PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Combining Structural Modification with In-Situ Transfer Path
Analysis to Solve Noise and Vibration Problems
Andrew ELLIOTT1; Nezam SANEI2; Martin GLESSER2
1
2

University of Salford, Greater Manchester, M5 4WT, United Kingdom.

Alstom Rolling Stocks & Components, 48 Rue Albert Dhalenne, 93400, SAINT-OUEN, FRANCE

ABSTRACT
In-situ TPA measurements provide blocked forces that can be used to diagnose structure borne noiseproblems in vehicles. One of the main advantages of in-situ TPA, also known as blocked force TPA, is that
all measurements are made with the source and receiver in a coupled state making measurements easier andensuring representative operation of the vibration source. Perhaps the greatest advantage however is that theblocked forces obtained, unlike contact forces, are an intrinsic property of the vibration source which means
they remain valid for modified or completely different receiver structures. In the paper, real world practicalexamples that exploit the advantages of in-situ TPA in terms of structure borne noise prediction and structuralmodification are presented. The first example is of a complex vibration source coupled at multiple points
through six degrees of freedom per interface to a test bench that is subsequently built into a new assembly forwhich structure borne noise predictions are made. A further example is then used to demonstrate how
structural modifications can be made to the receiver side of an assembly for the purposes of troubleshooting
noise and vibration problems using in-situ TPA.
Keywords: Transfer Path Analysis, Structure-Borne Noise, Sub-Structuring

1. INTRODUCTION
In-situ transfer path analysis (iTPA) and conventional transfer path analysis (TPA) bear many
similarities in terms of their application but the former has two distinct advantages. The first advantage
is that to implement an iTPA it is not necessary to separate the source and receiver structures during themeasurement of frequency response functions because the assembly is kept in the coupled state for all
measurements. The second advantage is that the iTPA approach yields blocked forces , an intrinsic
property of the source, whereas conventional TPA provides the operational forces at thesource-receiver interface. This subtle difference is perhaps the most significant advantage overall
because modifications to the receiver structure can be made and the blocked forces, by definition,
remain valid. Interface forces (from conventional TPA), on the other hand, are a property of theassembly and could therefore change significantly with only minor alterations to a receiver structure .
Beyond TPA, this freedom to transfer blocked forces from one assembly to another presents further
benefits because it allows one to characterize the vibration activity of a source on a test bench and touse the same blocked force dataset to virtually excite modelled systems obtained by experimental
sub-structuring, FEA, SEA or hybrid methods [1].
In this paper two case studies are presented to (a) illustrate the application of the blocked force
methodology combined with sub-structuring for the prediction of structure borne noise in a train and(b) to demonstrate the application of structural modification as a noise/vibration control measure.
For (a) an air generation and treatment unit (or AGTU) is characterized in terms of its blocked
forces using measurements on a test bench. This data is then combined with frequency response
functions of the AGTU and the train to predict structure borne noise. Comparisons are then made toactual measurements of the structure borne noise with the AGTU installed on a train. Case study (b)then demonstrates how design changes can be investigated by sub-structuring simple idealized
elements to this system using the combined methodology.
1
2

a.s.elliott@salford.ac.uk
nezam.sanei@alstomgroup.com

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2. THEORYIn this section of the paper the theory of in-situ transfer path analysis (iTPA), sub-structuring andstructural modification are outlined setting out the key terms and relationships used throughout the
paper. Useful references for the interested reader include [2-7].
2.1 In-situ Transfer Path Analysis
The blocked force, ܎‫܁‬ǡ‫ ܔ܊‬, of a structure borne sound source can be obtained from measurement
in-situ using the equation,(1)܎‫܁‬ǡ‫ ܔ܊‬ൌ ‫܇‬۱ି૚ ‫ܞ‬۱where f, Y and v are force vectors, mobility matrices and velocity vectors respectively.
Here, the uppercase subscript, S, denotes a property of source structure alone and, C, a property of
the coupled source and receiver assembly. The additional lower-case subscript, bl, indicates a blocked
condition. It is important to note here that blocked forces are a property of the source, S, and not theassembly, C, even though the source and receiver are coupled during measurements [2,3].
When performing an iTPA it is usual to measure a further set of frequency response functions, ۶۱ ,at the same time as measuring, ‫܇‬۱ , which relate forces at the source-receiver interface to a target
location (e.g. sound pressure or floor vibration). For the case of sound pressure, ‫ܘ‬۱ , we may write,(2)‫ܘ‬۱ ൌ ۶۱ ܎‫܁‬ǡ‫ܔ܊‬The combined dataset then allows one to investigate contributions to the interior noise fromdifferent paths by setting elements of the blocked force vector to zero and repeating the calculation ;thereby eliminating contributions from one or more paths [7]. This in turn allows one to identify thestrongest paths, the strongest forces and their combined contributions to a vehicles interior noise.
For example, in some cases just one source-path combination may dominate and, once identified,measures can potentially be taken to resolve the issue by structural modification. The advantage of
iTPA with respect to conventional TPA is then that changes to, ۶۱ , can be investigated without any
concerns regarding the potential effect on the interface forces (which are likely to be quite sensitive tochanges made to the receiver structure).
2.2 Sub-structuring and Structural Modification
The mobility of the source-receiver interface, YC , is a combination of the passive properties of thesource and receiver sub-structures, YS and YR respectively. Y C can expressed as the inverse of sum of
the source and receiver impedances ZS and ZR , where ࢆ ൌ ࢅି૚, i.e.
ି૚ି૚ࢅ࡯ ൌ ൣࢅି૚ࡿ ൅ ࢅࡾ ൧ି૚ൌ ൣࢆࡿ ൅ ࢆࡾ ൧

