USE OF MULTI-INPUT SINGLE-OUTPUT METHODS TO IMPROVE MEASUREMENT REPEATABILITY FOR ROAD NOISE IN AUTOMOBILES

1. The Pennsylvania State University
The Graduate School
Graduate Program in Acoustics
USE OF MULTI-INPUT SINGLE-OUTPUT METHODS
TO IMPROVE MEASUREMENT RELIABILITY
FOR ROAD NOISE IN AUTOMOBILES
A Paper in
Acoustics
by
Robert J. Schubert
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Master of Engineering in Acoustics
May 2009

2. iii
ABSTRACT
The automotive industry has a tendency to wish to measure minute changes in
sound packaging. Current methods do not provide high enough signal to noise ratio to
provide accurate results. Multiple Input Single Output method is reviewed and tested for
base line vs. an experimental case – constrained layer damping placed on 4 doors of a
sedan – in a “black box” method by measuring 4 triaxial wheel inputs and providing a
transfer function to the driver’s outboard ear; deeming all other inputs as noise. 1 and 4
Hz resolution is reviewed as well as comparing to the standard method of directly
comparing spectrums. Student’s T test is used to provide statistical significance between
the baseline and the experimental case – 616/2048 data points showed a statistically
significant difference in MISO methods whereas only 92/2048 points showed statistical
significance by comparing spectrums.

3. iv
TABLE OF CONTENTS
LIST OF FIGURES .....................................................................................................v
LIST OF TABLES.......................................................................................................vii
ACKNOWLEDGEMENTS.........................................................................................viii
Chapter 1: Introduction to noise measurement techniques..........................................1viii
Automotive NVH Background.............................................................................1viii
Theory of MISO techniques .................................................................................3
Discussion of vehicle noise sources .....................................................................5viii
Experimental test case: CLD applied to 4 doors ..................................................9
Chapter 2: Analysis of the Experimental case: CLD applied to 4 doors .....................12
Post processing discussion....................................................................................12viii
Current practice analysis methods for comparison...............................................13
MISO method analysis .........................................................................................15viii
Conclusions: comparison of standard practice vs. MISO.....................................23
Appendix 1: Scripts and Macros..................................................................................24
Prosig Script..........................................................................................................24viii
Matlab Script (Main) ............................................................................................27
Matlab Script (Function).......................................................................................30viii
Appendix 2: Raw Data and Information......................................................................31
Named Elements for Door Mastic Case ...............................................................31viii
Time series of DOE and 12 inputs........................................................................33
Example of Auto Spectral density: DOE in (Pa)²/Hz...........................................38
Example of Cross Spectral Density: DOE and front left wheel input X in
((Pa)*(m/sec²))/Hz................................................................................................38
viii

4. v
LIST OF FIGURES
Figure 1-1: Example of noise factors exceeding intended measurement ............................2
Figure 1-2: Multiple input – Single output model ...............................................................3
Figure 1-3: Rough Diagram of vehicle noise inputs............................................................5
Figure 1-4: Front wheel tri-axial placement. .......................................................................7
Figure 1-5: Right Rear Wheel tri-axial placement...............................................................7
Figure 1-6: Example of cobblestone road, similar to one used for testing. .........................8
Figure 1-7: Constrained layer damping material placed on 4 doors of a sedan...................9
Figure 1-8: Spray on damping material placed on vehicle in high-response locations. ....10
Figure 2-1: Spectrum averages from 5 runs.......................................................................14
Figure 2-2: Delta between the baseline vehicle and CLD vehicle.....................................15
Figure 2-3: Average total coherence for 1 Hz and 4 Hz ∆f for the baseline vehicle.........16
Figure 2-4: Average total coherence for 1 Hz and 4 Hz ∆f for the CLD vehicle..............16
Figure 2-5: Average total coherence for 1 Hz and 4 Hz ∆f for the baseline vehicle.........17
Figure 2-6: Average total coherence for 1 Hz and 4 Hz ∆f for the CLD vehicle..............17
Figure 2-7: Average Magnitude of FRFs for the Baseline vehicle transfer functions for
the 4 triaxial accelerometers ......................................................................18
Figure 2-8: Average Magnitude of FRFs for the CLD vehicle transfer functions for the 4
triaxial accelerometers ...............................................................................19
Figure 2-9: Delta of magnitudes of FRFs for the CLD vehicle transfer functions vs. the
baseline transfer functions .........................................................................20
Figure 2-10: Zoom of the 100-1000 Hz delta of magnitudes of FRFs for the CLD vehicle
transfer functions vs. the baseline transfer functions.................................20
Figure 2-11: Student’s T test, comparing the baseline vehicle with the CLD vehicle ......21

5. vi
Figure 2-12: The most statistically significant Transfer function: Front Left Y ...............21
Figure 2-13: Front Left Y delta of CLD vs. Baseline, only showing the 616 statistically
significant points........................................................................................22
Figure 2-14: All 24 transfer functions of both CLD (indicated with damper) and baseline
vehicles (indicated as no damper)..............................................................22

6. vii
LIST OF TABLES
No Tables Provided.

7. viii
ACKNOWLEDGEMENTS
Ford Motor Company for allowing the time and providing on the job experience: Eddie
Khan (for time and support), John Mathey (for training), and the rest of the NVH team
(background information, data, training, ideas, etc)
Drs. Karl M Riechard, Martin W. Trethewey, Stephen Hambric, Thomas B. Gabrielson
for the basic knowledge described in this paper
My family for providing the support and time to complete this paper.
Valerie Lamott and the team at Shure for support through the program and assistance
with this paper.

