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A Comparison of Two Source Characterisation Techniques Proposed for Standardisation


Abstract and Figures

Automotive industry shows an increased tendency towards characterisation of vibration sources by independent quantities such as blocked forces and free velocities. Currently two independent ISO working groups propose standards for this source characterisation process. Both standards are still under development. In this paper it is shown how the different approaches can be derived and compared using the general framework for Transfer Path Analysis (TPA). It is shown how one standard clearly relates to classical TPA methods (using interface forces), while the other standard adheres the component-based TPA principles (using blocked forces). Practical guidelines found in the standard proposals are reviewed, allowing for a qualitative comparison of the proposed procedures. To address typical problems regarding completeness of the interface, an addition is proposed that incorporates the use of 6-DoF Virtual Point forces and moments. It is shown how this approach can be applied to any force characterisation, improving the general usefulness of the found forces. A simulated numerical test case shows the procedure of both standards and discusses the added value of including rotational moments in the source-describing force vectors. An industrial application case demonstrates the application of the second standard with the addition of virtual point forces and moments, leading to perfect agreement with the on-board validation sensor.
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2019-01-1540 Published 05 Jun 2019
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A Comparison of Two Source Characterisation
Techniques Proposed for Standardisation
Daniël van den Bosch and Maarten van der Seijs VIBES Technology
Dennis de Klerk Müller-BBM VAS
Citation: van den Bosch, D., van der Seijs, M., and de Klerk, D., “A Comparison of Two Source Characterisation Techniques Proposed
forStandardisation,” SAE Technical Paper 2019-01-1540, 2019, doi:10.4271/2019-01-1540.
Automotive industry shows an increased tendency
towards characterisation of vibration sources by inde-
pendent quantities such as blocked forces and free
velocities. Currently two independent ISO working groups
propose standards for this source characterisation process.
Both standards are still under development.
In this paper it is shown how the dierent approaches can
bederived and compared using the general framework for
Transfer Path Analysis (TPA). It is shown how one standard
clearly relates to classical TPA methods (using interface forces),
while the other standard adheres the component-based TPA
principles (using blocked forces). Practical guidelines found in
the standard proposals are reviewed, allowing for a qualitative
comparison of the proposed procedures. To address typical
problems regarding completeness of the interface, an addition
is proposed that incorporates the use of 6-DoF Virtual Point
forces and moments. It is shown how this approach can
beapplied to any force characterisation, improving the general
usefulness of the found forces. A simulated numerical test case
shows the procedure of both standards and discusses the added
value of including rotational moments in the source-describing
force vectors. An industrial application case demonstrates the
application of the second standard with the addition of virtual
point forces and moments, leading to perfect agreement with
the on-board validation sensor.
In order to win in highly innovative and competitive
markets, automotive OEMs are continuously improving
their R&D methods to increase product quality, while
reducing time and costs of both engineering and production
processes. Following the transition to a more modular design
strategy- to cope with the ever-expanding product eet- it
appears that more R&D eorts are occurring at the suppliers
site. While suppliers assume more responsibility for the engi-
neering of particular components, it remains the task of the
OEM to safeguard their performance aer integration in the
full vehicle. With the shortening of development cycles and
time-to-market, clear means for communicating about
component performance become even more necessary.
In the area of engineering that concerns sound & vibra-
tion performance, oen denoted by NVH (Noise, Vibration
& Harshness), these challenges are clearly recognised. Indeed,
OEMs and suppliers have found renewed interest in methods
such as Transfer Path Analysis (TPA) [1], blocked force source
characterisation [2] and Dynamic Substructuring [3], to nd
technological answers to issues such as target specication
and test bench design for their components. More specica lly,
technological answers are sought to full the following goals:
1. Expressing the vibrational activity of a source
component by quantities that are independent of the
assembly in which the component is tested. In this way,
a supplier can evaluate the active source vibrations by
conducting measurements on a component test bench
rather than in the full vehicle. is goal has
implications for the test bench design, as well as the
methodology for source characterisation.
2. Transferring the measured quantities to a virtual
vehicle model to predict NVH performance in an early
phase. OEMs oen see development stages where full
vehicle prototypes are not already available, yet
important choices have to bemade regarding
placement and isolation of active components.
Dynamic Substructuring can greatly benet this
conceptual phase, as it allows to compute the relevant
transfer characteristics by coupling the passive
dynamics of the subsystems in the chain. It’s
application to TPA is oen denoted as Component-
based TPA [4] which assumes blocked forces as the
source-describing quantities.
3. Denition of simple, yet robust component targets that
sustain changes throughout the development cycle. A
clear separation of responsibilities is only possible if
targets can bedened that are robust enough to
withstand small changes to the subsystems, but also
easy to interpret and use. e success of this is highly
subject to the methodological choices as mentioned
above and the common understanding of both parties
of what these methods entail.
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Now that the challenges above have long been addressed by
scientic studies, industrialisation calls for a clear standardi-
sation of methods. To that end, two ISO standards are
currently in the making (from here on bedenoted by Standard
1 and Standard 2):
1. Standard 1: ISO/AWI 21955 “Vehicles— Experimental
method for transposition of dynamic forces generated
by an active component from a test bench to a vehicle
[5], based on French standard XP R 19-701.