(3)

Similarly, the mobility of a structurally modified assembly, ࢅԢ࡯ , or receiver, ࢅԢࡾ,can be obtained bysub-structuring using the equations,ି૚ି૚ࢅԢ࡯ ൌ ൣࢅି૚࡯ ൅ ࢅࡹ ൧ି૚ି૚ࢅԢࡾ ൌ ൣࢅି૚ࡾ ൅ ࢅࡹ ൧

ି૚

(4)

ି૚

(5)

ൌ ൣࢆ࡯ ൅ ࢆࡹ ൧ൌ ൣࢆࡾ ൅ ࢆࡹ ൧

where the dash denotes a structurally modified component or assembly and, ࢅࡹ , is the matrix ofelements that are used to make the modification. For example, this could be a matrix of ideal mass or
stiffness elements or more complex components such as beams, plates or resonant absorbers. The key
point to note is that the blocked forces from equation (1) can again be used to excite these modified
structures because blocked forces are an intrinsic property of the source. For example, equation 4 incombination with Equation 1 can be used to predict vibration levels at the source-receiver interface ofa modified assembly using data describing the individual sub-structures.
Perhaps more usefully however, the frequency response function, ۶۱ , from equation (2) which
relates forces at the interface to a point of interest can also be obtained by sub -structuring using theequation,428۶۱ ൌ ۶‫ ܀‬ሾ‫ ܁܇‬൅ ‫ ܀܇‬ሿି૚ ‫܁܇‬

(6)

where, ۶‫ ܀‬, is a vibro-acoustic frequency response function for the receiver structure alone
Similarly, we may also write,۶Ԣ۱ ൌ ۶Ԣ‫ ܀‬ሾ‫ ܁܇‬൅ ‫܇‬Ԣ‫ ܀‬ሿି૚ ‫܁܇‬

(7)

Where, ۶Ԣ۱, is a vibro-acoustic frequency response function of an assembly where the receiverstructures mobility has been modified using equation (5). Note that ሾ‫ ܁܇‬൅ ‫ ܀܇‬ሿି૚ ‫܁܎ ܁܇‬ǡ‫  ܔ܊‬is the actualforce applied to the original receiver structure, ܎‫܀‬, and that this will not be the same force applied tomodified assembly, ܎Ԣ‫܀‬, because,ሾ‫ ܁܇‬൅ ‫ ܀܇‬ሿି૚ ‫ ് ܁܇‬ሾ‫ ܁܇‬൅ ‫܇‬Ԣ‫ ܀‬ሿି૚ ‫܁܇‬

(8)

Note also that because, ۶‫ ܀‬, may no longer be equal to, ۶Ԣ‫܀‬, the vibro-acoustic frequency response
functions relating forces at the interface to a response location might also be changed. A discussion
regarding how ۶Ԣ‫ ܀‬may be obtained in practice is given later in the paper.