8. Chapter 1
Introduction to noise measurement techniques
1.1 Automotive NVH Background
Automotive manufacturers spend years designing vehicles, with many CAE
models to determine the best design to minimize noise inside the cabin from external
sources such as wind noise, powertrain noise, and road noise. This is done to
demonstrate to the customer higher quality as well as make traveling in the vehicle
generally more pleasing. Commonly, sound treatments are added to vehicles to reduce
cabin noise. Due to the extremely high complexity of automobiles, some of these CAE
models are not completely accurate. Ultimately, when prototypes are produced,
evaluations of sound packaging material occur by measuring noise inside the cabin. With
the high cost competitiveness in the automotive industry, it is common to question the
value of each sound packaging material, quite often individually—including size,
thickness and material properties. This can mean a very small change in measured noise,
which can be hard to measure due to background noise, weather conditions, driving
patterns and road conditions. Additional problems occur when A to B comparisons
cannot occur on the same vehicle, such as a material which has to be placed in-between
welded sheetmetal or a material which has to be baked in the paint ovens.
Historically, vehicle noise is measured at driver’s outboard ear (DOE), with either
overall dBA or Sones used to evaluate changes. Due to reasons described above,
measurement error can easily cloud evaluations, such as the example shown in Figure 1-

9. 2
1. In this example, the measured sones of the 2 vehicles with increased unconstrained
layer damping were not significantly different than the 2 vehicles without the increased
damping material. This can result in improper selection and wasteful use of sound
packaging that could better used in other areas.
50 MPH Semi-Coarse Road
Sones
21
21.5
22
22.5
23
23.5
24
VIN:135 VIN:280 VIN:385 VIN:308
Current production Increased Mastic
Sones(diffuse)
Figure 1-1: Example of noise factors exceeding intended measurement. Vehicles with
more unconstrained layer damping (increased mastic vehicles - right) should perform
better than the current production vehicle (left) with less unconstrained layer damping
material. However, the differences in measurements exceed differences in performance.
Multiple input – single output (MISO) measurements can be used to increase
signal to noise ratio (SnR). The MISO technique is commonly used in analytical models.
Input data is correlated back to the output data where the noise can be isolated, and
coherence can be used to indicate SnR. MISO measurements provide frequency response
functions (FRFs), which will be used here to more accurately indicate the abatement of
the sound packaging material. Sanderson, et al [2000] used similar methods to determine
tangential mobility of tires, which was used to correlate to a tire rolling noise prediction

10. 3
model. Fletcher and Sulisz [1990] studied laboratory simulations versus on road testing
using multiple input – multiple output methods, comparing the coherence of each to
indicate the validity of these laboratory simulations. Kompella and Bernhard [1997]
discussed similar computational MISO techniques for vehicles to calculate loudspeaker
and impact excited FRFs. This paper will use MISO techniques to measure FRFs from X-
, Y-, and Z-axis wheel inputs on entire vehicles, not previously attempted.
1.2 Theory of MISO techniques
Basic MISO theory states that multiple inputs, xi, pass through constant-parameter
linear systems with FRFs, Hi(f), produce a single measured output, y(t). The output, y(t),
will be the sum of the linear outputs, vi(t), plus included unknown n(t), shown in
Figure 1-2.[2]
If this system is converted to the frequency domain, it becomes a simple summation:
Figure 1-2: Multiple input – Single output model

11. 4
Where Y(f,T), Vi(f,T), N(f,T) and Xi(f,T) are the Fourier transforms of y(t), vi(t), n(t), and
xi(t) respectively. Starting with Equation 1.1, and multiplying through by the complex
conjugate of Y, Y*, as long as n(t) and xi(t) are uncorrelated, the result is
As well,
holds true. (Frequency and record length removed for simpler notation.) Using the
following definition,
Where Sxy(f) is the cross correlation of x(t) and y(t), T is the record length, E is the
expected value, Xk* (f,T) is the complex conjugate Fourier transform of x(t) and Yk is the
Fourier transform of y(t), the autospectrum of y(t) yields
Combining with equation 1.4, this is equivalent to
1.1
1.2
. 1.3
1.4
, 1.5
. 1.6
. 1.7

12. 5
Since Syy* = Syy, and Siy*=Syi, equation 1.7 can be written as
Note that Sny is equivalent to Snn when Sin = 0. A matrixed set of these equations will be
used later to back out FRFs for each input.
1.3 Discussion of vehicle noise sources
The common understanding of vehicle noise comes from 3 sources: wind noise,
powertrain noise and road noise as shown in Figure 1-3.
For measurements, there is a fourth source of noise not produced by the vehicle - external
noise - which can come in the form of environmental noise, such as gusting wind, or
man-made noise, such as cars passing or airplanes overhead. In most cases, these are
attempted to be minimized through the experimenters due diligence. This can be very
difficult, causing much delay in testing to wait for the right conditions. Generally, the
. 1.8
Figure 1-3: Rough Diagram of vehicle noise inputs

13. 6
changes made to vehicles are intended to improve a specific noise source, i.e.
improvements to engine mounts affect powertrain noise, improvements to windshield
mostly affects wind noise. In some cases, experiments are done in chambers such as the
wind tunnel or on dynamometers to assess changes. This can isolate sources, but these
facilities are expensive and limited, causing delays to assessments. The MISO method
will be explored to minimize inputs which are not of interest and correlate only to inputs
which are of interest. In the case reviewed, the input will be road noise, measured at the
suspension arms. The force would generally be in the vertical direction, but this cannot
be guaranteed to be on axis, so tri-axial accelerometers were used to measure this input at
the 4 wheels, as seen in Figure 1-4 and Figure 1-5.

14. 7
Figure 1-4: Front wheel tri-axial placement. Right front wheel shown. Similar
placement on left front wheel.
Figure 1-5: Right Rear Wheel tri-axial placement. Right rear wheel shown. Similar
placement on left rear wheel.

15. 8
Generally, the more input the experimenter can generate, the better the signal to noise the
resultant measurements will have, and although it is hypothesized that external noise will
not make a significant impact, reducing the other easily controllable inputs should
provide a more accurate result. Using some prior knowledge about noise sources in
automobiles, experiment parameters were chosen to reduce these more easily controllable
noise inputs: For wind noise, higher speeds cause more noise - proportional to the
velocity cubed. Higher RPMs from the engine cause louder engine noise. So for the
experiments run, a low speed was used (approximately 20MPH) to minimize wind noise
and a constant speed was used to minimize powertrain noise. To maximize input, a
cobblestone test track similar to Figure 1-6 was used to provide the maximum
displacement and acceleration from wheel inputs.
Figure 1-6: Example of cobblestone road, similar to one used for testing.