2. Standard 2: ISO/DIS 20270 “Acoustics—
Characterization of sources of structure-borne sound
and vibration- Indirect measurement of blocked
forces” [6].
e main focus of Standard 1 seems to beto help suppliers
design suitable test setups, while the focus of Standard 2 is
more in the direction of dening component specications.
is paper aims to highlight the propositions of both
standards and discuss their practical implementations. e
proposed method are reformulated using the TPA framework,
which is briey recalled from [1]. ereaer, the practical
aspects for implementation are discussed, along with a
comparison of application guidelines as proposed in the
respective standards. In answer to some potential shortcom-
ings that are identified, an extension is formulated that
augments the translational force descriptions with rotational
moments, easily obtained with roughly the sa me measurement
eorts. e last part of this paper demonstrates this approach
with an application of source characterisation of an
e TPA Framework [1] assumes that the structural transfer
path problem can beseparated into an active source compo-
nent A, hosting an excitation mechanism with (unknown)
forces f1, and a passive receiver structure B with target
response points of interest u3. The two subsystems are
connected at their interfaces, which are denoted by the set of
Degrees of Freedom (DoFs) u2. e assembled situation is
depicted by gure 1. e target response spectra are related
to the source excitation spectra by the assembled admittance
, namely:
e sub- and superscripts of the admittance terms are
understood as follows: ()31 means “responses at u3 for applied
forces at f1. e superscript()AB indicates that it concerns
the admittance of the assembly AB, hence the fully assembled
system. Furthermore, the term admittance is used, as a general
term to indicate any response due to an applied force or
moment. In practice this is oen the measured accelerance- as
obtained from the accelerometers on a structure- or mobility,
if one uses velocities in vector u. A more elaborate discussion
of the used notation and terminology can befound in [7].
Using Dynamic Substructuring theory, the assembled
response of equation (1) can be “split up” in the subsystem
FRFs YAand YB, as shown in g ure 2. Applying compatibility
of the interface coordinates and equilibrium of forces, the
interface forces
are found to be(dropping the explicit
frequency dependency):
and the target responses u3are obtained by multiplying
the passive-side FRFs
with the found interface forces:
3322 32 22 22
== +
Eq uat ion (3) is essentially a result of applying the LM-FBS
method for the special case where forces (f1) are only applied
on active side A. Nonetheless, the equation is generic for
multiple connection points and multiple sources, therefore
suited to derive many TPA methods from.
Based on the transfer path problem as described above,
the framework introduces three families of TPA. All methods
make use of operational measurements around the interfaces
of the active and passive systems. e rst two families then
use some notion of force to split up in a source-transmission-
receiver model, while the transmissibility-based TPA is a
response-only approach:
1. Classical TPA- intended to identify transfer path
contributions in existing products. e source
excitation is represented by interface forces, which are
a property of the assembly they are measured in.
2. Component-based TPA- powerful to simulate
component vibration levels in new products.
esource excitation is characterised by a set of
equivalent forces or velocities that are an intrinsic
property of the active component itself. More
popularly, these forces are known as blocked forces, as
they are the would-be forces (and moments) when
measured against a rigid boundary.
3. Transmissibility-based TPA- intended to identify and
rank transfer path contributions in existing products.
 FIGURE 1  Transfer problem from assembled admittance.
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 FIGURE 2  Transfer problem from subsystem admittances.
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ese methods use response measurements only and
derive a so-called transmissibility matrix from
“indicator” responses along the transfer paths.
e three fa milies of methods are br iey summarised nex t.
Classical TPA
e classical TPA uses operational interface forces as the
source-describing quantity. As seen from equation (3), these
interface forces straightforwardly lead to target responses by
multiplying them with the passive-side FRFs; see gure 3.
Interface forces can either bemeasured directly using
force transducers, or determined indirectly, typically by a
matrix-inverse operation with indicator responses measured
nearby the interfaces on the passive side. e resulting inter-
face forces do provide insight in the dynamics of the tested
assembly, but cannot be used in predicting dynamics in
dierent assemblies. is is now increasingly done using
component TPA methods.
Component-Based TPA
With component-based TPA, one is typically interested in
describing the source excitation is an independent manner,
such that it can beused to predict responses in new assemblies.
e most common independent descriptions are blocked
forces and free velocities. Dierent to equation (4), the assem-
bled-system transfer functions
are used for characteriza-
tion (shown in gure 4):
Blocked forces
can bemeasured directly using force
transducers between the active system and a rigid boundary,
in which case the blocked forces are the actually measured
“blocking” forces (discussed in detail in [1]). Indirectly, they
are determined in an assembly with e.g. a test bench, namely
using a matrix-inverse operation with indicator DoFs
measured on the test bench side. As the blocked forces (if
correctly determined) are invariant of the passive side,
response predictions can bedone using “substructured” FR Fs
, such that the same blocked forces can beused to predict
for an assembly of the active component A with any other
receiver B. is reads, for application of respectively blocked
forces and free velocities:
3322 32 22 22
22 2
AB bl BA
= (6)
Equation (6) can beregarded as the standard form of
component TPA in which the source activity is described by
blocked forces and the transfer path is fully substructured
from its components. Equat ion (7) is a variant that shows how
free veloc ities
- or actually free “accelerations”, if measured
by accelerometers- can beapplied to obtain theoretically the
same response prediction as equation (6).
Complete description of the interface is critical in compo-
nent-based TPA, especially when the test assembly is dierent
than the target assembly. is may have implications for the
inclusion of rotational DoFs in the force description, as will
bediscussed later on in this paper.
Transmissibility-Based TPA
Transmissibility-based TPA differs from the other two
methods in t he sense that no explicit notion of force is present
in the analysis: operational responses are the only inputs to
the TPA; hence the more popular name “Operational TPA
[8]. Typically, it is used to identify and rank dominant sources
and paths in vibrational behaviour. Central to the analysis
stands the transmissibility matrix
, established from indi-
cator sensors close to the transfer paths (DoFs u4). is is
illustrated by gure 5. By decorrelating their contributions
over multiple operational runs and load-cases, these u4
become adequate “indicators” of the path contributions to u3:
 FIGURE 3  Response prediction in classical TPA.
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 FIGURE 4  Response prediction in component-based TPA.
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 FIGURE 5  Transmissibility TPA.
