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TRANSFER PATH ANALYSIS METHOD APPLIED TO DIAGNOSTIC TESTING OF SOUND INSULATION PERFORMANCE OF CAVITY CONSTRUCTIONS

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Transfer Path Analysis methods are one of the most widely used techniques for diagnostic testing of structural and airborne sound transmission. Although widely used in the automotive sector, these methods however have not been adopted in the Building Acoustics domain and the paper intends to explore their usability in this context. Commonly used Inverse techniques such as Panel Contribution Analysis methods require extensive measurements usually involving reciprocal transfer functions and could be time consuming when the radiating structures/panels can be complex and large in size such as building elements. The presented work deals with defining an alternative method for predicting the receiving side pressure by using frequency response functions of the path and receivers and operational measurements. This removes the need for volume velocity sources and reciprocal measurement of frequency response functions. The accuracy of this method is dependent on the spacing of measurement points with respect to incident wavelength. Results are presented for the sound transmission through a cavity-backed plate.
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TRANSFER PATH ANALYSIS METHOD APPLIED TO
DIAGNOSTIC TESTING OF SOUND INSULATION
PERFORMANCE OF CAVITY CONSTRUCTIONS
Nikhilesh Patil, Andy Elliott, Andy Moorhouse
Acoustics Research Centre
University of Salford, Manchester, M5 4WT, UK
Email: n.patil@edu.salford.ac.uk
ABSTRACT
Transfer Path Analysis methods are one of the most widely used techniques for
diagnostic testing of structural and airborne sound transmission. Although widely used in the
automotive sector, these methods however have not been adopted in the Building Acoustics
domain and the paper intends to explore their usability in this context. Commonly used
Inverse techniques such as Panel Contribution Analysis methods require extensive
measurements usually involving reciprocal transfer functions and could be time consuming
when the radiating structures/panels can be complex and large in size such as building
elements. The presented work deals with defining an alternative method for predicting the
receiving side pressure by using frequency response functions of the path and receivers and
operational measurements. This removes the need for volume velocity sources and reciprocal
measurement of frequency response functions. The accuracy of this method is dependent on
the spacing of measurement points with respect to incident wavelength. Results are presented
for the sound transmission through a cavity-backed plate. Other potential applications of the
method include finding the pressure distribution, incident power on a panel or building
elements, etc.
1 INTRODUCTION
Standard test procedures [1] have been developed over the years for rating the performance of
building elements with respect to airborne sound insulation, absorption, etc. These ratings are
quantified by a single number or in third octave bands and, although convenient for
comparing the performance of building elements, provide little, if any, information on how
the sound transfer takes place and the contribution of various paths to the total sound transfer.
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Similar problems are faced by the automotive industry for structure borne sound transmission
and the Transfer Path Analysis (TPA) method has been used in vehicles for quantifying the
contribution of different paths to the vibration or sound level at a receiver position. A similar
technique can be therefore be applied to study the acoustic loads on a building element
subjected to an airborne sound source and the corresponding sound transfer paths to a
receiver position. The current work presents a novel application of the TPA, or more
accurately iTPA to the problem of airborne sound transmission through building elements.
2 TRANSFER PATH ANALYSIS
In applying TPA method, at first the system is discretized into a source-path-receiver model.
In the passive test, the source is disconnected from the receiver side to measure the transfer
functions or Frequency Response Functions (FRF’s). In-situ approaches [2, 3, and 4] have
also been developed so that source is not required to be separated for FRF measurements.
Reciprocal FRF measurements have been discussed in the literature [5, 6] for faster
measurements than the direct method. The active test is the operational phase where the
source excites the system and operational responses are measured. In iTPA, the blocked
forces are then found as per equation (1), or the actual force corresponding to the
conventional TPA, both are likely to be similar in this application. In equation (1), A is the
accelerance matrix formed from FRF measurements, and a is the operational acceleration
vector; capital letters denote a matrix and lower case letters a vector. In this way, the blocked
forces can be mapped onto the receiver surface points with the help of the path FRF’s to
determine the path contributions as will be explained below. Similar approaches such as
‘Panel Contribution Analysis’ or ‘Source Path Contribution Analysis’ can be found in
literature [7, 8] but this method differs in because the structure borne TPA, or rather iTPA is
used to analyse the transfer of airborne noise through a partition.

