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How to perform transfer path
analysis
How are transfer paths measured
To create a TPA model the global system has to be divided into an active and a passive part,
the former containing the sources, the latter the receiver points where the responses are
measured. Loads are defined at the interface between the active and passive part and the socalled Noise Transfer Functions (NTF’s), also referred to as Frequency Response Functions
(FRF’s), characterize the relationship between a load and a receiver. The paths are represented
by these NTF’s. See figure 1. The individual contribution of each transfer path to the total
response can be calculated by multiplying the load with the corresponding NTF. This model
presupposes that the load-response relationship is causal and the paths are system
characteristic of the global system. Using this model, a pressure target response can be
expressed as follows:
Figure 1: TPA Model schematic: Sources, receivers, loads, transfer functions on a vehicle
model
Technical info issued by: Siemens.
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Technical info | How to perform transfer path analysis?
The test procedure to build a conventional TPA model typically
requires two basic steps: 1. identification of the operational
loads during in-operation tests (e.g. run-up, run-down, etc.) on
the road or on a chassis dyno: and 2. estimation of the FRF
from excitation tests typically under laboratory conditions (e.g.
hammer impact tests, shaker tests, etc.). The procedure is
similar for both the structural and the acoustical loading cases,
but the practical implementation is of course governed by the
nature of the signals and the loads.
The separation into “loads” and “transfer” is the key to the use
of the TPA results to identify dominant causes and propose
solutions (act on specific load inputs, act on mount stiffness, act
on specific system transfer).
Building on evolutions on experimental TPA, the methodology
has found its way into simulation, resulting in the introduction
of “contribution analysis” concepts in numerical modeling,
extending the traditional “unit-force” FE validation models to
true engineering models with realistic loads and interpreting the
results in terms of critical problem area’s, panels, structural
parts, etc.. Experimental TPA has become a key part towards
successful simulation modeling by providing accurate load
estimates.
Today, the main driver for innovations in TPA is the industry’s
demand for simpler and faster methods. Several attempts have
been made to speed up the TPA process. One example is the
Operational Path Analysis (OPA) approach. This approach
attracts quite some attention as it requires only operational data
measured at the path references (e.g. passive-side mount
accelerations, pressures close by vibrating surfaces, nozzles and
apertures, etc.) and target point(s). The OPA method is indeed
very time-efficient, but has several limitations, that are
discussed in the “advanced transfer path analysis techniques”
section.
A fast, test-based procedure which supports troubleshooting of
vibro-acoustic problems in a very efficient way is LMS OPAX.
This approach is nearly as accurate as conventional TPA and
almost as fast as purely operational path methods that often fail
to identify the root cause of vibrations and find remedies to
NVH problems. The LMS OPAX solution separates loads and
transfer paths so that vibro-acoustic energy can be traced right
from the source. This helps engineers identify the problem
quicker than ever before with the minimum of time-consuming
measurements.
1. Loads identification
Loads identification is probably the main accuracy factor for a
successful TPA campaign. Different methods may be employed
to identify both vibro-acoustics and acoustics loads.
1.1 Direct measurements
Direct measurement of the loads is done by placing force
transducers between the engine and the engine mounts.
Although the most effective method, direct measurement of the
loads is not possible in the majority of cases as the load cells
require space and well-defined support surfaces, which often
makes application impractical or even impossible without
distorting the natural mounting situation. In those cases where
direct measurement is possible (i.e. large machinery) it remains
the preferred method.
1.2 Mount stiffness method
In case the active and passive structures are connected through
flexible mounts, the mount stiffness method can be used. The
operational forces can be determined from a knowledge of the
complex dynamic stiffness of the mounts K(w) and of the
differential displacement over the mount during operation.
applying the mount stiffness method, it is required to measure
the operational displacement at both the source and the receiver
side. It is therefore important to place the accelerometers as
close as possible to the mount connection points – even though
this is not always easy. If measured further away, the measured
acceleration signals will not be representative for the problem at
higher frequencies
Nevertheless, this method has its limits as accurate mount
stiffness data are seldom available and furthermore depend on
the excitation amplitude due to their non-linear behavior:
modern mounts have a stiffness that changes depending on the
operational load on the mount.
1.3 Matrix inversion method
For transfer paths which comprise of rigid connections, or
where the mount stiffness is very large with respect to the body
impedance, inducing even the minimum relative displacement
over the mount is not possible, and thus the mount stiffness
method can not be used to identify the load.
Technical info issued by: Siemens.
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Technical info | How to perform transfer path analysis?
In these cases, a technique based upon inversion of a measured
accelerance matrix between structural response on the receiver
side due to force excitation at all transfer paths can be used.