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Also here it holds that any change made to the active or
passive side warrants a new operational measurement to
update the path contribution analysis.
is section will- for both standards- relate the theory as
described in the respective standards to the TPA framework
introduced in the previous chapter. Aer this, some practica li-
ties from both standards are compared.
Standard 1
e theory of Standard 1 essentially follows the Classica l TPA
theory, as it chooses interface forces as medium to describe
the active source vibrations. However, in order to beable to
translate interface forces measured on a test bench to a vehicle,
the relationship between interface forces for two assemblies
(AB and AR) is sought.
When considering the assembly depicted in gure 6, the
interface admittance is a summation of the interface admit-
tance of the active structure (A) and receiving structure (B),
in case of a rigid connection. When a resilient mount is incor-
porated, an additional term (−ω2/Zmt) can beadded to accom-
modate for the added exibility and damping eects. e
interface force in target assembly AB ca n then bedescribed by:
21 1
w (9)
Similarly, the interface force in test assembly AR (with
similar rigid and/or resilient mounting properties) reads:
w (10)
Rearranging and elimination of terms in equations (9)
and (10) yields the relation between the interface forces for
both assemblies:
22 22
With sucient knowledge of the active component (A),
the vehicle (B) and the test rig (R), this relation provides the
possibility to predict dynamics in any assembly of interest
(AB) by applying equation (11) and (4).
e standard provides a variety of methods to determine
the interface forces for the test rig assembly (AR), e.g. using
force transducers or from matrix inversions with indicator
responses. It should benoted that strict application of equation
(11) requires a lot of individual interface admittances, which
may render this method sensitive to (measurement) errors.
e standard therefore provides simplications for cases
where some subsystem FRFs are equal or dierent enough to
bele out of the calculation.
Standard 2
In contrast to Standard 1, the theory of Standard 2 is in line
with the component-based TPA family, more specically the
blocked force representation. Rather than using admittances
of individual components that need to beobtained under
free-floating conditions, admittances of assemblies are
used here.
Standard 2 describes a so-called in-situ characterization
[2] of the blocked forces using indicator sensors around the
coupling points; see gure 7. By applying a matrix-inverse
operation with the FRFs of the assembly’s interfaces to the
indicators (
), blocked forces can becalculated:
bl AB
Even though determined from operational measurements
on the target assembly, these blocked forces are an indepen-
dent property of the active source (A), which makes them
transferable to other receiving structures. Indeed, blocked
forces are determined in a similar manner on a test bench,
using FRFs
Predicting vibrational responses in a target assembly
is now as straightforward as applying equation (5), which
needs the FRFs of the target assembly
. There’s a variety
of methods to obtain this, ranging from using a FEM
approach to a full Experimental Dynamic Substructuring
approach [7].
 FIGURE 6  Standard 1: calculating interface forces.
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 FIGURE 7  Standard 2: using indicator sensors
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Now that the theory behind both methods is understood, this
section discusses several practicalities for both standards. e
following subsections denote the choices and denitions made
in respectively Standard 1 and 2, on the aspects of (a) interface
denition, (b) elastic mounts, (c) varying receiver dynamics,
(d) admittance measurements, (e) force identication, (f) force
validation and (g) response prediction.
(a)  Interface Definition
In the theory section above, ()2 is continuously used to
indicate interface DoFs. It is, however, not evident which DoFs
to take into account here, besides the fact that it is logical to
choose the same set for all measurements that concern
the analysis.
Std. 1 is practical guide is fairly straightforward. It
is described that at each coupling point, transla-
tions in X-, Y- and Z-direction comprise
the interface.
Std. 2 is norm does not provide an explicit denition
of the interface. It does mention that a ‘complete’
description is required and how incompleteness
and misalignment of interface DoFs are a main
source of errors.
e denition of the interface is further discussed later
on in this paper.
(b)  Elastic Mounts
Elastic mounts or bushings are commonly found in the auto-
motive world to decouple active vibrating structures and their
receiving counterparts.
Std. 1 As was already seen in the theory part of this
method, resilient mounts can beincorporated at
the interface. e application to do so is well
documented in the standard.
Std. 2 Although not explicitly mentioned here, when
considering these bushings to be part of the
receiving structure, they can beaccounted for.
(c)  Varying Receiver Dynamics
Since both standards consider an active source to betested in
combination with two receiving structures (B and R), all
dierences in structural interface admittance is implicitly or
explicitly accounted for.
Std. 1 Since the interface admittance of each individual
component is explicitly part of this method, a
variety of situations is discussed. In most cases
it is shown how it is safe to neglect one admit-
tance term in equation (11), enhancing the prac-
tical feasibility of this method.
Std. 2 For this method, component admittances are
implicitly included in assembly admittances.
Although this method yields a transferable
source characterisation, similar stinesses for
receiving structures are advised.
Besides the eect of subsystem admittances on the passive
dynamics, it can beargued that a signicant change in receiver
admittance may have an inuence on the origina l source exci-
tation. An example is a gearbox mounted to a very sti test
bench under signicant pre-load, inducing deection of the
housing. Slight misalignment of the internal gears might
already cause drastic increase of the active vibration levels.
(d)  Admittance Measurements
Both TPA methods involve measuring admittances in the
form of FRFs and/or NTFs (“noise transfer functions”, the
sound pressure response due to an applied force/moment).
Although shaker measurements are also commonly used to
obtain FRFs, both standards mostly speak of impact
hammer measurements.
Std. 1 Practical guidelines on performing a basic impact
measurement are given using an impact hammer
and accelerometers. It is also discussed how to
measure oset positions, as well as how to average
to nd measurement va lues for the desired position.
Std. 2 Similar basic impact hammer procedures are
discussed. One interesting addition in this
document is the description of reciprocal
measurements. Reciprocal measurement can bea
useful alternative to obtain of the NTFs in case
of hard-to-reach measurement locations for the
impact hammer.