3. Prediction of Structure Borne NoiseIn this section of the paper a case study is presented that demonstrates the real-world application ofequations 1, 2 and 6 for the prediction of structure borne noise within a train. This involved themeasurement of source blocked forces, source mobility, receiver mobility and a set of vibro-acoustic
frequency response functions for the train (without the vibration source installed). The passive FRF
data was then combined to make an experimental model of source-receiver assembly and this model
was excited using measured blocked forces to predict structure borne noise within the train carriage.
3.1 Blocked Force Measurements
An air generation and treatment unit (AGTU) was characterized in terms of its mobility andblocked forces taking into account six degrees of freedom at each connection point (three translational
and three rotational) with the AGTU supported on air springs as shown in figure 1. In order to take into
account six degrees of freedom at each connection point four accelerometers were oriented in thevertical z direction in order to capture translation in the z axis and rotation about the x and y axes. Twofurther accelerometers oriented in the x direction then capture translation in the x direction androtation about the z axis. A single accelerometer was the oriented in the y direction to capture theremaining degree of freedom. A description of the method used can be found in [8].
After performing measurements with the source resiliently mounted on air springs the source wasthen rigidly coupled to the test bench as shown in figure 1b. In this configuration an additional
accelerometer was installed at a remote location on the test bench. The measurements were thenrepeated but this time obtaining ‫܇‬۱ and ‫ܞ‬۱ to satisfy equation 1. The combination of measurementsin the free and rigidly coupled conditions on the test bench allowed the blocked forces to be va lidated
using two methods:
1. The blocked forces from the free and rigidly coupled test setups were compared for each
degree of freedom to confirm they were not affected by the boundary condition, and
2. The blocked forces obtained from the freely suspended condition were used to make a
prediction of the test bench vibration at a remote location away from the interface.
In theory both of the above should be satisfied because equations 1 and 2 are known to be exact for
linear, time invariant systems. However, experimental uncertainty and the number of degrees of
freedom included in the model are known to affect the agreement between blocked forces measured indifferent states and this in turn affects the accuracy of any subsequent sound or vibration predictions.
Furthermore, in some cases it is possible that source operation could be affected by the mounting
condition, i.e. the source’s behavior can be altered. Thus, by making checks 1 and 2 above thereliability of the blocked force data for structure borne noise predictions on the train can be assessed.

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Figure 1: (a) Air compressor installed on test benchsupported by air springs (top left) (b) air compressor
installed on test bench by rigid coupling, showing also
the position of the validation reference sensor (topright) and (c) instrumentation of the interface used tocapture 6 degrees of freedom (bottom left).

Shown in figure 2 is a comparison of the blocked forces measured in the free and rigidly coupledstates for one of the AGTU connection points in the vertical z direction. It can be seen that blocked
forces measured under both mounting conditions agree well over the majority of the frequency range
shown (20-2000Hz). Note that the operation of the AGTU was found to vary from one day to the next
by a similar order of magnitude, perhaps due to variations in environmental conditions (as observed inacceleration measurements made on the core of the compressor).
Shown in figure 3 is the reference vibration level measured on the test bench with the AGTU
operational (blue line) when mounted as shown in figure 1b. This is compared to a prediction of thevibration acceleration obtained using the blocked forces measured in the free condition (data check 2
above). Except for a few tonal peaks the agreement between measurement and prediction is very good,
especially when the repeatability of the AGTU’s operational behavior is considered.

Figure 2: Comparison of blocked forces measured on the test bench under two different boundary conditions- rigidly coupled (blue) and mounted on air springs (red). The blocked forces obtained under both boundary
conditions are in good agreement despite the different mount conditions demonstrating that the data is
independent of the installation condition [9].

430Figure 3: Prediction of test rig reference vibration levels in the vertical z direction with the AGTU operational.
The blue line shows the actual vibration level measured on the test rig when the source and receiver wererigidly coupled, and the orange line was predicted using in-situ measured blocked forces obtained when thesource was freely mounted [9].

3.2 Sub-Structuring
With the blocked forces of the compressor validated as described above a further measurement
campaign was carried out to validate the full prediction methodology. In order to do so frequency
response function measurements were made on a train with and without the compressor installed andthe sound pressure inside the train with the air compressor operational was measured. A photograph of
the AGTU installed on the train is shown in figure 4 below.

Figure 4: The air generation and treatment unit (AGTU) installed on the train.
In order to make a prediction of structure borne noise in the train it was first necessary to performmeasurements of the train mobility at the degrees of freedom where the AGTU was to be mounted andof the transfer functions relating the interface degrees of freedom to the interior sound pressure. Thiswas done by instrumenting the train using the same accelerometer arrangement as shown in figure 1cbut with an additional three microphones in the train carriage. This test setup allowed the simultaneous
acquisition of the train mobility and the vibro-acoustic frequency response functions by exciting, one
by one, all the interface degrees of freedom. Once these measurements had been completed the AGTU
was reinstated and the interior structure borne noise was measured for validation purposes.
The final result of this section is therefore a comparison of the train interior noise with a prediction431

of the structure borne component of the interior noise obtained using equation s 6 and 2 (see figure 5).
Note that the measurements on the train were performed in a reverberant space (a factory) and that themeasured train interior noise can be expected to include both the structure borne component and aflanking airborne paths, e.g. through door seals and windows, so one would not expect a perfectcomparison. Nevertheless, the prediction result is very encouraging with most of the frequency range
shown displaying a good agreement between the measured and predicted response (the difference to in
the overall A-weighted sound level was 2.5dBA). The under prediction in the frequency range
1000-2000Hz is thought to be in part due to airborne transmission. Recall also that the source
repeatability may not be perfect, for example it can be seen that the operational speed of the AGTU on
the train was slightly lower than on the test bench.

