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218 Advances in Productive, Safe, and Responsible Coal Mining

The hybrid method is described in several papers [6–8]. This particular implementa-
tion of the hybrid FE/SEA method specifically involves coupling an FE structural
model to a SEA acoustic model. In this case, the acoustic space is an infinite space
(as opposed to an enclosed cavity). The structure “feels” the effect of the fluid and
radiates sound. The SEA model of the fluid structure interaction allows for a few more
approximations than the other methods. Exact approximations depend on how sur-
faces are meshed. Surfaces are broken up into simply connected regions, called faces.
Faces are the key to the hybrid coupling and determine where assumptions are made.
Assumptions made on each face are: (1) each face is assumed to be uncorrelated from
adjacent faces, (2) the curvature of each face is ignored, and (3) each face is considered
to have baffled boundary conditions. Making the faces as large as possible typically
makes the analysis more effective, mostly due to the first assumption, but somewhat
due to the third assumption. However, sometimes large surfaces of a structure are not
well approximated as flat faces. Gentle curves do not present a problem, but some
curvatures have an impact. Nevertheless, even with these assumptions, the hybrid
method was developed for and should have good accuracy in the midfrequency region
(500–2000Hz). The hybrid method can be as much as two orders of magnitude faster
than some of the other methods.

12.3.2 Microphone phased arrays and beamforming

One of the first steps in any noise control program is the identification and location of
dominant noise sources. It is critical that control measures attenuate the sound radiated
by these dominant sources or they will not be effective. This is especially true in large
machines where there are numerous noise sources and where treating a lower-level
source may have no effect on the overall noise level.
Microphone phased array (MPA) technology is an effective and very efficient tool
to identify the physical location and the frequency content of dominant noise sources
in mining equipment. The main advantage of MPA technology is the improved speed
for the noise source identification process. In general, it takes a few minutes to collect
and process the data using MPA technology, in contrast to several hours or even days
of data collection required when using acoustic intensity measurements to identify
dominant noise sources.
MPA technology comprises two components: (1) hardware, which consists of an
array of microphones distributed in a predetermined pattern and a data acquisition sys-
tem capable of sampling microphone data simultaneously up to the maximum fre-
quency of interest; and (2) a computational algorithm known as beamforming. This
algorithm adjusts the phase of the microphone signals based on a grid of assumed
source locations, and a source model. The most commonly used model is that of a
monopole source.
In its most simple form, the beamforming algorithm assumes that a sound source
(e.g., a monopole source) exists at each grid point location. Then, for each assumed
noise source, the time delay between the grid point and each of the microphones is
computed. Next, the measured microphone signals are time shifted according to
the computed time delays and summed up. If an actual noise source is located at