Partial Field Decomposition Research Articles

A partial field decomposition algorithm and its examples for near-field acoustic holography

In this paper we introduce a practical algorithm that can accurately implement partial field decomposition for near-field acoustic holography (NAH). Unlike other methods, the algorithm does not require sensors near sources because it uses calculations rather than measured signals in order to decompose a holography image into the images of individual sources. Therefore it makes holography measurement easier than other methods. The algorithm is composed of five steps: measurement of pressure on a hologram plane, estimation of pressure on a source plane, selection of maximum pressure, estimation of the sound field from one source, and estimation of the remaining sound field. In this paper we also report two experiments that verify and demonstrate the algorithm. In one experiment six speakers are operated independently. The other is a vortex shedding experiment. Their results show that the decomposition method is useful for identifying hidden sources and estimating the power of individual sources.

Partial sound field decomposition in multireference near-field acoustical holography by using optimally located virtual references

It has been shown previously that the multiple reference and field signals recorded during a scanning acoustical holography measurement can be used to decompose the sound field radiated by a composite sound source into mutually incoherent partial fields. To obtain physically meaningful partial fields, i.e., fields closely related to particular component sources, the reference microphones should be positioned as close as possible to the component physical sources that together comprise the complete source. However, it is not always possible either to identify the optimal reference microphone locations prior to performing a holographic measurement, or to place reference microphones at those optimal locations, even if known, owing to physical constraints. Here, post-processing procedures are described that make it possible both to identify the optimal reference microphone locations and to place virtual references at those locations after performing a holographic measurement. The optimal reference microphone locations are defined to be those at which the MUSIC power is maximized in a three-dimensional space reconstructed by holographic projection. The acoustic pressure signals at the locations thus identified can then be used as optimal “virtual” reference signals. It is shown through an experiment and numerical simulation that the optimal virtual reference signals can be successfully used to identify physically meaningful partial sound fields, particularly when used in conjunction with partial coherence decomposition procedures.

A comparison of partial coherence and singular value partial field decomposition in the context of near-field acoustical holography

Sound fields radiated by complex noise sources, e.g., automotive engines, generally comprise superposed individual fields generated by incoherent subsources. When applying near-field acoustical holography (NAH) to such fields it is first necessary to decompose the total sound field measured on the hologram plane into coherent partial fields, each of which is then projected to a reconstruction plane where they are summed on an energy basis. The partial field decomposition is performed after first calculating the cross spectra between a number of reference microphone signals that have been conditioned by using either partial coherence or singular value decomposition procedures, and the spatially sampled sound pressures on the hologram plane. That cross-spectral information then allows the partial fields to be created. In this presentation, the performance of the two reference signal decomposition procedures will be compared theoretically and experimentally. In particular, it will be shown that partial coherence decomposition allows the partial fields to be associated with the fields radiated by individual subsources if the latter are sufficiently separated spatially. In contrast, the singular value decomposition procedure usually results in partial fields that combine the properties of the subsources, and are thus not directly related to the fields radiated by individual subsources.