Figure 5: Prediction of structure borne noise in the train with the AGTU operational (dashed red line)
compared to the actual interior noise (solid black line). The y-tick divisions each represent 10dB.

4. Structural Modification
As explained in the introduction and theory sections of the paper, one of the main advantages ofblocked forces over contact forces is that they remain valid even after a modifications to a source
receiver assembly (providing the modifications are made downstream of the interface). This wasshown experimentally to be the case in figures 2 and 3 in the previous section. By means of an example
it is therefore interesting to experiment with the possibility of sub -structuring simple elements orcomponents to the coupled source-receiver assembly using equation (4). The purpose of doing so inreal world applications would be to investigate the influence of structural modifications to an assembly
to solve noise and vibration problems.
Shown in figure 6 is the accelerance of the z-direction at one of the interface points of thesource-receiver assembly (blue line). To implement the structural modification approach, theaccelerance of the z-direction degrees of freedom were modified by sub-structuring virtual lightly
damped springs (of stiffness, k=3x106 Nm-1) to each node of the 4 z-oriented nodes at each connection
point. Applied in practice, this would have the effect of stiffening the receiver structure in thez-direction and rotationally about the x and y axes. It can be seen in the figure that the orange line
(representing the modified assembly) now has a lower accelerance than the original source receiver
assembly. It can be expected therefore that the vibration at the source receiver interface will also be
significantly altered by this structural modification.
After artificially modifying the source-receiver interface the vibration response of the modified
assembly was then predicted using equation (1). The resulting vibration level is shown in figure 7 witha comparison to vibration the vibration level at the same point prior to structural modification. It canbe seen in the figure that the vibration acceleration at the interface (in the vertical z -direction) would
be reduced significantly in the frequency range 0-800Hz by making such a change to the receiverstructure. Similar plots could also be made for the force on the receiver or the transmitted power
making it a useful tool for the investigation of noise and vibration mitigation measures. What is often
required however is the vibration or sound level at a response position that is remote from thesource-receiver interface.
As previously mentioned in section 2 of the paper, when the response at a remote location isrequired the process of artificial structural modification is somewhat more challenging because432equation 7 might then be used and any alteration to the transfer function relating the remote responseto the interface degrees must also be taken into account. This is inconvenient because additional
measurement positions are required for every position on the system where a structural modification
might be made. In such instances it is likely therefore to be more useful to either excite a numericallymodelled system (e.g. obtained using SEA or FEA) or a modal model obtained by measurement. Thisis a promising area for further research.

Figure 6: Example of modification to the accelerance of the coupled source receiver assembly in the verticalz-direction. The source receiver assembly was modified by sub-structuring damped springs of stiffness
k=3x106 Nm-1 to each of the nodes oriented in the z direction (orange line). This is compared to theaccelerance before structural modification (blue line).

Figure 7: Example of the influence of artificially stiffening the source receiver interface on the vibration
acceleration at the interface in the z-direction (orange line). The vibration level of the unmodified system isshown as a blue line.

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5. CONCLUDING REMARKS
Described in the paper are two case studies that demonstrate the use of the in -situ blocked force
approach in combination with sub-structuring, sometimes referred to as component TPA. The first casestudy describes measurements made to characterize a real-world vibration source on a test bench andthe data checks that were carried out to ensure the blocked forces obtained were suitable for making
predictions of structure borne noise. Six degrees of freedom were taken into account at each terminalof the source structure in these measurements which is unusual for a system of such complexity. The
blocked force data was then used to make predictions of structure borne noise in a train and it was
shown that the combined blocked force and sub-structuring methodology provide an estimate thatagrees with measurements made on the train (within 2.5dBA overall).
The second case study presented uses the same source-receiver assembly but investigates the use ofstructural modification by means of a simple example. For this case study it is shown how the effect ofstiffening of the receiver structure can be investigated by sub-structuring ideal springs to the source
receiver interface. The combination of methods and techniques presented in the paper provide a usefultoolset that can be employed for noise/vibration prediction, diagnostic testing and virtual prototyping.

ACKNOWLEDGEMENTS
We would like to thank Faiveley Transport in Turin (Italy) and also Alstom rolling stocks factory in
Katowice (Poland) for providing the equipment case study and for their hospitality and support
provided during the measurement campaigns. This contribution reflects the views of the authors.

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