(e)  Force Identification
Force identication- whether it concerns interface forces or
blocked forces- is a crucial component in classical and compo-
nent-based TPA methods. e available options to perform
force identication depends on the chosen type of TPA.
Std. 1 When interface forces are required, there is a
variety of options to consider. In this standard,
three are mentioned:
a. Direct force method. is can in practice
bea challenge since assemblies are typically
not designed to accommodate for force
transducers in between the coupling points.
b. Indirect (or in-situ) method. By measuring
accelerations in the vicinity of the coupling
points (indicator points) under operation
and measuring the transfer functions
between the interface and indicator points,
the interface forces can becalculated.
c. Mount-stiness method. By measuring
accelerations on both sides of the mount,
interface forces can becalculated when the
stiness properties of the mounts are known.
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Std. 2 As blocked forces are a non-physical force in an
assembly with anything other than a rigid
boundary, direct measurement is not applicable
in-situ. Indirect determination using the in-situ
method is therefore the preferred method to
determine blocked forces and this is described
accordingly in the standard.
As it appears, force identication for both methods can
be done using in-situ measurements. The difference in
obtaining interface forces or blocked forces is induced by using
respectively the receiving component’s FRFs or the assembly
FRFs in the matrix-inverse procedure.
(f)  Force Validation
Being able to rebuild one of the original measured signals
using processed data as a validation can provide a welcome
quality check.
Std. 1 For this method, no validation step is provided.
Std. 2 For the source characterisation step, a so-called
“on-board validation” is discussed. On the test
structure (R) a structural point is chosen where
vibrations from all coupling points are expected
to beobserved. is signal is not used as an input
for the blocked force characterisation and can
therefore beregarded as an independent valida-
tion quantity. e response for this signal can
be synthesised using the measured transfer
function and can be compared to the original
signal to assess, to some extent, the quality of the
blocked force description. e last part of this
paper shows an example of an on-board va lidation.
(g)  Response Prediction
e biggest dierence between the methods lies in the appli-
cability of the obtained source characterisation and what is
required accordingly.
Std. 1 Since t his method uses interface forces as the means
to characterise the source, this is never a property
of solely the active component, but always of a
particular assembly. In order to transfer the char-
acterisation to an assembly with a new receiving
struct ure, new interface forces need to becalculated
using equation (11) or one of its simplications.
Std. 2 This is different when using blocked forces.
Blocked forces are determined independent from
the receiving structure, i.e. they are a sole
property of the active structure. As a result, the
blocked forces are directly transferable to a
dierent receiving structure, without the need of
recalculating. In order to perform a TPA response
prediction however, the admittance of the target
assembly (including the active component) is
required, which cannot always be obtained
directly without Dynamic Substructuring
measures, or alternative indirect procedures such
as the “round-trip” concept described in [9].
From the above, it can beconcluded that neither of the
methods is a one-method-ts-all solution, but that application
is case-specic.
In the previous section. the denition of the interface between
the active and receiving structure has been identied as a
critical aspect. As said in Standard 2, incompleteness and
misalignment of the blocked force DoFs can bea common
source of errors. Also, one can question the straight-forward-
ness and practicability of a 3-DoF description (translational
forces only) as obtained according to Standard 1.
As an addition to the interface denition in both stan-
dards and to mitigate the potential eects of incompleteness
and misalignment of forces, an approach can befollowed
based on the Virtual Point Transformation method [10, 7].
is approach circumvents both issues: the completeness
assumption is reinforced by having (by default) 6 DoFs per
coupling point instead of only 3, while alignment of DoFs is
guar anteed by the introduction of orthogona l XYZ-translations
and rotations in the global reference frame. e resulting
interface denition shows high resemblance with a node in
FEM. A brief recap of the virtual point transformation method
is presented next.
Virtual Point Transformation
e virtual point transformation is visually summarised in
gure 8. A virtual point is dened in the centre of the inter-
faces, described by the m=6 virtual DoFs for translations/
rotations q and forces/moments m. All nu > m measured
displacements (or accelerations, velocities) u around the inter-
face are transformed to the virtual point, by means of a kine-
matic relation between u and q. is relation is governed by
the so-called “Interface Displacement Mode” (IDM) matrix
for the displacements Ru, dened from the position and orien-
tation of the sensors with respect to the associated virtual
point. A similar relation Rf can beset up for the nf>m forces
f and virtual point forces/moments m.
e following transformations can beestablished sepa-
rately for the displacement and force DoFs:
T (14)
 FIGURE 8  The virtual point transformation.
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© 2019 SAE International. All Rights Reserved.
e inverted IDM matrices (Ru)+ and (Rf)+ are the actual
transformation matrices that convert an nu×nf measured FRF
matrix Y) to an m×m virtual point FRF matrix Yqm(ω).
qm qm
with (16)
e resulting v irtual point transformed model is governed
by the new FRF matrix Yqm(ω). As it comprises perfectly collo-
cated force and displacement DoF with correct driving-point
behaviour, the virtual point FRF matrix is very similar to a
super-element description in FEM. Also note that, as the two
IDM matricesRu and Rf may bedierent, it is not necessary
to excite the structure at the same points as the sensors
are located.
Virtual Points in Force
It is not always necessary to transform both displacements
and forces of the measured FRF matrix. For use with source
characterisation techniques specically, oen only forces are
transformed. ese forces are later to beequated or transferred
to another assembly, while the displacements DoFs- actually
denoted by u4 in the matrix-inverse equations- merely serve
as the “intermediate” quantities for the characterisation of
the operational source by interface or blocked forces. For
example, for the characterisation of blocked forces and
in-situ, this reads:
42 42 42 2
uf f
() ()
This leaves the acceleration DoFs u4 intact, yet
createsacharacterisation consisting of forces and moments
in the virtual coupling point, ready to transfer to
another assembly.