16. 9
Unfortunately for this experiment, the test track was very limited in length, only allowing
for approximately 6 to 10 seconds of the higher level of road noise inputs. This will be
taken into account for choosing the parameters in the post-processing to maximize the
number of samples that will be measured to provide the final average results for ASDs
and CSDs. Also, the best practices of FRF (Frequency Response Function)
measurements have been reviewed, which are similar in their processing.
1.4 Experimental test case: CLD applied to 4 doors
This paper will focus on one test case where constrained layer damping material
was placed on the 4 doors of a sedan (Figure 1-7). This particular vehicle design had
numerous design iterations developing the damping material volume and location
throughout the vehicle. Previous measurements have been conducted on this vehicle
design such as laser vibrometry, which measures response of body panels to varying
Figure 1-7: Constrained layer damping material placed on 4 doors of a sedan. The
material was placed on the outside of the vehicle for ease of application and removal. It
is assumed similar results would be achieved if damping material was placed on the
inside of the vehicle.

17. 10
frequencies. This vehicle design was found to have large displacement for various body
panels which had damping materials placed in these locations (Figure 1-8). The doors
were recommended, but with the equipment constraints and cost constraints and value
determinations, the door damping material was not implemented. This particular vehicle
line had numerous customer complaints for road noise, which provided cause for re-
evaluating much of the NVH design of the vehicle. This experiment will attempt to
evaluate the effectiveness of the addition of damping material (approximately $0.80 per
door) in a method that will correlate back to the DOE, in a “black box” manner, which is
considered a measurable for evaluating performance. “Black box” would be defined as
Figure 1-8: Spray on damping material placed on vehicle in high-response locations.

18. 11
measuring inputs while measuring the output without regard as to what goes on inside the
“black box”. This would mean the process is assumed to be linear, time invariant and
ergodic. What will also not be addressed is the correlation of DOE to the customer
experience, which has previously been attempted, but still has some unknown variability
and parameters which are not completely understood.
In this experiment, we will treat wind noise and powertrain noise, two common measured
sources of vehicle noise, as unwanted background noise leaving it unmeasured. The
investigation will focus on the use of multiple input - single output methods for this
minor adjustment to the sound package, through the use of the 4 wheel inputs (X-, Y-,
and Z-axis of each) and the resultant DOE. From this data, FRFs, correlated to only road
inputs, will be computed and compared to evaluate these changes. Repeatability from
run to run and reproducibility from vehicle to vehicle will also be evaluated for this
method.

19. Chapter 2
Analysis of the Experimental case: CLD applied to 4 doors
2.1 Post processing discussion
The ASDs and CSDs were processed using DATS software, the native software
for the acquisition equipment. The data was then exported for Matlab processing to take
advantage of a pre-programmed routine – Gausian Elimination – to assist in the creation
of the transfer functions. All processing scripts are included in Appendix A.
The original choice to measure with near full audio spectrum of 32 kHz was
found to provide little information above 2 kHz, as well as requiring extremely long
processing times – the decision was made to down-sample the data to 4 kHz for
processing. The recordings were also trimmed to include only the length which exhibited
the high input, which was anywhere from 6 seconds to 10 seconds in length; this was due
to the short test track available. A visual example of one run is provided in Appendix B.
6 to 10 seconds seems rather short, so two Δfs were chosen for comparison: 1 Hz and 4
Hz, which provide 1 second and 0.25 second record length, respectively. Additionally,
75% overlap was used with a Hanning window. DATS processing software provides
only 4 choices for overlap: 0%, 25%, 50%, 75%; from previous class discussions it was
noted 65% is ideal - 75% was chosen as the closest, as well as providing the most
possible averages with the short available acquisition length. This gave more than 24
averages for the 1 Hz processing choice, and more than 90 averages for the 4 Hz

20. 13
processing choice. The 24+ averages is well above the standards for impact hammer
FRFs. Based on this, we expect a relatively high coherence.
Six runs of each case were completed – six with the constrained layer damping
(herein called the CLD vehicle) on the door and six without the constrained layer
damping (herein called the Baseline vehicle). If the hypothesis is correct, the six runs
should provide almost identical results run to run and show some significant difference
between the two cases. Statistics, such as the Students T test, will be used to verify this
hypothesis.
2.3 Current practice analysis methods for comparison
As previously mentioned, overall level, in either dB or Sones is commonly used
to measure the change, but sometimes more detail is used. Since this change is very
small, spectrum analysis is commonly used to measure change. This section will show
even these levels are immeasurable for this case, showing a need for the improved
measurement methods.
Figure 2-1 is the average spectrum level for 5 runs in dB for the two cases. There
is no easily identifiable improvement shown for the CLD case. It would then be logical
to compare the difference of these cases, as in Figure 2-2. This again, does not lend itself
to any quick conclusions. Averaging the difference between the two, an overall 0.12 dB
improvement is found for the CLD case, easily dismissed as measuring error. The
Student’s T test can be used to provide a 95% confidence that two samples are
statistically different. By running independent Student’s T test on each frequency – 5
runs provide 5 measurements for each vehicle configuration - only 92 points of the 2048
frequencies measured show any statistically significant difference. Two areas show more

21. 14
than two consecutive frequencies with significant difference: 750-752 Hz where the CLD
vehicle was 2 to 3.2dB better, 1825-1828 Hz where the baseline vehicle is 2.5 dB to 4 dB
better. If this were used to come to a conclusion, the baseline vehicle would be
considered better. 1825 Hz is also approaching the Niquist frequency, which could be
prone to aliasing issues.
Figure 2-1: Spectrum averages from 5 runs. Baseline vehicle is blue, CLD vehicle is
pink. These spectrums show very little difference.

22. 15
Figure 2-2: Delta between the baseline vehicle and CLD vehicle. No answer readily
available. Averaging the entire spectrum, data shows 0.12 dB improvement for CLD case.
2.3 MISO method analysis
The first method used to review these results was examining the coherence for the
6 runs independently for each Δf. Coherence is a measure of the percentage of the output
which be accurately described by the input. The average and the maximum and
minimum coherence of each frequency measured was reviewed (Figure 2-3, 2-4, 2-5, 2-
6). The rule of thumb from impact hammer measurements is coherence should be 0.8 or
higher (although 0.8 would be low from prior experience). The 1 Hz coherence is quite a
bit higher than the 4 Hz coherence and the unusual variability from neighboring
frequencies is observed as compared to typical hammer impact FRFs. Also noted was the
six runs of each did not provide the same level of coherence run to run. This appears as
though possibly the runs are plagued with noise. Unfortunately this may indicate that the

23. 16
runs needed to be longer. One point of interest is 200Hz (plus or minus a few Hz), which
seems to have high coherence for both.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 10 100 1000
Average 1Hz coherence Average 4Hz coherence
Figure 2-3: Average total coherence for 1 Hz and 4 Hz Δf for the baseline vehicle. The
pink is 1 kHz coherence and the blue is 4 kHz coherence. The 1 kHz coherence is
significantly better.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 10 100 1000
Average 1Hz coherence Average 4Hz coherence
Figure 2-4: Average total coherence for 1 Hz and 4 Hz Δf for the CLD vehicle. The pink
is 1 kHz coherence and the blue is 4 kHz coherence.

