Comparison of Microphone Array Methods for the Characterization of Rotating Broadband Noise Sources
2.2 Experimental Methods for Localizing / Characterizing Sources
The localization of rotating sound sources with a microphone array is a major task to reduce broadband axial fan noise. Depending on the adjusted operating point and considered frequency band, the sound sources are located on the leading or trailing edges of the fan blades. Considerable effort has been put into compensating the relative motion of the sound sources to the microphone array and to understand the rotating sound source mechanism. Motion compensation can be done in time domain or frequency domain. In time domain, the emitted signals from the moving sources can be reconstructed at the microphone array by an acoustic transfer function, taking into account the time delays and the Doppler effect due to the rotation. In frequency domain, the signals are first Fourier transformed. Afterwards, the resulting cross spectral matrix is multiplied with the steering vectors to shift the phase of the microphone signals according to the focus points. Motion compensation in frequency domain can be done in different ways, e.g. employing virtual rotating microphones to transform the pressure signals into a rotating reference frame or modal decomposition of the rotating sound field.
After motion compensation beamforming is used to localize the sound sources. For some standard and high-resolution beamforming methods the cross spectral matrix is needed. The cross spectral matrix can be calculated in time domain with Welch’s method or in frequency domain with Daniell’s method.
This paper contains a comparison of the results of different methods. At first, a simulated benchmark case with discrete rotating sound sources is considered. The evaluation is done with respect to the correct estimation of the source position and source amplitude at various rotational speeds. Based on these findings, recommendations of the number of microphones to be used for actual measurements on rotating systems are given. In a second case, a benchmark fan is analyzed for different operating points to compare the source distribution and source amplitudes. Advantages, disadvantages and limits of the considered methods are shown.