Regarding completeness of a blocked-force vector, it is
evident that a vector comprising only translational forces
cannot always constrain or couple the rotations of the active
system. Indeed, every 3-DoF coupling point would simulate
a hinge or ball-joint connection (unable to transition
moments), while the 6-DoF description is more likely to fully
couple the dynamics of the two subsystems. is presumption
will befurther investigated in the next section.
e following simulated test case illustrates the way of
working of both standards, with focus on the calculation of
the force vector. Figure 9 shows a test assembly of an “active
subsystem” A in blue, mounted at two coupling points on a
“test rig” R in green (see [11] for a full description of this
benchmark structure). An excitation force f1 is placed on the
tip of A to represent the excitation of an active source. For
the purpose of this test case, a at impact force spectrum
was chosen of 1N over a frequency band of 0 to 2000 Hz,
which is equivalent to using the column from the FRF matrix
corresponding to the excitation point. e virtual experi-
ment was simulated as follows:
1. Design of substructures and assemblies in CATIA, FE
modelling in ANSYS. e substructure models
comprise about 30k nodes and 90k DoFs per
substructure. Coupling of the substructures is dened
as rigid coupling over the full contact surface. e
base plate of the test rig is constrained at its four
corner points to suppress rigid body motion.
2. Design of experiment in DIRAC from VIBES.
technology. Placement of 2 times 3 tri-axial
accelerometers as indicators (
), 1 on-board
validation sensor (
). Denition of 2 times 12
impact points on substructure A around the coupling
point, plus one impact point for the source
excitation f1.
3. Test case simulation using VIBES Toolbox for
MATLAB. Import of FE model and instrumentation
from ANSYS and DIRAC. Synthesis of FRFs by modal
reduction and superposition of 100 vibration modes
with 1% modal damping.
4. Force calculation, virtual point transformation and
response prediction are performed using standard
matrix operations on the obtained FRF matrices
and spectra.
A target receiver structure B was designed as well; the
target assembly AB is shown in gu re 10. On this assembly,
impact points have been placed in the same manner, and the
source excitation is present as well.
 FIGURE 9  Test assembly of the active structure (A) on test
rig (R).
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 FIGURE 10  Target assembly of the active structure (A)
connected to the receiver (B).
© 2019 SAE International. All Rights Reserved.
© 2019 SAE International. All Rights Reserved.
Standard 1: Interface Forces
First, the procedure of Standard 1 is simulated, using interface
forces to describe the activity of the source. “Operational
responses” at the indicators and on-board sensor on the test
rig are simulated using the following equations:
= (18)
To determine the interface forces between A and R, a
classical matrix-inverse procedure was used, namely with the
admittance of just the test rig (in practice, such forces could
bemeasured directly using force transducers):
Two interface force variants were chosen here: one which
only uses 3 translational forces in X, Y, and Z direction (so
6in total) and a second one which applies a virtual point
transformation on the FRF columns, similar to equation (17),
to obtain 3 translations and 3 rotations per coupling point
(12in total).
Although standard 1 does not explicitly propose a method
for force validation, it was chosen to apply these forces to the
test rig admittance, i.e.
. is yields a reconstruction of the
response at the on-board sensor
, which can becompared
to the direct “operational” response as obtained by applying
equation (18). e result of on-board validation is shown in
the le diagram in gure 11. e 3-DoF variant matches the
validation response reasonably well, with deviations mostly
in the higher frequency end. e 6-DoF variant shows a
perfect match, mea ning that the total of 12 forces and moments
capture the source activity fully.
Next, the interface forces as measured on the test rig are
“transposed” to interface forces acting on the receiver struc-
ture using the procedure of Standard 1, namely by applying
equation (11). e newly obtained interface forces
are nally
multiplied with the receiver admittance to predict the target
responses in assembly AB.
22 22 2
e results of the response prediction are shown in the
right diagram of gure 11. Again, a 3-DoF and 6-DoF case is
considered, while the validation response was calculated using
equation (1). Here, the 3-DoF source description is clearly
unable to provide a good response prediction. e 6-DoF
variant performs better but is not perfect.
It must benoted that application of equation 20 and 21
requires a signicant number of subsystem admittances to
bemeasured. For this simulation, all subsystem admittances
have been modelled according to the steps
described above. As mentioned before, simplications to
equation 11 are proposed in the Standard; a thorough study
of this is beyond the scope of this paper.
Standard 2: Blocked Forces
Secondly, the in-situ blocked force approach is presented
according to Standard 2. The simulation of operational
responses is identical to the previous approach, namely by
application of equation (18). Blocked forces are computed by
equation (12), again for both 3-DoF translational forces and
6-DoF virtual point forces and moments. e on-board valida-
tion is shown in the le diagram of gure 12. e results are
similar to the ones obtained by interface forces: the 3-DoF
source description performs rather well, whereas the 6-DoF
blocked forces and moments completely match the on-board
validation response.
Finally, the response prediction using the obtained sets
of blocked forces is shown in the right diagram of gure 12.
For this prediction equation (5) was used, which applies the
blocked forces- determined from a test rig assembly- straig ht-
away to the target assembly FRFs. It can beseen that for the
6-DoF VP blocked force vector, near perfect agreement is
achieved with the validation response. is outperforms the
3-DoF prediction, which can beseen to deviate up to one order
of magnitude. is suggests that the 6-DoF blocked forces and
moments are preferable, especially when the target assembly
is very dierent from the testing assembly.
is industrial application case demonstrates the blocked
force method as described in Standard 2, enhanced with the
 FIGURE 11  Application of Standard 1: interface forces. Left:
on-board validation on test rig AR. Right: Response prediction
on target assembly AB.