24. 17
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 10 100 1000 10000
Average 1Hz coherence Average 4Hz coherence 4Hz max
4 Hz min 1 Hz max 1 Hz min
Figure 2-5: Average total coherence for 1 Hz and 4 Hz Δf for the baseline vehicle. The
pink is 1 kHz coherence and the blue is 4 kHz coherence. Max/min for 1Hz case is in
red, Max/min for 4 Hz case is in light blue.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 10 100 1000 10000
With Damper Average 1Hz coherence With Damper Average 4Hz coherence
4Hz max 4 Hz min
1Hz Max 1Hz min
Figure 2-6: Average total coherence for 1 Hz and 4 Hz Δf for the CLD vehicle. The pink
is 1 kHz coherence and the blue is 4 kHz coherence. Max/min for 1Hz case is in red,
Max/min for 4 Hz case is in light blue.

25. 18
Due to higher coherence, and even though the 4Hz processing had more averages,
the decision was made to review the 1 Hz results. Figures 2-7 and 2-8 show the average
transfer function magnitudes for the 4 wheel inputs with directions X, Y and Z. It is
interesting to note the peak occurs at approximately 25 Hz, and most of the energy
transfer is under 50 Hz. This is mostly outside of the audible range of human hearing.
Rear right Y direction (side to side) claims the largest peak, followed by rear left Y
direction. Rear right and left X direction (front to back) claim the 3rd
and 4th
positions, 5th
and 6th
positions are front right and front left Y.
Figure 2-7: Average Magnitude of FRFs for the Baseline vehicle transfer functions for the
4 triaxial accelerometers.
0
1
2
3
4
5
6
7
8
9
1 10 100 1000 10000
No Damper DOE frontleftx
No Damper DOE frontlefty
No Damper DOE frontleftz
No Damper DOE frontrightx
No Damper DOE frontrighty
No Damper DOE frontrightz
No Damper DOE rearleftx
No Damper DOE rearlefty
No Damper DOE rearleftz
No Damper DOE rearrightx
No Damper DOE rearrighty
No Damper DOE rearrightz
No Damper DOE rearrightz

26. 19
Figure 2-8: Average Magnitude of FRFs for the CLD vehicle transfer functions for the 4
triaxial accelerometers.
If we look at the difference between the two case averages (Figure 2-9), we unfortunately
find a similar result to the spectrum averages in Figure 2-2 – no easy conclusion as to
which case is better. If we focus on the 100-1000 Hz range (Figure 2-10), still no clear
winner is shown. When we run a Student’s T test on each transfer function (Figure 2-11),
we do find better results than the original spectrums – a minimum of 195 points show
95% confidence in the difference, averaging around 300 points of significance for all
twelve transfer functions, and a maximum 616 points of 95% confidence around the front
left Y direction (Figures 2-12 and 2-13). From this info, we can conclude the addition of
the CLD modification effects the transfer function of the front left Y direction the most.
Returning to the coherence findings, the 200 Hz area was reviewed, and interestingly
enough, no real conclusion could be made (Figure 2-14).
0
1
2
3
4
5
6
7
8
9
1 10 100 1000 10000
with Damper DOE frontleftx
with Damper DOE frontlefty
with Damper DOE frontleftz
with Damper DOE frontrightx
with Damper DOE frontrighty
with Damper DOE frontrightz
with Damper DOE rearleftx
with Damper DOE rearlefty
with Damper DOE rearleftz
with Damper DOE rearrightx
with Damper DOE rearrighty
with Damper DOE rearrightz

27. 20
Figure 2-9: Delta of magnitudes of FRFs for the CLD vehicle transfer functions vs. the
baseline transfer functions.
Figure 2-10: Zoom of the 100-1000 Hz delta of magnitudes of FRFs for the CLD vehicle
transfer functions vs. the baseline transfer functions.
-4
-3
-2
-1
0
1
2
3
4
1 10 100 1000 10000
avg delta DOE frontleftx
avg delta DOE frontlefty
avg delta DOE frontleftz
avg delta DOE frontrightx
avg delta DOE frontrighty
avg delta DOE frontrightz
avg delta DOE rearleftx
avg delta DOE rearlefty
avg delta DOE rearleftz
avg delta DOE rearrightx
avg delta DOE rearrighty
avg delta DOE rearrightz
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
100 1000
avg delta DOE frontleftx
avg delta DOE frontlefty
avg delta DOE frontleftz
avg delta DOE frontrightx
avg delta DOE frontrighty
avg delta DOE frontrightz
avg delta DOE rearleftx
avg delta DOE rearlefty
avg delta DOE rearleftz
avg delta DOE rearrightx
avg delta DOE rearrighty
avg delta DOE rearrightz

28. 21
396
616
288 280 300
368
195 209 204 218
335
205
95
0
500
1000
1500
2000
Student's T Test at each frequency
Figure 2-11: Student’s T test, comparing the baseline vehicle with the CLD vehicle. All
transfer function measurements show more statistical significance than the original
spectrum analysis.
Figure 2-12: The most statistically significant Transfer function: Front Left Y.
0
0.5
1
1.5
2
2.5
3
3.5
10 100 1000 10000
No Damper DOE frontlefty with Damper DOE frontlefty

