Modal Testing of a Helicopter Airframe Using the INSET Method∗
J. E. Coote, N. A. J. Lieven,
G. W. Skingle
University of Bristol
QinetiQ Ltd.
Department of Aerospace Engineering
A9 Building, Cody Technology Park
Queens Building, University Walk
Ively Road, Farnborough
Bristol, BS8 1TR, UK
Hampshire, GU14 0LX, UK
ABSTRACT
The Interleaved Spectral Excitation Technique (INSET) is a
recently-developed method for vibration testing. This paper
summarises the method and presents results obtained during
tests on a helicopter airframe. Data acquisition and processing was accomplished using custom software with dSpace
hardware, and is discussed along with comments on the
method and results.
NOMENCLATURE
DAC
FRF
RMS
Sf f (ω)
Sxx (ω)
Sf x (ω)
H1 (ω),H2 (ω)
1
digital-to-analogue conversion
frequency response function
root mean square
Autospectra of force
Autospectra of response
Force-response cross-spectra
Transfer functions
INTRODUCTION
Modal testing is necessary to ensure the integrity of modern
light aerospace structures. The aim is to identify structural
dynamic response characteristics, so as to verify analytical
models or demonstrate compliance with design requirements.
Tests may take a number of forms, with the simplest using
one source of excitation force and one response measurement transducer, typically an accelerometer, with frequency
domain signal processing revealing the associated frequency
response function[1]. Multiple measurement transducers may
be used to accelerate the process. The excitation source is
usually a hammer or shaker. The hammer allows quick testing at different locations, but there is limited control over the
excitation spectrum, and the large instantaneous forces bring
out non-linear characteristics. Shaker testing affords greater
control and longer test runs, at the cost of longer setup times,
∗ University
c
force drop-off around resonance, and potential loading complications from the stinger/pushrod system. It is often necessary
to shake the structure at multiple points in order to ensure that
all modes are excited. Simultaneous multiple excitation has
the advantage that energy is distributed more evenly throughout the structure, thus reducing the occurrence of amplitudedependent non-linear behaviour. It also can be a more realistic representation of in-service loadings. The test time is
reduced, and shaker force drop-out at resonance is less of an
issue as shakers are not required to produce as much force.
Various excitation signals may be chosen when using shakers. Commonly, random noise is used, although windowing
of the excitation and response signals is required in order to
prevent leakage. Pseudorandom noise can be synthesised in
the frequency domain and transformed into a time domain signal which is periodic in the measurement window, and therefore inherently leakage-free, avoiding the need for windowing.
Stepped or chirped sine signals are also used, although nonlinearity may be more evident in the results. The amplitude of
excitation may be chosen to be constant across the spectrum,
or alternatively it may be desirable to alter the excitation spectrum so as to result in a flat response spectrum instead, in
order to ensure that no amplitude-dependent characteristics
are expressed. All such choices regarding the test method
will reflect the particular situation and the resources available.
2
SUMMARY OF INSET
The Interleaved Spectral Excitation Technique was introduced
in [2] as a method which offers potential advantages when testing large structures. Single-shaker methods result in localised
energy inputs applied to the structure, and require strong levels of forcing which may result in the emergence of local nonlinearity or damage. The aim is to use multiple dispersed
shakers to spread the excitation energy through the structure
more evenly.
In the method, the shaker output channels are each allocated
of Bristol/QinetiQ, used with permission
unique discrete spectra in such a way that all frequencies of
interest are covered, whilst ensuring that the signals are completely uncorrelated. In this application, the discrete spectra of
a white noise signal have been distributed evenly among the
channels, as illustrated in Figure 1. The actual force applied
to the structure is required to be identical to the signals generated, in order to maintain the absence of correlation. One
method of achieving this is via feedback-driven power amplifiers to drive the shakers, measuring and controlling force by
monitoring the armature current. Such active control of the
shaker force is necessary to prevent the structure from driving the shaker at frequencies where no energy transfer is desired. Similarly, at resonance, greater armature voltage is required to prevent force dropout and ill-conditioned response
functions. With this setup, the armature coil and pushrod are
effectively part of the structure. However with large structures,
the change of mass is insignificant, and could be accounted
for in a corresponding FE model if comparisons were desirable.