(1)
2.1 TPA for Airborne sound transmission through a building element
Unlike a structure borne sound source with finite connections with the receiver and transfer
paths, the sound field produced by an airborne source (where air is effectively the source)
results in a continuum over receiver resulting in an infinite number of paths to the receiver
position. The intuitive TPA approach would be to measure the acoustic FRF (pressure to
volume velocity). However, the accelerance can instead be measured with impact testing to
give the blocked forces associated with each path. Interestingly, this sound field can be
mapped as a set of blocked forces or blocked pressures which are blocked forces per element
area. These blocked pressures represent the blocked sound field on the surface. In a sense,
they act as pressure sensors over the paths which are otherwise used in conventional TPA for
finding the acoustic FRF’s. Similar to Panel Contribution Analysis methods, this blocked
sound field can then be mapped with the vibroacoustic FRF’s (pressure to force) to predict
the path contributions to the final pressure.
For our current work, sound transmission through a plate was studied to see if the
pressures inside a cavity in an airborne sound transmission scenario could be predicted. Work
has done by [9] for pressure prediction inside a cavity for a structure borne sound
transmission. Our work essentially explores the application of TPA for an airborne sound
transmission. The schematic of the experiment is shown in Figure 1. To study the sound
transmission through a cavity backed plate the first part would be to find the blocked forces
over the plate. With impact testing, the accelerance for the plate and vibroacoustic FRF’s for
the receiver points inside the cavity can be measured. In the second phase, operational
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measurements of accelerations over the plate and pressures inside the cavity are measured.
After finding the blocked forces over the plate, they can be used with the vibroacoustic
transfer functions to predict the pressures inside the cavity.
Figure 1: Phase 1-Passive test (left), Phase 2-Operational test (right).
2.2 Pressure validation test: Setup and Measurements
The actual wooden box is shown in Figure 2 and sealed with a Perspex plate. Silicone sealant
was used between the plate and box edges to minimise any flanking transmission from the
walls to the plate. The only assumption in this work is that all the sound transmission into the
cavity takes place through the plate. It is important to notice that however thick and hard the
cavity walls are, there would be some transmission through them especially through low
frequencies.
Figure 1: The test setup- the wooden box (top left), Perspex plate (top right), free-field
microphones (bottom left), and the assembled box (bottom right).
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Accelerometers were placed over the plate surface and Type MCE 212 (free field)
microphones were used inside the box. With impact testing on the plate, the FRF
measurements yield an accelerance matrix as,
 
 
 
(2)
Aij represents the FRF matrix with transfer functions (a/f). ‘a’ is the acceleration and
f’ is the impact force, ‘i’ are the response points and ‘j’ the excitation points. Simultaneously
the vibroacoustic FRF’s were measured for the forces on the plate and pressures inside the
box with the help of pressure microphones.
 
 
 
(3)
Hkj represents the vibroacoustic FRF matrix with transfer functions (p/f). ‘p’ is the
pressure at a point inside the cavity and f is the impact force over the plate, ‘k’ is the
number of pressure points. For the operational phase, a loudspeaker was used with a pink
noise excitation driven through a B&K noise generator. A pink noise excitation has constant
energy in third octave bands and easy to analyse. The airborne sound from the loudspeaker
excites the plate which excites the sound field in the cavity. The operational accelerations and
pressures were measured with respect to the driving voltage of the noise generator which
ensures that the signals are synchronous. With the operational accelerations over the plate,
the blocked forces are calculated as

(4)
fblrepresent the block forces over the plate and ‘athe operational accelerations.
These blocked forces map the sound field on the plate by using vibration responses instead of
pressure responses. The pressure inside the box can thus be predicted as

