Regularization plays an important role in Near-field Acoustical Holography (NAH), and choosing the right amount of regularization is crucial in order to get a meaningful solution. An automated method such as the L-curve or Generalized Cross-Validation (GCV) is often used in NAH to choose a regularization parameter. These parameter choice methods (PCMs) are attractive, since they require no a priori knowledge about the noise. However, there seems to be no clear understanding of when one PCM is better than the other. This paper presents comparisons of three PCMs: GCV, L-curve and Normalized Cumulative Periodogram (NCP). The latter method is new within NAH and it is based on the Fourier transform of the residual vector. The methods are used in connection with three NAH methods: Statistically Optimized Near-field Acoustical Holography (SONAH), the Inverse Boundary Element Method (IBEM), and the Equivalent Source Method (ESM). All combinations of the PCMs and the NAH methods are investigated using simulated measurements with different types of noise added to the input. Finally, the comparisons are carried out for a practical experiment. This aim of this work is to create a better understanding of which mechanisms that affect the performance of the different PCMs.

The spherical wave expansion with a single origin is sometimes used in connection with near-field acoustical holography to determine the sound field on the surface of a source. The radiated field is approximated by a truncated expansion, and the expansion coefficients are determined by matching the sound field model to the measured pressure close to the source. This problem is ill posed, and therefore regularization is required. The present paper investigates the consequence of using only the expansion truncation as regularization approach and compares it with results obtained when additional regularization (the truncated singular value decomposition) is introduced. Important differences between applying the method when using a microphone array surrounding the source completely and an array covering only a part of the source are described. Another relevant issue is the scaling of the wave functions. It is shown that it is important for the additional regularization to work properly that the wave functions are scaled in such a way that their magnitude on the measurement surface decreases with the order. Finally, the method is applied on nonspherical sources using a vibrating plate in both simulations and an experiment, and the performance is compared with the equivalent source method.

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Among the popular techniques for acoustic source identification in complex environments are the Statistically Optimal Near Acoustic Holography (SONAH) and the Inverse Boundary Element Method (IBEM). These two methods are quite different regarding the underlying assumptions and the practical implementations: Whereas SONAH performs the back-propagation of the sound field to a plane surface; the IBEM has no restrictions on the radiating geometry. On the other hand, IBEM requires the generation of a surface mesh and a time consuming solution process. The present paper compares the performance of the methods for a number of experimental test cases and studies the influence on the performance of the models when changing selected parameters.

Summary. This paper describes a pass-by measurement technique that has been developed for localization and visualization of noise sources on moving rail vehicles using beamforming. Based on measurements with an array of microphones, while also measuring the position of the vehicle, the technique calculates the contribution of noise, and visualizes it as a contour plot on top of a picture of the train. Deconvolution is applied in addition to traditional beamforming in order to get an improved spatial resolution in the noise map. A set of measurements was made on two different types of regional trains on the Danish railway: the Oresund trains and the IR4 trains. The speed of all the trains was approximately 120 km/h. The results show that deconvolution is efficient for identifying wind noise on the pantograph of the Oresund trains. The IR4 trains turned out to have a strong source at the very front part of the train for frequencies around 600 Hz -800 Hz with a radiated sound power that was approximately 5 dB above the noise radiated by the noisiest bogies. The cause of this noise is yet unknown, but a potential explanation could be an aerodynamic phenomenon at the front.