D_{s}\) computed in the analysis. Transparent bars represent the ratio between the grid step and the wavelength of the center frequency of the band. With the single array, error is quite large independently from the attenuation of hidden sources, while with the dual array, it is significantly lower, even if it increases with the attenuation. When the dual array is used, the body of the model mainly masks the sources at the right side of the car, which are hidden to both arrays, especially to the lateral one. The identified source position \(\mathbf{r}_{s,id}\) parameter reveals that the source localization error is smaller than the grid step when the attenuation is low and dual array is used.  
As no background noise is present in this simulation, a power concentration of 100% is expected when sources are correctly reconstructed. Figure 5 shows that this is the case only when adopting a dual array. In fact, when the top array is used to map tire noise, the power concentration is about 70% for 6 dB of attenuation and falls to almost 0% for 20 dB of attenuation. The combined use of two planar arrays allows one to concentrate the energy of equivalent sources near the exact source position in any case.  
In Figures 6-8, the effect of masking on sources quantification is quite evident. In fact, masked source powers are underestimated (even when well localized), and this increases as \(M.A.\) increases.  
Figure 4: Non-dimensional distance error \(D_{s}\) obtained with single and dual array. Average value obtained from identified sources only. Transparent bars represent the ratio between grid step (50 mm) and \(\lambda\). (**a**) 800 Hz. (**b**) 1600 Hz. (**c**) 2500 Hz.  
Figure 5: Power concentration \(W_{\%}\) obtained with single and dual array. (**a**) 800 Hz. (**b**) 1600 Hz. (**c**) 2500 Hz.