(5)
pp is the pressure predicted at points inside the cavity. These predicted pressures
were then compared with the operational pressures at the same points to check the validity of
the applied TPA method.
3 RESULTS
A sample experiment with a 3x3 grid of accelerometers was carried out to see if the
validation test works. The grid size was eventually increased and results are shown in Figure
3 and Figure 4 for a 4x4 and 8x8 grid sizes over the plate respectively. For the 8x8 test only
16 accelerometers were available, hence the test was divided into 4 parts, by applying a 4x4
measurement grids on a quarter of the plate. Each quarter run gives a measurement of transfer
functions with 64 force and 16 points over the plate. 3 more runs on different quarters of the
plate were carried out to finally give an accelerance matrix of 64x64.
From the results, the pressure validation improves with the spatial resolution. Note
that the validation results for the 8x8 grid are without any regularisation which shows the
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value of a good measurement. The validation results are convincing assuming sound
transmission only through the plate. The prediction is a representative of the sound
transmitted through the plate only and hence the difference in sound pressure levels in the 80-
120 Hz region might be attributed to the sound transmission through the walls at low
frequencies.
Figure 3: Pressure validation results for a 4x4 measurement grid over the plate.
Figure 4: Pressure validation results for an 8x8 measurement grid over the plate.
Overall, these results give confidence in applying the TPA theory towards a much
complex structure such as a ribbed structure. Here lies the true application of this TPA
method which would give us a quantitative estimate of how different parts of a complex
building element contribute to the total sound transfer. Such an analysis was also applied to
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the plate case. The plate was divided into different paths with equal areas (figure 5) to study
their individual path contributions. The results are shown in figure 6.
Figure 5: Plate divided into four paths (left) mentioned by color codes (right)
Figure 6: Path contributions of different paths over the plate.
It is interesting to see that at low frequencies up to 100 Hz, the majority of sound
transfer takes place through the centre region of the plate. As we go higher up the frequency
range, the sound transfer through the corners and sides become more significant. This helps
to illustrate the potential for diagnostic analysis of path contributions.
4 CONCLUSIONS
1) A novel application of TPA on Building elements has been developed and applied for
studying the airborne sound transmission into the cavity through the plate. Without using real
pressure sensors, the sound field can be mapped onto the path using vibration responses. The
pressures have been predicted with good confidence inside the cavity.
2) The real application now lies in applying this TPA method on a ribbed structure or a point
connected structure. This could potentially give valuable information about the path
behaviour and contributions to the total sound transmission.
3) The prediction of pressures inside the cavity in any frequency range of interest depends on
the paths of sound transmission taken into account. In the present study, the plate is the most
dominant path of sound transfer into the cavity as the validation results show. Any other
sound transfer may be attributed to the walls.
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4) The spatial resolution of the measurement points on the plate determine the frequency
range of signals captured and hence determines the applicability of the method in the required
frequency range of interest. This follows from the Nyquist theorem which calls for use of at
least 2 points within the wavelength of a signal to capture/measure that wavelength
effectively.
5) Results for the inversion of a 64x64 FRF matrix were obtained without any regularisation
and apparently without significant inversion errors. This was attributed to good quality input
data.
5 REFERENCES
[1] BS EN ISO 10140-2:2010. Acoustics. Laboratory measurement of sound insulation of
building elements. Measurement of airborne sound insulation, 2010.
[2] A.S. Elliott, A.T. Moorhouse. In-situ characterisation of structure borne noise from a
building mounted wind turbine. Proceedings of ISMA2010 including USD2010, 2055-2068,
2010.
[3] A.T. Moorhouse, A.S. Elliott and T.A. Evans. In situ measurement of the blocked force of
structure-borne sound sources. J. of Sound & Vib., 325(4-5), 679-685, 2009.
[4] P. Gajdatsy, K. Janssens, Wim Desmet, H. Van der Auweraer. Application of the
Transmissibility Concept in Transfer Path Analysis. Proceedings of ISMA2010 including
USD2010, 3909-3925, 2010.
[5] F.J. Fahy. Some applications of the reciprocity principle in experimental vibroacoustics.
Acoustical Physics, 49(2), 217-229, 2003.
[6] K. Rissler. Applying the reciprocal Transfer Path Analysis (TPA) for the airborne sound
of power train components. MSc Thesis, Chalmers University, 2011.
[7] J. Hald and Masaki Tsuchiya. Panel Contribution Analysis using a Volume Velocity
Source and Double Layer Array with the SONAH algorithm. Internoise 2006, 2006.
[8] A.S. Elliott, A.T. Moorhouse, T. Huntley, S. Tate. In-situ source path contribution
analysis of structure borne road noise. J. Sound &Vib., 332(24), 6276-6295, 2013.
[9] P. Schevenels, Van Der Linden, G.J. Peter and G. Vermeir. An Inverse Force
Measurement Method to Determine the Injected Structure-Borne Sound Power from an
Installation into a Building Element. J. of Building Acoustics, 17(3), 199-219, 2010.
... Such pressure validation will be used throughout the paper to validate the methodology of the test. Some pressure validation results for single leaf panels are presented in an earlier work [6]. ...
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