29. 22
Figure 2-13: Front Left Y delta of CLD vs. Baseline, only showing the 616 statistically
significant points.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
190 192 194 196 198 200 202 204 206 208 210
No Damper DOEfrontleftx
No Damper DOEfrontlefty
No Damper DOEfrontleftz
No Damper DOEfrontrightx
No Damper DOEfrontrighty
No Damper DOEfrontrightz
No Damper DOErearleftx
No Damper DOErearlefty
No Damper DOErearleftz
No Damper DOErearrightx
No Damper DOErearrighty
No Damper DOErearrightz
No Damper DOErearrightz
with Damper DOEfrontleftx
with Damper DOEfrontlefty
with Damper DOEfrontleftz
with Damper DOEfrontrightx
with Damper DOEfrontrighty
with Damper DOEfrontrightz
with Damper DOErearleftx
with Damper DOErearlefty
with Damper DOErearleftz
with Damper DOErearrightx
with Damper DOErearrighty
with Damper DOErearrightz
Figure 2-14: All 24 transfer functions of both CLD (indicated with damper) and baseline
vehicles (indicated as no damper). There seems to be no clear indicator.
T T est Filtered front left Y T ransfer function delta
-2
-1.5
-1
-0.5
0
0.5
1
1.5
10 100 1000 10000
Damper improved
Baseline better

30. 23
2.4 Conclusions: comparison of standard practice vs. MISO
The MISO method did not provide the results hoped for; that is, a clear
determination of the improvement the CLD modification should provide. This could be
due to measurement and data constraints: perhaps the acquisition length could be
significantly longer, the background and unmeasured inputs could have been lower or
measured. Additionally, the change was possibly not large enough to be measurable.
The significant finding was the vastly improved number of frequencies which showed a
statistically significant improvement – 616 verses 92. This provides a level of indication
that this method is better at measuring the difference between the two test cases. It would
be recommended this method be further investigated; manly with the increase of the
acquisition length to approximately 60 seconds, and perhaps adding triaxial engine
measurements to reduce the unmeasured inputs. Additionally, a slightly larger sound
package change would be recommended to be the subject matter of the trial.

31. Bibliography
1. Sanderson, M.A.; Ivarsson, L.; Larsson, K.(2000), “In-plane FRF measurements
using a MIMO technique: Vehicle tire application,” Proceedings of SPIE - The
International Society for Optical Engineering, 4062(I) 104-108.
2. Fletcher, Jeffrey; Sulisz, Dennis.(1990), “Application of multiple and partial
coherence techniques to laboratory simulation testing,” American Society of
Mechanical Engineers, Applied Mechanics Division, V108, 225-236.
3. Kompella, Murty S.; Bernhard, Robert J. (1997), “Techniques for prediction of
the statistical variation of multiple-input-multiple-output system response,” Noise
Control Engineering Journal, V45, 133-142.
4. Bendat, Julius S.; Piersol, Allan G. (1993) Engineering Applications of
Correlation and Spectral Analysis, Wiely-Interscience Publication

32. Appendix A
Scripts and Macros
A. Prosig Script (underlined file names can be changed)
'$SCRIPTSTYLE=ADVANCED
';=====================================================
';= Exported DATS Basic Script
';= Auto-Generated by DATS For Windows
';=
';= Worksheet Name :
';= DATS Version : 5.0.37
';= Date/Time : Fri Mar 31 16:14:59 2006
';=
';=====================================================
Option Explicit
Dim InputSignals As String
Dim OutputSignals As String
Dim Parameters As String
Dim fle As String
Dim A As String
Dim B(12) As String
Dim X As Integer
Dim Y As Integer
Dim Z As Integer
Dim totB As Integer
Dim totRun As Integer
'=============================
'= Main Procedure
'=============================
Sub Main
DatsStartModuleTracking
fle="C:Documents and Settingsrschube1My DocumentsD219-258RoadNoiseMulti-inputbaseD-r"
A = "DOE"
B(1) = "front left x"
B(2) = "front left y"
B(3) = "front left z"
B(4) = "front right x"
B(5) = "front right y"
B(6) = "front right z"
B(7) = "rear left x"
B(8) = "rear left y"
B(9) = "rear left z"
B(10) = "rear right x"
B(11) = "rear right y"
B(12) = "rear right z"
totB=12
totRun=5
Z = 4

33. 25
InputSignals = fle & Z & ".dac{" & A & "}"
OutputSignals = fle & "-CSDs" & Z & ".dac{" & A & "+" & A & "}"
Parameters = "'Revision_1',,,1.0,4,0,-1,0,0"
DatsExecute "[ASDAV]", InputSignals, OutputSignals, Parameters 'Auto Spectral Density
ID={0}
For X = 1 To totB
InputSignals = fle & Z & ".dac{" & A & "}," & fle & Z &".dac{" & B(X) & "}"
OutputSignals = fle & "-CSDs" & Z & ".dac{" & A & "+" & B(X) & "}"
Parameters = "'Revision_1',,,,1.0,4,0,-1,0,0,0"
DatsExecute "[CSDAV]", InputSignals, OutputSignals, Parameters 'Cross Spectral
Density ID={0}
DatsCheckFatalError
Next X
For Y = 1 To totB
For X = 1 To totB
If Y = X Then
InputSignals = fle & Z & ".dac{" & B(X) & "}"
OutputSignals = fle & "-CSDs" & Z & ".dac{" & B(X) & "+" & B(X) & "}"
Parameters = "'Revision_1',,,1.0,4,0,-1,0,0"
DatsExecute "[ASDAV]", InputSignals, OutputSignals, Parameters 'Auto Spectral Density
ID={0}
Else
InputSignals = fle & Z & ".dac{" & B(Y) & "}," & fle & Z &".dac{" & B(X) & "}"
OutputSignals = fle & "-CSDs" & Z & ".dac{" & B(X) & "+" & B(Y) & "}"
Parameters = "'Revision_1',,,,1.0,4,0,-1,0,0,0"
DatsExecute "[CSDAV]", InputSignals, OutputSignals, Parameters 'Cross Spectral
Density ID={0}
DatsCheckFatalError
End If
Next X
Next Y
Z = 4
InputSignals = fle & "-CSDs" & Z & ".dac{$ALL}"
OutputSignals = ""
Parameters = ",'" & fle & Z & "CSD.mat',0,'',1"
DatsExecute "[MATEXPORT]", InputSignals, OutputSignals, Parameters 'Export MATlab5 matrix data
ID={0}
DatsCheckFatalError
' mastic runs here
fle="C:Documents and Settingsrschube1My DocumentsD219-258RoadNoiseMulti-inputmasticD-r"
totB=12
totRun=6
Z = 5
InputSignals = fle & Z & ".dac{" & A & "}"
OutputSignals = fle & "-CSDs" & Z & ".dac{" & A & "+" & A & "}"
Parameters = "'Revision_1',,,1.0,4,0,-1,0,0"
DatsExecute "[ASDAV]", InputSignals, OutputSignals, Parameters 'Auto Spectral Density
ID={0}

