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We present the capabilities of a recently developed inverse scheme for source localization at low frequencies within an arbitrary acoustic environment. The inverse scheme is based on minimizing a Tikhonov functional matching measured microphone signals with simulated ones. We discuss the sensitivity of all involved parameters, the precision of geometry and physical boundary modeling for the numerical simulation using the finite element (FE) method, and the automatic determination of the positions of the recording microphones being distributed around the object of investigation. Finally, we apply the inverse scheme to a real-world scenario and compare the obtained results to state-of-the-art signal processing approaches, e.g. Clean-SC.

Acoustic source localization techniques in combination with microphone array measurements have become an important tool for noise reduction tasks. A common technique for this purpose is acoustic beamforming, which can be used to determine the source locations and source distribution. Advantages are that common algorithms such as conventional beamforming, functional beamforming or deconvolution techniques (e.g., Clean-SC) are robust and fast. In most cases, however, a simple source model is applied and the Green’s function for free radiation is used as transfer function between source and microphone. Additionally, without any further signal processing, only stationary sound sources are covered. To overcome the limitation of stationary sound sources, two approaches of beamforming for rotating sound sources are presented, e.g., in an axial fan.Regarding the restrictions concerning source model and boundary conditions, an inverse method is proposed in which the wave equation in the frequency domain (Helmholtz equation) is solved with the corresponding boundary conditions using the finite element method. The inverse scheme is based on minimizing a Tikhonov functional matching measured microphone signals with simulated ones. This method identifies the amplitude and phase information of the acoustic sources so that the prevailing sound field can be with a high degree of accuracy.

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