The synthesis of spatially correlated random pressure fields

Abstract

The feasibility is considered of synthesizing a spatially correlated random pressure field having specified statistical properties. Of particular interest is the use of a near-field array of acoustic sources to synthesize a pressure field whose statistical properties are similar to either a diffuse acoustic sound field or to that generated by a turbulent boundary layer (TBL). A formulation based on least-squares filter design is presented. Initially, the more fundamental question is addressed of how many uncorrelated signal components are required to approximate the pressure field. A one-dimensional analysis suggests that two uncorrelated components per acoustic wavelength are required to approximate a diffuse pressure field. Similarly, for a TBL pressure field, about one uncorrelated component per correlation length is required in the spanwise direction and about two uncorrelated components per correlation length are required in the streamwise direction. These estimates are in good agreement with theoretical predictions for an infinite array, based on the Fourier transform of the spatial correlation function. When a full simulation is performed, including the acoustic effect of an appropriately positioned array of monopole sources, it is found that the number of acoustic sources required to reasonably approximate the diffuse or TBL pressure field is only slightly greater than the lower bound on this number, set by the number of uncorrelated components required

The experimental synthesis of random pressure fields: Methodology

“…24 Recently, the multichannel simulation of a TBL excitation over a plane grid of microphones using a near-field array of acoustic sources has been theoretically investigated. [25][26][27] But, to the best of our knowledge, the experimental reproduction of two-dimensional random processes such as those described in the above using an array of near-field loudspeakers has not yet been achieved. A recent preliminary experiment studied the invertibility of the plant matrix between a set of loudspeakers and microphones housed within an enclosure on top of which is mounted a test panel.…”

“…A recent preliminary experiment studied the invertibility of the plant matrix between a set of loudspeakers and microphones housed within an enclosure on top of which is mounted a test panel. 27 It was recommended that the enclosure modal resonances should be heavily damped so that the plant transfer functions can be equalized.…”

The experimental synthesis of random pressure fields: Practical feasibility

“…1͒. Previous studies 8,9 have shown that a −10 dB mean-square error J e can be considered as a threshold below which an accurate reproduction of the desired pressure field is achieved. For completeness, comparisons are also made between the assumed and predicted spatial correlation structures, C dd and C yy , for each of the three random pressure fields to be synthesized ͑top and middle rows of Figs.…”

“…Such an approach builds upon previous theoretical works concerning the synthesis of TBL wall-pressure fluctuations using a number of suitably driven acoustic monopoles. 8,9 Subsequently, an experimental setup has been designed for the laboratory reproduction of spatially correlated random pressure fields with a near-field array of 4 ϫ 4 loudspeakers. 1, 10 Preliminary investigations have shown that this arrangement should a priori be able to reproduce the statistics of an acoustic diffuse field and a grazing incident plane wave over a broad frequency range whereas the simulation of TBL loads appears to be restricted to the very low frequency domain.…”

Modeling local active sound control with remote sensors in spatially random pressure fields

“…In the simulations below it will be assumed that the primary sources are uncorrelated, so that S vv is a diagonal matrix, although this is not necessary in the general formulation. The spectral density matrix could, for example, be used to define a spatially correlated pressure field 22 or a set of original primary and secondary sources and their image sources, to approximate an enclosed sound field. 3 The block diagram for the control system is illustrated in Fig.…”