The peak-RMS ratios of the individual channels are then minimised. This enables larger RMS forcing amplitudes to be
used during testing, thereby increasing the signal-to-noise ratio of transducers at locations with weak response. A further
benefit is that when the shaker drive signal passes out from
the computer, the ADC conversion makes better use of the
range available (in systems with adjustable range).
linear structural responses will all be periodic within the duration of the block as well, eliminating the requirement to compensate for the leakage of incomplete cycles with application
of windowing functions.
Because any particular frequency spectra of excitation is output via only one shaker at a time, it is necessary to repeat the
test with the excitation signals rotated around the shakers. In
this way, in the 2-shaker case, the signal which in the first test
went to shaker 1 is now output to shaker 2, and the original
shaker 2 signal is now passed to shaker 1, thus ensuring that
in the end all points will have been excited by all shakers at all
frequencies of interest.
Having completed a series of tests with the signals rotated
around all the shakers, the process is repeated with new forcing signals in order to provide additional results for averaging.
In order to arrive at the frequency response functions (FRFs)
H1 (ω) and H2 (ω) from the time domain responses, some additional postprocessing is required. The structure is required
to be linear, because excitation energy at a given frequency
is assumed to be the only cause for structural response at
the same frequency. For each rotation of the excitation signal
blocks around the shakers, the FRFs are calculated between
every shaker and every response in the usual way, as in Equation 1
The signals are generated individually for each shaker through
the following process:
Sf x (ω)
Sf f (ω)
Sxx (ω)
H2 (ω) =
Sxf (ω)
H1 (ω)
Coherence(ω) =
H2 (ω)
H1 (ω) =
1: Generate a signal in the frequency domain with unity
value at the chosen comb of spectra, and zero elsewhere;
(1)
2: transform the signal to the time domain;
3: clip all magnitudes to a fixed proportion of the maximum
value, and transform the signal back to frequency domain;
where Saa (ω) and Sab (ω) denote auto-spectra and crossspectra, and subscripts ‘x ’ and ‘f ’ denote the response and
forcing signals respectively.
4: whilst preserving phase, replace the spectral magnitudes
with unity for the desired comb of spectra, and set to zero
elsewhere. Transform the signal to the time domain;
However, these FRFs are only valid for the spectra at which
the shaker of interest has excitation components; the other
spectra are used to produce FRFs from other shakers. Thus
a sparse comb of valid FRFs is extracted. The gaps are filled
by examination of the equivalent FRF resulting from the next
rotation of the test, and thus a full valid FRF is obtained in
each shaker/response combination. Each particular FRF is
then linearly averaged across a number of repeated tests to
yield a final result with reduced noise.
5: repeat steps 3 and 4 until the peak-RMS ratio of the resulting time domain signal is satisfactory.
Having generated signal blocks in this way, they can then be
output to the shakers while recording structural responses. In
practice, the signal block is surrounded by additional copies
of the block with a cosine fade-in factor applied to allow the
structure response to spool up to steady-state amplitudes; the
inherent periodicity of the original block ensures that the signal remains continuous and smooth at the joins between the
blocks. Another consequence of the block periodicity is that
3
EXPERIMENTAL IMPLEMENTATION
The test subject was a stripped-down time-expired rotorcraft
airframe in the QinetiQ test labs, suspended by bungee from
the rotor hub.
The signal generation and processing was carried out using
dSpace hardware with a PC with 256Mb RAM and a 650Mhz
Pentium 3 processor. Real-time data acquisition was via a
dSpace DS1005 modular system with 32 channels of analogue input and output. A Simulink model was written and
compiled onto the hardware, and then run from a MATLAB
script, interfacing with the hardware via the provided MLIB
command library and ControlDesk software. This enabled
complete automation of the testing. Time-intensive signal processing was performed on the PC whilst the separate data
acquisition board acquired sequential blocks of information,
minimising time taken for subsequent analysis.
the dSpace unit were low-pass filtered to prevent aliasing of
frequency components present above the Nyquist frequency.
This was not originally thought to be necessary; with a linear structure, higher frequencies would not be present in the
signal in the absence of any excitation energy at the same frequencies. However, signal noise was found to carry high frequency components, contributed to by interference from the
power amplifiers. The force response measurements were filtered similarly so as not to distort the final frequency response
functions.