34. 26
For X = 1 To totB
InputSignals = fle & Z & ".dac{" & A & "}," & fle & Z &".dac{" & B(X) & "}"
OutputSignals = fle & "-CSDs" & Z & ".dac{" & A & "+" & B(X) & "}"
Parameters = "'Revision_1',,,,1.0,4,0,-1,0,0,0"
DatsExecute "[CSDAV]", InputSignals, OutputSignals, Parameters 'Cross Spectral
Density ID={0}
DatsCheckFatalError
Next X
For Y = 1 To totB
For X = 1 To totB
If Y = X Then
InputSignals = fle & Z & ".dac{" & B(X) & "}"
OutputSignals = fle & "-CSDs" & Z & ".dac{" & B(X) & "+" & B(X) & "}"
Parameters = "'Revision_1',,,1.0,4,0,-1,0,0"
DatsExecute "[ASDAV]", InputSignals, OutputSignals, Parameters 'Auto Spectral Density
ID={0}
Else
InputSignals = fle & Z & ".dac{" & B(Y) & "}," & fle & Z &".dac{" & B(X) & "}"
OutputSignals = fle & "-CSDs" & Z & ".dac{" & B(X) & "+" & B(Y) & "}"
Parameters = "'Revision_1',,,,1.0,4,0,-1,0,0,0"
DatsExecute "[CSDAV]", InputSignals, OutputSignals, Parameters 'Cross Spectral
Density ID={0}
DatsCheckFatalError
End If
Next X
Next Y
Z = 5
InputSignals = fle & "-CSDs" & Z & ".dac{$ALL}"
OutputSignals = ""
Parameters = ",'" & fle & Z & "CSD.mat',0,'',1"
DatsExecute "[MATEXPORT]", InputSignals, OutputSignals, Parameters 'Export MATlab5 matrix data
ID={0}
DatsCheckFatalError
DatsStopModuleTracking
End Sub

35. 27
B. Matlab Script (main) (underlined file names/FFT size can be changed)
clear
load masticD-r5CSD5.mat
Gyy=real(DOEDOE(:,2)).';
Gxy=zeros(12,1,513);
Gxy(1,1,:)=DOEfrontleftx(:,2).';
Gxy(2,1,:)=DOEfrontlefty(:,2).';
Gxy(3,1,:)=DOEfrontleftz(:,2).';
Gxy(4,1,:)=DOEfrontrightx(:,2).';
Gxy(5,1,:)=DOEfrontrighty(:,2).';
Gxy(6,1,:)=DOEfrontrightz(:,2).';
Gxy(7,1,:)=DOErearleftx(:,2).';
Gxy(8,1,:)=DOErearlefty(:,2).';
Gxy(9,1,:)=DOErearleftz(:,2).';
Gxy(10,1,:)=DOErearrightx(:,2).';
Gxy(11,1,:)=DOErearrighty(:,2).';
Gxy(12,1,:)=DOErearrightz(:,2).';
Gxx=zeros(12,12,513);
Gxx(1,1,:)=frontleftxfrontleftx(:,2).';
Gxx(2,1,:)=frontleftyfrontleftx(:,2).';
Gxx(3,1,:)=frontleftzfrontleftx(:,2).';
Gxx(4,1,:)=frontrightxfrontleftx(:,2).';
Gxx(5,1,:)=frontrightyfrontleftx(:,2).';
Gxx(6,1,:)=frontrightzfrontleftx(:,2).';
Gxx(7,1,:)=rearleftxfrontleftx(:,2).';
Gxx(8,1,:)=rearleftyfrontleftx(:,2).';
Gxx(9,1,:)=rearleftzfrontleftx(:,2).';
Gxx(10,1,:)=rearrightxfrontleftx(:,2).';
Gxx(11,1,:)=rearrightyfrontleftx(:,2).';
Gxx(12,1,:)=rearrightzfrontleftx(:,2).';
Gxx(1,2,:)=frontleftxfrontlefty(:,2).';
Gxx(2,2,:)=frontleftyfrontlefty(:,2).';
Gxx(3,2,:)=frontleftzfrontlefty(:,2).';
Gxx(4,2,:)=frontrightxfrontlefty(:,2).';
Gxx(5,2,:)=frontrightyfrontlefty(:,2).';
Gxx(6,2,:)=frontrightzfrontlefty(:,2).';
Gxx(7,2,:)=rearleftxfrontlefty(:,2).';
Gxx(8,2,:)=rearleftyfrontlefty(:,2).';
Gxx(9,2,:)=rearleftzfrontlefty(:,2).';
Gxx(10,2,:)=rearrightxfrontlefty(:,2).';
Gxx(11,2,:)=rearrightyfrontlefty(:,2).';
Gxx(12,2,:)=rearrightzfrontlefty(:,2).';
Gxx(1,3,:)=frontleftxfrontleftz(:,2).';
Gxx(2,3,:)=frontleftyfrontleftz(:,2).';
Gxx(3,3,:)=frontleftzfrontleftz(:,2).';
Gxx(4,3,:)=frontrightxfrontleftz(:,2).';
Gxx(5,3,:)=frontrightyfrontleftz(:,2).';
Gxx(6,3,:)=frontrightzfrontleftz(:,2).';
Gxx(7,3,:)=rearleftxfrontleftz(:,2).';
Gxx(8,3,:)=rearleftyfrontleftz(:,2).';
Gxx(9,3,:)=rearleftzfrontleftz(:,2).';
Gxx(10,3,:)=rearrightxfrontleftz(:,2).';
Gxx(11,3,:)=rearrightyfrontleftz(:,2).';
Gxx(12,3,:)=rearrightzfrontleftz(:,2).';
Gxx(1,4,:)=frontleftxfrontrightx(:,2).';
Gxx(2,4,:)=frontleftyfrontrightx(:,2).';
Gxx(3,4,:)=frontleftzfrontrightx(:,2).';
Gxx(4,4,:)=frontrightxfrontrightx(:,2).';
Gxx(5,4,:)=frontrightyfrontrightx(:,2).';
Gxx(6,4,:)=frontrightzfrontrightx(:,2).';
Gxx(7,4,:)=rearleftxfrontrightx(:,2).';
Gxx(8,4,:)=rearleftyfrontrightx(:,2).';
Gxx(9,4,:)=rearleftzfrontrightx(:,2).';
Gxx(10,4,:)=rearrightxfrontrightx(:,2).';