© 2019 SAE International. All Rights Reserved.
 FIGURE 12  Application of Standard 2: blocked forces. Left:
on-board validation on test rig AR. Right: Response prediction
on target assembly AB.
© 2019 SAE International. All Rights Reserved.
© 2019 SAE International. All Rights Reserved.
virtual point method to obtain a 6-DoF description in the
source characterisation. Validation will be done using the
on-board validation method.
In the case at hand, an automotive OEM needs to decide
on packaging of an e-compressor in an early stage of develop-
ment of an electrical vehicle. ere is no full-vehicle prototype
available yet. What is known, is that the e-compressor will
ultimately beconnected at its three coupling points. e goal
is to characterise the operat ional vibrat ions of the e-compressor
from tests on a test bench, which can beused as input for NVH
simulations using component-based TPA. e nal aim is to
assess the noise in the cabin of the vehicle for several possible
placements and packaging concepts, so to design an
optimal xture.
is execution of this case is split in four steps:
1. FRF measurement (including virtual point
transformation) of the compressor on a test bench
2. Operational measurement of the compressor under
various operational conditions
3. Blocked force calculation
4. On-board validation
When the blocked forces are validated, they can beusing
to synthesise NVH levels using component-based TPA (not
part of the discussion).
FRF Measurement
e measurement is rst prepared in a 3D environment, in
this particular case in the DIRAC soware of
nology; see gure 13. Locations for indicator sensors u4 are
chosen, as well as the impact locations for the measurement.
For every coupling point, 3 tri-axial accelerometers are
used as indicators and a minimum of 12 impact positions.
Before the start of the measurement, it is validated whether
the choices for sensor positions and impact locations are
sucient and robust to construct virtual point DoFs (refer
to [10] for a discussion on sensor and impact locations).
Locations that were chosen in the preparation phase, but
turn out to be unfeasible (typically due to geometric
constraints) are on-the-y adjusted in the measurement
setup. e instrumentation of one of the three coupling
points is shown in gure 14.
Finally, the measured FRF matrix
is transformed on
the right-hand-side only (equ ation 17), such that the columns
of the FRF matrix are the 6-DoF virtual point forces and
moments. Consequently, any resulting matrix-inverse opera-
tion with this matrix will have forces expressed in virtual
point forces and moments.
Operational Measurement
In the second step, the operational excitations of the
compressor under normal conditions are measured. e
operational conditions are chosen such that all compressor
states can later besimulated in the vehicle. Note that the sensor
locations remain unaltered compared to the FRF measure-
ment in step 1.
During the operational runs, suction and discharge
temperatures are measured, as well as static and dynamic
pressures; see gure 15. ese signals are used to monitor the
operational conditions of the e-compressor.
Blocked Force Calculation
Now that both admittance and operational responses are
obtained, blocked forces can becalculated; this is done by
application of equation (12).
 FIGURE 13  Measurement preparation in DIRAC.
© 2019 SAE International. All Rights Reserved.
 FIGURE 14  Sensor/impact placement around the
virtual point.
© 2019 SAE International. All Rights Reserved.
 FIGURE 15  Operational spectra and reference signals.
© 2019 SAE International. All Rights Reserved.
© 2019 SAE International. All Rights Reserved.
For every operational condition, a total of 18 blocked
forces (6 DoF times 3 coupling points) is obtained. An impres-
sion is shown in gu re 16. Owing to the virtual point force
characterisation, the resulting blocked forces are now:
a. a description of the source’s activity in operation;
b. independent from the testing environment;
c. transferrable to other source/receiver combinations;
d. suitable for NVH predictions.
ese properties are all highly desired and allow for a
clear separation of responsibilities between the OEM and the
component supplier.
On-Board Validation
To ensure the quality of the characterisation, it can bechecked
whether the calculated blocked forces describe the source
activity completely. is is done by means of an on-board
validation as described for Standard 2. is comprises a TPA
synthesis on the compressor/test-bench assembly, calculating
the response to a validation sensor. e on-board validation
sensor in this case is situated at the intersec tion of the Y-shaped
test bench support, as shown in the le picture in gure 14.
As this accelerometer was not used for the characterisation
itself, it ensures an objective assessment.
Synthesising t he response for the validation sensor is done
by application of equation (5). e synthesised response is
compared to the originally measured sensor signal; this is
shown in gu re 17. e orange-shaded areas represent the
noise floors of the response predictions, which allow to
estimate the eective signal-to-noise aer characterisation.
The validation gives an accurate prediction of the
on-board signal, i.e. the on-board validation is successful. is
implies that the calculated blocked forces indeed f ully describe
the active vibrations from the e-compressor and can now
be transferred to a dierent receiving structure, such as
a vehicle.
In this paper a variety of Transfer Path Analysis methods has
been discussed. It was shown which TPA method is being
incorporated in the proposed ISO standards and we have
briefly touched upon the practical implications that
come along.
A numerical test case was presented that provides insights
in the way-of-working and performance of both standards.
As an extension to the default 3-DoF translational force
vectors, a virtual point approach was chosen, resulting in
6-DoF descriptions with rotations as an addition to the trans-
lations. The presented results suggest that 6-DoF source
descriptions enhance both methods signicantly.
Standard 2 has been demonstrated on an industrial appli-
cation case, for which the blocked force characterisation has
proven to besuccessful. However, this does not imply that this
is a one-size-ts-all solution. e most convenient source
characterisation or TPA method remains to becase-specic.
is paper has attempted to provide some grip on the aspects
at play when choosing the right method for your application.
1. van der Seijs, M.V., Rixen, D.J., and de K lerk, D., “General
Framework for Transfer Path Analysis: History, eory and
Classication of Techniques,” Mechanical Systems & Signal
Processing 68:217-244, 2016.