4
3.1
Forcing setup
Four LDS400-series shakers were used, with the frequencydomain spectra evenly dealt out between them. The dSpace
system provided four analogue ±10 V outputs at a range of
fixed sample times. These outputs were lowpass-filtered, to
remove the high-frequency DAC timestep component, and
taken to power amplifiers. The amplifiers use armature current feedback to flatten the dynamic response characteristics,
thus reducing force drop-out at resonances. The achieved
force was returned as a signal derived from armature current,
thereby providing a method of assessing the shaker transfer
characteristics. However, the measured force is that applied
to the shaker armature, and not necessarily that transmitted
to the structure. This discrepancy will be minor when the
structural mass is much greater than armature mass and the
pushrod modes are above the frequency range of interest. If
these conditions do not apply, the actual forcing signals may
no longer be completely uncorrelated, and it will no longer be
possible to associate responses with particular shakers.
The nose and tail shakers were mounted on fixed platforms,
shown in Figures 2 and 3. The remaining two shakers were
suspended with base masses to provide lateral forcing to the
rear of the engines, with the starboard engine shaker shown
in Figure 4.
The frequency composition of the excitation signals was a flat
noise spectrum between 3.2 Hz and 100Hz with a peak-toRMS ratio of less than two. The lower limit was chosen to
avoid exciting shaker suspension frequencies, as well as to
ensure that there was no steady-state component to the signals which would result in a runaway escalation of current in
the suspended shakers on failing to sustain the demanded
steady force. The upper frequency limit was selected as most
of the interesting structural responses were known to occur in
this range.
3.2
Response measurement setup
The response accelerations were measured at 12 points by
strain-gauge cantilever bridge accelerometers. The inputs to
EXPERIMENTAL RESULTS
A typical example of the signals acquired from the 12 accelerometers is given in Figure 5. By comparing the shaker
demand and force signals, the shaker frequency response
functions were found to be as shown in Figure 6. A slight disturbance is seen at 50 Hz, caused by mild interference from
the mains electrical supply.
A subset of the 48 FRFs is shown divided by y (lateral) or
z axis (vertical) orientation of both excitation and response
between Figures 7 and 8. As a group, they show high levels of damping and noise, with more modes observed at localities than across the whole structure. The FRFs with lowest coherence occur with the longest load paths, and hence
greatest energy dissipation, between shaker and response.
In the remaining FRFs, with the response in a different axis
from the excitation, the results appear similar but with more
plots strongly affected by noise. The construction techniques
used for the rotorcraft fuselage have particular potential for
high damping levels. Many rivets and bolts are used, resulting in a large number of joints capable of dissipating energy.
Manufacturing techniques involving large integrally machined
components or tailored composites, produce inherently lower
levels of damping.
The results have been compared with reference data generated by previous QinetiQ tests to establish repeatability both of
the method and of the structural response. Figure 9 shows the
lateral point FRFs at the port engine exhaust. The same characteristics are seen in both responses, although a frequency
shift is evident. The coherence of the test data is good, except at the antiresonance where the response signal is more
succeptible to noise. In Figure 10, showing vertical starboard
engine inlet response to a vertical shaker at the tail boom,
the same is true up to around 25 Hz. Beyond this point, the
reference data appears noisier, with a shift of response characteristics evident also. Figure 11 (vertical point FRF at nose)
has good coherence, but a distinctly different response to the
reference data. The 50 Hz coherence notch is believed to be
due to mains interference, as the nose cable runs had to pass
by electrical equipment. Finally, Figure 12 compares vertical
point FRFs at the tail boom. The coherence is excellent, and
there is approximate agreement with the reference data.
The coherence of the results suggests that INSET is success-
fully generating frequency response functions. The smoothness of the FRFs further indicates that the structural response
is consistent between tests shaking the structure with the excitation signals rotated among the shakers. If the response was
not consistent, there would be a periodic change in magnitude
of FRF, spanning every n spectra in the n-shaker case.