36. 28
Gxx(11,4,:)=rearrightyfrontrightx(:,2).';
Gxx(12,4,:)=rearrightzfrontrightx(:,2).';
Gxx(1,5,:)=frontleftxfrontrighty(:,2).';
Gxx(2,5,:)=frontleftyfrontrighty(:,2).';
Gxx(3,5,:)=frontleftzfrontrighty(:,2).';
Gxx(4,5,:)=frontrightxfrontrighty(:,2).';
Gxx(5,5,:)=frontrightyfrontrighty(:,2).';
Gxx(6,5,:)=frontrightzfrontrighty(:,2).';
Gxx(7,5,:)=rearleftxfrontrighty(:,2).';
Gxx(8,5,:)=rearleftyfrontrighty(:,2).';
Gxx(9,5,:)=rearleftzfrontrighty(:,2).';
Gxx(10,5,:)=rearrightxfrontrighty(:,2).';
Gxx(11,5,:)=rearrightyfrontrighty(:,2).';
Gxx(12,5,:)=rearrightzfrontrighty(:,2).';
Gxx(1,6,:)=frontleftxfrontrightz(:,2).';
Gxx(2,6,:)=frontleftyfrontrightz(:,2).';
Gxx(3,6,:)=frontleftzfrontrightz(:,2).';
Gxx(4,6,:)=frontrightxfrontrightz(:,2).';
Gxx(5,6,:)=frontrightyfrontrightz(:,2).';
Gxx(6,6,:)=frontrightzfrontrightz(:,2).';
Gxx(7,6,:)=rearleftxfrontrightz(:,2).';
Gxx(8,6,:)=rearleftyfrontrightz(:,2).';
Gxx(9,6,:)=rearleftzfrontrightz(:,2).';
Gxx(10,6,:)=rearrightxfrontrightz(:,2).';
Gxx(11,6,:)=rearrightyfrontrightz(:,2).';
Gxx(12,6,:)=rearrightzfrontrightz(:,2).';
Gxx(1,7,:)=frontleftxrearleftx(:,2).';
Gxx(2,7,:)=frontleftyrearleftx(:,2).';
Gxx(3,7,:)=frontleftzrearleftx(:,2).';
Gxx(4,7,:)=frontrightxrearleftx(:,2).';
Gxx(5,7,:)=frontrightyrearleftx(:,2).';
Gxx(6,7,:)=frontrightzrearleftx(:,2).';
Gxx(7,7,:)=rearleftxrearleftx(:,2).';
Gxx(8,7,:)=rearleftyrearleftx(:,2).';
Gxx(9,7,:)=rearleftzrearleftx(:,2).';
Gxx(10,7,:)=rearrightxrearleftx(:,2).';
Gxx(11,7,:)=rearrightyrearleftx(:,2).';
Gxx(12,7,:)=rearrightzrearleftx(:,2).';
Gxx(1,8,:)=frontleftxrearlefty(:,2).';
Gxx(2,8,:)=frontleftyrearlefty(:,2).';
Gxx(3,8,:)=frontleftzrearlefty(:,2).';
Gxx(4,8,:)=frontrightxrearlefty(:,2).';
Gxx(5,8,:)=frontrightyrearlefty(:,2).';
Gxx(6,8,:)=frontrightzrearlefty(:,2).';
Gxx(7,8,:)=rearleftxrearlefty(:,2).';
Gxx(8,8,:)=rearleftyrearlefty(:,2).';
Gxx(9,8,:)=rearleftzrearlefty(:,2).';
Gxx(10,8,:)=rearrightxrearlefty(:,2).';
Gxx(11,8,:)=rearrightyrearlefty(:,2).';
Gxx(12,8,:)=rearrightzrearlefty(:,2).';
Gxx(1,9,:)=frontleftxrearleftz(:,2).';
Gxx(2,9,:)=frontleftyrearleftz(:,2).';
Gxx(3,9,:)=frontleftzrearleftz(:,2).';
Gxx(4,9,:)=frontrightxrearleftz(:,2).';
Gxx(5,9,:)=frontrightyrearleftz(:,2).';
Gxx(6,9,:)=frontrightzrearleftz(:,2).';
Gxx(7,9,:)=rearleftxrearleftz(:,2).';
Gxx(8,9,:)=rearleftyrearleftz(:,2).';
Gxx(9,9,:)=rearleftzrearleftz(:,2).';
Gxx(10,9,:)=rearrightxrearleftz(:,2).';
Gxx(11,9,:)=rearrightyrearleftz(:,2).';
Gxx(12,9,:)=rearrightzrearleftz(:,2).';
Gxx(1,10,:)=frontleftxrearrightx(:,2).';
Gxx(2,10,:)=frontleftyrearrightx(:,2).';
Gxx(3,10,:)=frontleftzrearrightx(:,2).';
Gxx(4,10,:)=frontrightxrearrightx(:,2).';
Gxx(5,10,:)=frontrightyrearrightx(:,2).';
Gxx(6,10,:)=frontrightzrearrightx(:,2).';
Gxx(7,10,:)=rearleftxrearrightx(:,2).';