This accelerance matrix must be measured when the source is
disconnected from the receiver. This matrix is then combined
with operational measurements of the structural vibration at the
receiver side in order to obtain force estimates.
In the matrix inversion method so-called “indicator
accelerations” are measured in a first step at multiple locations
on the support structure during operating conditions. Typical
locations for indicators are points at the passive side on the
subframe to which the engine mount is connected. In a second
step, the relation between the interface forces and the
motion/deformation is characterized by a measured accelerance
matrix in the form of multiple complex transfer functions in the
frequency domain (FRF). These FRFs from the passive side
mount location to the indicator locations are measured in
controlled, non-operational conditions.
The FRF accelerance matrix data and the operational indicator
acceleration data are combined to calculate the forces as shown
in the following equation:
with Fi the calculated operational force through path i,
FRFik(w) the local transfer function between the transfer path
location i and indicator point k, and ak(w) the operational
accelerations at indicator location k. So, the FRF matrix
describes the local relationship between a known force input at
the transfer path location and a measured response acceleration
output due to this known input. It is this very relationship that is
also valid in an operational situation (such as the runup of a
vehicle) and allows to calculate the force by inverting this
matrix and multiplying it with the operational accelerations.
Calculating the inverse of the accelerance matrix in practise
requires some numerical stability issues to take into account.
The number of measured indicator acceleration signals should
therefore well exceed the number of forces to be identified. This
allows calculation of a pseudo-inverse with a least squares
optimized estimation of the forces. The condition number of the
accelerance matrix (ratio between the largest and smallest
eigenvalue) is a measure of the potential amplification of errors.
Small or large inaccuracies in the FRF of the accelerance
matrix, as well as in the operational indicator acceleration
vector can lead to large errors in the force estimation if the
condition number is high. Singular value decomposition
elimination or smoothing can not compensate for thus
introduced bias errors.
Technical info issued by: Siemens.
The disadvantage of the inverse method is that all potential and
correlated forces that act need to be analyzed simultaneously
because all forces may cause motion/deformation throughout
the structure. Also, to limit the errors in the identification, an
over-determination (at least 2 times more indicator responses
than excitations) is advised, leading to a relatively large number
of signals and a large number of measurements to fill the FRF
matrix. Furthermore, all constraints with respect to impact
location and direction and FRF phase accuracy also apply to
this problem.
For FRF measurements, reciprocal techniques can be used,
allowing the reuse of the in-operation response instrumentation
(and exciting at the indicator positions). This not only saves
time, but also guarantees consistency. The reciprocal method
will be discussed in more detail in the section VII.
1.4 OPAX
OPAX is a parametric force identification method, which is
based on operational data and complete vehicle reciprocal FRF
measurements.
The OPAX approach differentiates from the existing methods in
the identification of the operational loads. Key is the use of
parametric models characterizing the operational forces and
acoustics loads as a function of measured paths input such as
mount accelerations and acoustics pressures. The parametric
load models are estimated from (i) in-situ measured operational
path inputs and target response signal(s) and from (ii) transfer
path FRFs.
The OPAX method is discussed in more detail in the section
”Advanced transfer path analysis techniques".
2. FRF measurements
2.1 Direct measurements
Direct measurement of vibro-acoustic FRF is often done by
instrumented hammer excitation of the structure, where a
normal microphone measures the pressure response. When
more accurate data are needed, an electro-mechanical shaker is
used for excitation. But, access to the correct location is often
impossible with normal shakers, and even difficult with an
instrumented hammer. In the example of a vehicle, surrounding
parts are sometimes disassembled to be able to reach locations
like strut towers, ventilation system supports, screen wiper
supports, etc.
The estimation of the vibro-acoustic (or acoustic-acoustic) FRF
is probably the easiest to determine. Still, direct measurements
are often complex with respect to setup constraints (apply a
force at the connection points or apply an acoustic load near the
radiating surface) and accuracy (direction errors when using
impact testing, connection lateral or moment constraints when
using shakers).
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Technical info | How to perform transfer path analysis?
2.2 Reciprocal measurements
Using reciprocal measurements (exciting at the target locations,
measuring the response at the interface) has alleviated this
problem significantly. Verification experiments show that
acoustic-acoustic and acoustic-structural reciprocity hold in
nearly all cases, for large ranges of excitation amplitudes and
types of structures. Even in case non-linear and/or local
damping effects may cause a slight breakdown of reciprocity,
the corresponding errors are typically an order smaller than
these of impact location and orientation, sensor cross-talk and
sensor sensitivity.