The FRF shift between the results and the reference data is
most likely caused by environmental changes. Slight differences in shaker attachment, suspension conditions, temperature and humidity, and rerouting of signal runs, would all contribute. Another variable which has been further investigated
is the amplitude of forcing. Figure 13 compares the reference
data with tests at two different forcing amplitudes. The light
forcing RMS amplitude is 40% of the strong, which in turn
represented roughly half the maximum power output available
from each air-cooled shaker. Significant changes in response
frequencies and magnitudes are evident with the different amplitudes, suggesting that excitation strength could account for
a sizeable part of the variation from the reference dataset[3].
The mechanism behind the amplitude dependence is likely to
be some cubic softening in the engine mounting; the engines
responded strongly during testing, and the phenomenon has
not been observed in other tests of the structure with the engines removed.
A further experimental test was conducted in which a simulated structure replaced the rotorcraft structure. Instead of using shakers, the excitation signals were output to analogue
input channels of the data acquisition hardware, which was
configured to run a real-time simulation of a dynamic system. The virtual responses were output via DAC channels
to replace the conditioned accelerometer signals. The virtual
system was built in Simulink to have 3 uncoupled degrees of
freedom, with resonances at 8, 26 and 28 Hz with 6, 5 and
7% damping. Figure 14 shows the FRF of the second freedom obtained using the same INSET setup. The modal parameters were extracted using the single-degree-of-freedom
circle-fit method, and found to match the design frequency
and damping ratios very closely, further verifying the implementation of the method.
5
COMMENTS ON INSET
The advantages of using INSET for the testing of large structures have been discussed: a more even distribution of larger
amounts of excitation energy with reduced expression of
amplitude-dependent effects; uncorrelated excitation forces;
avoidance of windowing; minimisation of peak loads. Other
factors also merit consideration. To achieve the precise forcing
signals, it is necessary to employ feedback control to prevent
the forcing channels from becoming correlated. Shaker armature current feedback/measurement techniques result in the
coil and pushrod becoming an extension of the tested structure, so in this instance INSET would be most appropriate for
large structures where the extra mass would be insignificant.
A programming overhead of the technique is the data han-
dling required to reconstitute the FRFs from the spectra of appropriate tests. Real-time synchronised analogue inputs and
outputs are necessary.
One of the prerequisites of INSET (and indeed of most testing techniques) is that the test subject responds linearly[3].
Responses occurring at frequency spectra different from the
shaker in question would be incorrectly interpreted as a linear
response to an alternative shaker. However, there is potential
to turn this to an advantage; if for example every other spectral line was not excited by any of the shakers, any responses
at these particular frequencies would indicate the presence of
non-linearity.
6
CONCLUSIONS
The results of the rotorcraft vibration test using INSET showed
excellent coherence. They broadly agreed with previous
independently-collected data when allowing for known sensitivity of the subject to test parameters. The technique was
found to be more demanding of shaker performance and data
handling/postprocessing than other methods, but offers the rewards of enhanced signal-to-noise ratios of transducers and a
greater linearisation of measured response under more realistic loading conditions.
7
ACKNOWLEDGEMENTS
The authors would like to thank MoD and QinetiQ for supporting this work with access to their labs and equipment.
8
FIGURES
Complete frequency spectrum
Spectrum to first shaker
Spectrum to second shaker
(Two−shaker configuration)
Figure 1: Illustration of frequency spectra distribution
between shakers
Figure 4: Starboard engine shaker mounting
Figure 2: Tail shaker attachment
0.8
0.6
Signal voltage, v
0.4
0.2
0
−0.2
−0.4
−0.6
0
Figure 3: Nose shaker attachment
2
4
6
Time, s
8
10
12
Figure 5: Sample of response signals at beginning of test
Measured H2 FRFs between all excitations and responses in z direction
0
10
72
−1
10
Receptance, Mag.