2. Moorhouse, A.T., Elliott, A.S., and Evans, T.A., “In Situ
Measurement of the Blocked Force of Structure-Borne
Sound,” Journal of Sound & Vibration 325(4-5):679-685, 2009.
3. de Klerk, D., Rixen, D.J., and Voormeeren, S.N., “General
Framework for Dynamic Substructuring: History, Review
and Classication of Techniques,” AIAA Journal 46(8):1169-
1181, 2 008.
4. de Klerk, D. and Rixen, D.J., “Component Transfer Path
Analysis Method with Compensation for Test,” Mechanical
Systems & Signal Processing 26(6):1693-1710, 2 010.
 FIGURE 16  Impression of blocked forces and moments.
© 2019 SAE International. All Rights Reserved.
 FIGURE 17  Results of on-board validation.
© 2019 SAE International. All Rights Reserved.
© 2019 SAE I nternational. All rights re served. No part of this pu blication may be rep roduced, store d in a retrieval system , or transmitted , in any form or by any mean s,
electronic, me chanic al, photo copying, recording, or other wise, without the prior written permission of SAE International.
Positions and opinions adva nced in this work are those of the author(s) and not necessarily those of SA E International. Responsibility for the content of the work lie s
solely with the author(s).
ISSN 0148-7191
5. ISO/TC43/SC1, “ISO/AWI 21955 Vehicles- Experimental
Method for Transposition of Dynamic Forces Generated by
an Active Component from a Test Bench to a Vehicle,”
International Organization for Standardization [Online].
Available at:
6. ISO/TC43/SC1, “ISO/DIS 20270 Acoustics- Characterization
of Sources of Structure-Borne Sound and Vibration-
Indirect Measurement of Blocked Forces,” International
Organization for Standardization [Online]. Available at:
7. van der Seijs, M.V., “Experimental Dynamic Substructuring:
Analysis and Design Strategies for Vehicle Development,”
Ph.D. Dissertation, Del University of Technology, 2016.
8. de Klerk, D. and Ossipov, A., “Operational Transfer Path
Analysis: eory, Guidelines and Tire Noise Application,”
Mechanical Systems and Signal Processing 24(7):1950-
1962 , 2 010.
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for Reconstruction of Green's Functions at Passive
Locations,” e Journal of the Acoustical Society of America
134(5):3605-3612, 2013.
10. van der Seijs, M.V., van den Bosch, D.D., Rixen, D.J., and de
Klerk, D., “An Improved Methodology for the Virtual Point
Transformation of Measured Frequency Response Functions in
Dynamic Substructuring,” in COMPDYN 2013: 4th ECCOMAS
ematic Conference on Computational Methods in Structural
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11. van der Seijs, M.V., Pasma, E.A., van den Bosch, D.D., and
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Symbols and Abbreviations
u - dynamic responses, e.g. accelerations, velocities,
sound pressures
f - applied forces
g - interface forces
q - virtual point displacements and rotations
m - virtual point forces and moments
Y - admittance FRF matrix, e.g. accelerance
Z - impedance matrix, e.g. dynamic stiness
T - transmissibility matrix
R - IDM matrix
BF - blocked force
DoF - degree of freedom
FEM - nite element model
FRF - frequency response function
IDM - interface displacement mode
NTF - noise transfer function
NVH - noise, vibration and harshness
LM-FBS - Lagra nge multiplier frequenc y-based substr ucturing
OEM - original equipment manufacturer
TPA - transfer path analysis
VP - virtual point
... This section briefly summarizes the theory of the in-situ blocked force TPA method. In accordance with the proposal for standardization in [1] for the application of the method, the following five steps will be carried out: ...
... A comfortable way to measure equivalent forces is in-situ [6], i.e., in the assembled configuration of source and receiver. On the receiver side, sufficient indicator sensors are required to calculate the blocked forces as follows: (1) In order to determine the equivalent forces from equation (1), an FRF measurement and an operational measurement must first be carried out. The indicator admittance and target admittance in the assembly can be measured by impact testing. ...
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Modern vehicles are increasingly demanding in terms of driving comfort. For this purpose, various methods have been developed in the last decades to determine the critical paths for sound transmission, also known as Transfer Path Analysis (TPA). As a relatively new approach, the in-situ TPA method can be used for gaining more flexibility in the pre-development design phase. The vehicle dynamics as well as the vibration behavior of a vehicle is essentially determined by the behavior of the powertrain. The aim of this paper is the characterization of the excitation source based on the powertrain using the in-situ TPA method on an academic structure. The test setup consists of an excitation and receiver substructure. The former represents the engine-transmission unit and the latter the vehicle body coupled via the aggregate rubber mounts. Subsequently, first applications on a vehicle are performed.
... In accordance with the proposal for standardization in [10] for the application of the method, the following five steps will be carried out: ...
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Over the past decades, engineers have developed methods to determine critical paths for sound transmission, also known as Transfer Path Analysis (TPA). This demand stems, for instance, from the need to prevent undesired vibrations in modern vehicles. A relatively new method that allows for the characterization of a source in the assembled state is called in-situ TPA (iTPA). Generally, the excitation forces cannot be measured. Although the iTPA makes the development process more complex, it provides insight into the forces generated by active components that are transferred to the receiver structure. The vehicle dynamics as well as its vibration behavior is essentially determined by the behavior of the powertrain. For this more complex system, several challenges affect the method’s applicability, such as the accessibility to the engine mount interfaces and the modeling of coupling degrees of freedom. The aim of this paper is the characterization of the excitation source based on the engine-transmission unit using the iTPA method. It is analyzed and evaluated in terms of its accuracy and applicability. Equivalent forces of two different vehicle configurations, stiff and soft engine rubber mounts, are compared and used to predict the total vehicle vibration responses.
