# 3D Acoustic Mapping in Automotive Wind Tunnel: Algorithm and Problem Analysis on Simulated Data
## 1 Introduction  
The acoustic performance of vehicles is crucial for automotive industries, both from a legislative point of view and for the quality perceived by customers. Three main sources of noise can be identified in a car: engine, structure-borne, and airborne. With the advancement of electric engines, the latter two sources of noise are gaining increasingly more importance and deserve to be studied in more detail. Wind tunnel tests allow performing measurements in controlled operational condition. Generally, one or more microphone arrays are installed in wind tunnels in order to acquire pressure data as input for acoustic mapping techniques, also called acoustic imaging. A detailed review of these techniques is available in [1]; they are an important tool for engineers that is exploitable during the design and testing phase to localize and rank the acoustic sources in vehicle exterior noise source identification. Two non-trivial challenges must be faced when mapping acoustic sources on three-dimensional objects. The first issue is the masking effect that the object itself produces between some sound sources and some microphones. Considering thiseffect in the propagation model could be prohibitive, as it involves complex scattering and the transmission of sound waves. The other aspect regards the choice of the spatial region to map. Commonly, the region of interest (ROI) chosen is a surface that represents the object. This could produce inaccurate results, as sound sources could be located outside the surface, especially the aeroacoustic ones. For this reason, in this work a volumetric three-dimensional approach is adopted. Unfortunately, real experiments do not allow the complete control of all parameters and phenomena (especially aeroacoustic ones), thus the necessity of evaluating each effect singularly arises. Therefore, simulated virtual experiments, reproducing a realistic measurement setup in a wind tunnel, have been produced to study the effect of these issues on acoustic maps. Moreover, the simulations allow us to compare the source retrieved with the exact ones in terms of localization and sound power quantification. The choice of acoustic mapping technique is conditioned by the volumetric mapping approach. Indeed, on the one hand, a good spatial resolution is required in all directions and, on the other hand, the problem size (i.e., the number of potential sources in the ROI) hugely increases. One acoustic imaging method is Conventional Beamforming (CB), but the poor spatial resolution in the radial direction from the array center and the high sidelobe level make it not well suited for volumetric maps. Another method is based on computationally expensive deconvolution algorithms like CLEAN-PSF or CLEAN-SC [2] that exhibit higher computational time than CB and comparable accuracy in terms of source localization. However, [PERSON] [3,4] showed how to produce good volumetric maps with CLEAN-SC using different steering-vector formulations. [PERSON] et al. [5] described and compared several techniques for volumetric mapping with two planar arrays oriented on orthogonal planes. The exploitation of multiple arrays, the so-called \"multiplicative beamforming\" principle, has been proposed in literature in different formulations and array/source configurations, but always with the purpose of enhancing the computed acoustic map and reducing the effect of side-lobes and artifacts in the acoustic image [6, 7, 8]. Another powerful deconvolution approach is DAMAS and its variants [9]. These techniques enable achieving good spatial resolution and accuracy in all directions, but they are computationally expensive (especially for the Point Spread Functions calculation phase) and often not compatible with the problem size of volumetric mapping. An application of DAMAS 3D was proposed in [10], where the focusing ability of beamformers with planar arrays was evaluated both in lateral and longitudinal directions.