The reciprocal determination of vibro-acoustic FRF is attractive
when multiple FRF need to be determined, and when access to
the suspension support location is constrained. A low frequency
volume acceleration source is positioned at ear location, and the
acceleration response at the suspension locations is measured in
parallel for multiple suspension connection points and for
multiple directions per location. Accelerometers are easily
placed in narrow and concealed places.
According to theory exactly the same information is measured.
In practice the experiments have shown that the vibro-acoustic
FRF, thus measured, are very close to direct measurements.
Small residual differences exist. These deviations in the
observed reciprocity are only partially caused by non-linearity
of the vehicle body structure. The imperfect alignment of the
force excitation in a direct measurement and alignment of the
accelerometers in a reciprocal measurement have proved to be
highly critical in obtaining good vibro-acoustic reciprocity.
Especially on complete vehicle, reciprocal transfer function
tests have a major advantage in required effort and in
positioning accuracy around mounts. Acoustics excitation at the
ear location, and response accelerometers around the mounts,
allow more freedom in positioning the sensors close to mount
center, and it is more feasible to surround mounts with sensors.
2.3 New excitation methods
An important contribution to speeding up TPA measurements
while supporting the improvement of accuracy is offered by the
advances in instrumentation technology, for excitation as well
as measurement.
Technical info issued by: Siemens.
Reciprocal tests for example require accurate acoustic sources
which behave like point sources and have approximately omnidirectional characteristics in the applicable frequency ranges
while not disturbing the sound field too much. For these tests,
engineers need calibrated Volume Velocity Sources (VVS) such
as LMS Qsources, with dimensions and characteristics adapted
to specific frequency ranges. To have access to the in-situ
source levels, volume velocity sources need to have integrated
volume acceleration sensors. For structural excitations,
advanced and lightweight (inertial) shaker systems can be used.
Figure 2: From left to right: LMS Qsources mid-high
frequency volume velocity source, integral shaker, and lowfrequency volume velocity source. These sources provide an
accurate real-time reference signal of the acoustic source
strength.
Other innovative measurement techniques find their way into
transfer path analysis, such as using strain sensors the measure
displacement as used in the mount stiffness method. This
indirect force identification approach uses strain responses and
easy-to-apply strain sensors. Strain responses are much more
localized than acceleration responses, eliminating to a large
extent the concerns on cross-coupling between the interface
locations.
Important when mixing different signal types in level-sensitive
procedures like the matrix inversion, is the proper balancing of
the different quantities (acceleration-pressure, accelerationstrain) since acceleration levels are generally much higher than
pressure levels. This is a well-known problem from modal
analysis, addressed in vibro-acoustic and strain modal analysis.
When (burst) random excitation techniques are unable to excite
the structure at sufficiently high levels this results in signal to
noise ratio problems, long measurement times (many averages)
and noisy FRFs. High quality FRFs can be measured using
stepped sine excitation techniques that are able to concentrate
the excitation energy at a single frequency and excite the
structure at much higher energy levels. A MIMO sine testing
technique has been introduced that used a digital
implementation of the classical swept sine excitation. The
technique acquires leakage-free spectra, which are processed
into multiple-input-multiple-output FRFs. A ‘system
identification’ approach is implemented to control the excitation
level during the test without using a time-consuming online
closed loop control scheme.
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Technical info | How to perform transfer path analysis?
For vibro-acoustic noise transfer functions, the new technique
was compared with the traditional burst random and stepped
sine techniques. It was proven that this technique is able to
measure FRF and coherence function of similar high quality as
the stepped sine technique, but at drastically reduced
measurement times, which are comparable with the burst
random technique.
2.4 Decoupling the system
Because of the system’s modal behavior, a single force in one of
the mounts causes vibrations at all path references. Excitation at
a transfer path point would also cause energy to travel through
the engine mount, passed via the engine through a second
engine mount, and from there travels to the receiver location
(e.g. the driver’s head). So the response at the receiver is not
anymore directly caused by energy traveling directly from the
excitation point to the receiver. Therefore, Noise Transfer
Functions should be measured after disassembling the sources
from the assembly structure to eliminate source coupling, or
cross-coupling. In case of a vehicle, this means that the engine
needs to be removed.
In some cases, the effect of cross-coupling is not significant.
This can be the case if the mounts are rigid, and the excitation
at the transfer path points is low due to e.g. reciprocal
measurements.
Apart from the theoretical reason to remove the engine,
practically, there is a severe lack of physical space between the
engine and engine mount to place force transducers. A
pragmatic approach is to remove the engine to gain access to
the body-side of the mount directly, and use a hammer or shaker
to directly excite the system. Likewise, the suspension should
be removed when measuring body side FRFs related to road
noise.
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Technical info issued by: Siemens.
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