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pyFBS is an open-source Python package for frequency-based substructuring. The package implements an object-oriented approach for dynamic substructuring. This tutorial is intended to introduce structural dynamics and NVH engineers to the research toolbox in order to overcome vibration challenges in the future. The focus will be on experimental modeling and post-processing of datasets in the context of dynamic substructuring applications. The state-of-the-art methods of frequency-based substructuring, such as the virtual point transformation, the singular vector transformation, and system-equivalent model mixing, are available in pyFBS and will be presented. Furthermore, basic and application examples, as well as numerical and experimental datasets that are provided, are intended to familiarize users with the workflow of the package. pyFBS is demonstrated with two example structures. First, a simple beam-like structure is used to demonstrate how to start with the experimental modeling, FRF synthesis, virtual point transformation, and mixing of system equivalence models. Second, an automotive test structure is used to demonstrate the use of the pyFBS on a complex structure where in-situ transfer path analysis is used to characterize the blocked forces. This tutorial is intended to provide an informal overview of how research can be powered by open-source tools.
Transfer path analysis (TPA) and source characterization using the in-situ blocked force methodology is becoming increasingly common in the automotive world. While robust techniques exist for this type of characterization in general, there are certain conditions where the analysis is more straight-forward than others. In this work, several techniques are presented to help improve the characterization across different frequency ranges. At the very low frequencies, where structures should behave rigidly, TPA results can be improved by filtering out any non-rigid body motion from a set of measured FRFs. In the mid-frequency range, testing can be simplified using a volume source to capture reciprocal FRFs and then predict sound levels at the driver’s ear. In the mid- and high- frequency ranges, the addition of rotational FRFs can help improve TPA predictions. These techniques are demonstrated using recent test results on various components and vehicles in this paper.
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This paper presents a practical study on popular Experimental Dynamic Substructuring topics. A series of substructures is designed of such complexity to fit in right between “real life” structures as often found in industrial applications and “academic” structures which are typically the simplest models to identify a particular phenomenon. The designed benchmark structure comprises an active side with a vibration source, a passive side and a test rig for source characterisation. The connectivity is scalable in complexity, meaning that a single-point, two-point and continuous interface can be established. Substructuring-compatible component models are obtained from impact measurements using the Virtual Point Transformation. The vibration source on the active structure is characterised on the test rig using the in-situ TPA concept. Hereafter the component TPA method is applied to simulate the response on the passive side of the coupled structure, in turn obtained using dynamic substructuring.
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An expression for the Green's function at an arbitrary set of passive locations (no applied force) is derived and validated by experiment. Three sets of points are involved, the passive reconstruction points, c, which lie on a virtual boundary and two sets of auxiliary points, denoted a and b, located either side. The reconstruction is achieved using Green's functions forming a "round trip" from and to the reconstruction points via a and b. A two stage measurement procedure is described involving excitation at b and a but with no excitation required at the reconstruction points. A known "round trip" relationship is first introduced which is theoretically exact for points on a multi-point interface between two linear, time invariant subsystems. Experimental results for frequency response functions of a beam-plate structure show that this relationship gives good results in practice. It is then shown that the theory provides an Nth order approximation for the Green's function at arbitrary points, where N is the number of points at b. The expression is validated by reconstructing point and transfer frequency response functions at two passive points on an aluminum plate.
The operational transfer path analysis (OTPA) method is the subject of research in this article, which starts with a discussion on it's theory. Here clear similarities with the MIMO technique in experimental modal analysis are found. Based on the knowledge of MIMO, one finds that input signals are allowed to be coherent to a certain extend. As coherence can be larger in OTPA in practice, the method is extended with the singular value decomposition method to reduce influences of noise. The article proceeds with a discussion on points of attention, or boundary conditions, in practical applications. An analysis on tire noise is included to illustrate the points of attention and the methods strength in, for example, vehicle TPA on tires.
In this article a component transfer path analysis (TPA) procedure is proposed. The method allows one to calculate the total system response resulting from a subcomponent's source excitation. It is based on the knowledge of the frequency response functions (FRFs) of the total system and on a measurement of the stand-alone subcomponent on a test bench. As the true source excitation, for example an engines combustion, is not measurable, equivalent forces at the subcomponent interface are found. The equivalent forces are multiplied with the total system FRFs from the subcomponent interface to response nodes of interest. The resulting responses at and in front of the subcomponent interface are shown to be physically exact for linear, time invariant and stationary operating systems.However, for the method to succeed, the source forces will have to be independent of the global dynamics. In addition, the test bench needs to be rigid in the frequency range of interest. This is typically hard to achieve for analysis in the mid frequency range (100–1000Hz in vehicle acoustics). Therefore, a way to compensate for the test bench dynamics is also discussed. It is shown that one needs the receptance matrix of the free component at its interfaces and the operational motions of the interface on the test bench. Knowledge of the test bench dynamics is not needed.Measuring excitation and response at the source interface may not be feasible in practice due to space restrictions. In this case, the proposed TPA method can be extended with substitute nodes on the subsystem which are reachable on the test setup and the total system. With the knowledge of the free subcomponent FRFs, physically exact responses at and in front of the gearbox interface can also be calculated.
It is shown that the blocked force of a structure-borne sound source can be obtained from measurements made in situ, i.e. when the source is connected to a receiver structure. This potentially removes the need for special test rigs employing blocked terminations. A corollary of this relationship is that a theoretically exact ‘in situ transfer path analysis’ is possible with a fully assembled structure, such as a vehicle, without at any stage needing to separate the substructures. The results are validated by numerical simulation and measurement on beam-like sources and receivers.
A Benchmark Structure for Validation of Experimental Substructuring
  • M V Van Der Seijs
  • E A Pasma
  • Van Den
  • D D Bosch
  • M W F Wernsen