70
H2 Magnitude, dB
68
66
−2
10
−3
10
Response 2, Shaker 3
Response 2, Shaker 4
Response 4, Shaker 3
Response 4, Shaker 4
Response 6, Shaker 3
Response 6, Shaker 4
Response 8, Shaker 3
Response 8, Shaker 4
Response 10, Shaker 3
Response 10, Shaker 4
Response 12, Shaker 3
Response 12, Shaker 4
64
−4
10
62
60
58
56
−5
Shaker 1
Shaker 2
Shaker 3
Shaker 4
0
10
10
20
30
40
50
60
15
20
25
30
35
Frequency, Hz
40
45
50
55
70
Figure 8: All H2 receptance FRFs in z direction
Frequency, Hz
Figure 6: Shaker transfer functions
0
Gain magnitude
10
−1
10
−2
Reference H1
Test H1
Test H2
10
−3
10
Measured H2 FRFs between all excitations and responses in y direction
0
15
20
25
30
35
40
45
Phase angle, degrees
−1
10
−50
−100
Reference H1
Test H1
Test H2
−150
−2
10
−200
15
−3
Response 1, Shaker 1
Response 1, Shaker 2
Response 3, Shaker 1
Response 3, Shaker 2
Response 5, Shaker 1
Response 5, Shaker 2
Response 7, Shaker 1
Response 7, Shaker 2
Response 9, Shaker 1
Response 9, Shaker 2
Response 11, Shaker 1
Response 11, Shaker 2
10
−4
10
20
25
30
20
25
30
35
40
45
20
25
30
35
Frequency, Hz
40
45
50
55
35
40
Frequency, Hz
45
55
0.8
0.6
0.4
0.2
Test coherence
−5
15
50
1
Coherence
Receptance, Mag.
55
0
10
10
50
0
15
50
55
Figure 7: All H2 receptance FRFs in y direction
Figure 9: Comparison of lateral point FRFs at port engine
exhaust
−1
Reference H1
Test H1
Test H2
−2
10
−1
10
−3
10
−4
10
15
20
25
30
35
40
45
50
55
Phase angle, degrees
500
Gain magnitude
Gain magnitude
10
−2
10
Reference H1
Test H1
Test H2
−3
10
−4
10
0
20
25
30
35
40
45
50
55
1
Coherence
0.8
Phase angle, degrees
−1000
15
35
40
45
50
55
−200
0.8
Coherence
1
0.2
Test coherence
30
35
40
Frequency, Hz
45
50
55
Reference H1
Test H1
Test H2
−300
0.4
25
30
0
−400
20
25
−100
0.6
0
15
20
100
Reference H1
Test H1
Test H2
−500
15
0
50
100
150
200
250
300
0.6
0.4
0.2
Test coherence
0
15
20
25
30
35
40
Frequency, Hz
45
50
55
Figure 10: Comparison of vertical FRFs with excitation at
tail boom and response at starboard engine inlet
Figure 12: Comparison of vertical point FRFs at the tail
boom
−1
Gain magnitude
10
−2
10
−3
Reference H1
Test H1
Test H2
10
−4
10
15
20
25
30
35
40
45
50
55
Reference H1
Test H1
Test H2
150
100
50
0
15
20
25
30
35
40
45
50
55
Receptance, Mag.
Phase angle, degrees
200
−2
10
−3
Reference H1
Test H1, light forcing
Test H2, light forcing
Test H1, strong forcing
Test H2, strong forcing
10
1
Coherence
0.8
0.6
16
18
20
22
24
Frequency, Hz
26
28
0.4
0.2
Test coherence
0
15
20
25
30
35
40
Frequency, Hz
45
50
55
Figure 11: Comparison of vertical point FRFs at the nose
Figure 13: Comparison of responses with different forcing
amplitudes
0
Gain magnitude
10
Test H1
Test H2
−2
10
−4
10
−6
10
0
10
20
0
10
20
30
40
50
60
70
80
90
100
50
60
Frequency, Hz
70
80
90
100
Phase angle, degrees
0
−100
−200
−300
−400
−500
−600
Test H1
Test H2
30
40
Figure 14: Point FRF measured at second simulated
freedom
REFERENCES
[1] Ewins, D. J., Modal Testing: Theory, Practice and Application, Research Studies Press Ltd, Baldock, England, 2nd
edn., 2000.
[2] Skingle, G. W., A New Multiple-Input Multiple-Output Vibration Testing Technique - Interleaved Spectral Excitation, Proceedings, 13th International Modal Analysis Conference, pp. 892–901, 1995.
[3] K. Worden, G. R. T., Nonlinearity in Structural Dynamics;
Detection, Identification and Modelling, Institute of Physics
Publishing, 2nd edn., 2001.