37. 29
Gxx(8,10,:)=rearleftyrearrightx(:,2).';
Gxx(9,10,:)=rearleftzrearrightx(:,2).';
Gxx(10,10,:)=rearrightxrearrightx(:,2).';
Gxx(11,10,:)=rearrightyrearrightx(:,2).';
Gxx(12,10,:)=rearrightzrearrightx(:,2).';
Gxx(1,11,:)=frontleftxrearrighty(:,2).';
Gxx(2,11,:)=frontleftyrearrighty(:,2).';
Gxx(3,11,:)=frontleftzrearrighty(:,2).';
Gxx(4,11,:)=frontrightxrearrighty(:,2).';
Gxx(5,11,:)=frontrightyrearrighty(:,2).';
Gxx(6,11,:)=frontrightzrearrighty(:,2).';
Gxx(7,11,:)=rearleftxrearrighty(:,2).';
Gxx(8,11,:)=rearleftyrearrighty(:,2).';
Gxx(9,11,:)=rearleftzrearrighty(:,2).';
Gxx(10,11,:)=rearrightxrearrighty(:,2).';
Gxx(11,11,:)=rearrightyrearrighty(:,2).';
Gxx(12,11,:)=rearrightzrearrighty(:,2).';
Gxx(1,12,:)=frontleftxrearrightz(:,2).';
Gxx(2,12,:)=frontleftyrearrightz(:,2).';
Gxx(3,12,:)=frontleftzrearrightz(:,2).';
Gxx(4,12,:)=frontrightxrearrightz(:,2).';
Gxx(5,12,:)=frontrightyrearrightz(:,2).';
Gxx(6,12,:)=frontrightzrearrightz(:,2).';
Gxx(7,12,:)=rearleftxrearrightz(:,2).';
Gxx(8,12,:)=rearleftyrearrightz(:,2).';
Gxx(9,12,:)=rearleftzrearrightz(:,2).';
Gxx(10,12,:)=rearrightxrearrightz(:,2).';
Gxx(11,12,:)=rearrightyrearrightz(:,2).';
Gxx(12,12,:)=rearrightzrearrightz(:,2).';
[Hi] = gaussElim5(Gxx,Gxy);
% Hi is the 12 transfer functions from the 12 inputs to DOE
zHiP=Hi.'
% transposed for easier review
Ghatyy = zeros(1,513);
for x = 1:12
for y = 1:12
Gxt(1,:)=Gxx(x,y,:);
Ghatyy = Ghatyy + (conj(Hi(x,:)) .* Hi(y,:) .* Gxt(1,:));
% Ghatyy is the complex conjugate TF (Hi) multiplied by TF (Hj), multiplied by each of the 144
auto and cross correlations (Sij) akin to Equation 1.6 in the main text
end
end
y2yx = Ghatyy ./ Gyy;
% y2yx is the coherence function, indicating where the transfer function is valid.
y2yxP=y2yx.'

38. 30
C. Matlab Script (function) (underlined FFT size can be changed)
function [x] = gaussElim(A,b)
% File gaussElim.m
% This subroutine will perform Gaussian elmination
% on the matrix that you pass to it.
% i.e., given A and b it can be used to find x,
% Ax = b
%
% To run this file you will need to specify several
% things:
% A - matrix for the left hand side.
% b - vector for the right hand side
%
% The routine will return the vector x.
% ex: [x] = gaussElim(A,b)
% this will perform Gaussian elminiation to find x.
%
%
N =12;
x = zeros(N,513);
for R=1:513,
% Perform Gaussian Elimination
for j=2:N,
for i=j:N,
m = A(i,j-1,R)/A(j-1,j-1,R);
A(i,:,R) = A(i,:,R) - A(j-1,:,R)*m;
b(i,R) = b(i,R) - m*b(j-1,R);
end
end
% Perform back substitution
x(N,R) = b(N,R)/A(N,N,R);
for j=N-1:-1:1,
x(j,R) = (b(j,R)-A(j,j+1:N,R)*x(j+1:N,R))/A(j,j,R);
end
end

39. Appendix B
Raw data and information
A. Named Elements for Door Mastic case
%%%%%%%%%%HEADER%%%%%%%%%%
signal name DOE
file name C:Documents and Settingsrschube1My DocumentsD219-
258RoadNoiseMulti-inputmasticD-178859-r5-p1-spectrum.dac
date created 26/Feb/2007
time created 12:01:22
number of values 513
sampling rate 4096
origin 0
increment 4
associate value 16
dB reference value 1
points per decade 0
data type Real
real maximum 2.32633280754
real minimum 7.29489329387e-005
%%%%%%NAMED ELEMENTS%%%%%%
#$ANALYSIS ASDLEV
#$LAYOUT_STYLE ASD
$ACQ_CONTROL NORMAL
$ACQ_ENG_MAX 50.2901573181
$ACQ_ENG_MIN -50.2916908264
$AC_COUPLED Yes
$ADC_AUTOZERO_MODE Clear
$ADC_CHANNEL 16
$ADC_CLOCK_MODE Internal
$ADC_GAIN 4
$ADC_LEVEL 2
$ADC_SIGNAL_SOURCE Signal
$ADC_TRIGGER_LEVEL 0
$ADC_TRIGGER_MODE None
$AFILT_FREQ 6553.60009766
$AMP_OFFSET 0
$ASSOC_DESC Channel
$ASSOC_UNITS
$ASSOC_VAR 16
$AZ_LEVEL 0
$CAL_OFFSET 0
$DATA_WINDOW Hanning
$DECIM_FACTOR 4
$DECIM_FREQ 1843.19995117
$DECIM_dBRATE 72
$DEVICE P5650_bnc_16
$ENBW 6
$FAN_STATE OFF
$FFT_RANGE Half Range
$FREEDOM 34
$FT_SIZE 1024
$GRAPH RMS Harmonic Level
$IND_DESC Frequency
$IND_TYPE Time

40. 32
$IND_UNITS Hz
$INPUT_RANGE -10.00000v -> 10.00000v
$ORIG_DATE 04/07/2006
$ORIG_SIG mastic-178859-r5{DOE}
$ORIG_TIME 4:39:54 PM
$Overall_Unw_dB 13.4999236845
$PROM_REV 03024m4v
$SAMPLE_RATE_DESC Samples/Sec
$SENS_MODE 1
$SENS_STYLE mV/Pa
$SERIAL_NO 0
$SIG_DESC DOE
$SIG_NAME DOE
$SIG_TYPE Spectrum
$SIG_TYPE2 rms
$SIG_UNITS Pa
$SPECTRUM_OVERLAP 50
$SPECTRUM_TYPE RMS Harmonic Level
$SSP_TYPE 3
$TRANS_CALDATE Unknown
$TRANS_EXCIT 0
$TRANS_EXCIT_CLASS ICP
$TRANS_ID Not Set
$TRANS_OFFSET 0
$TRANS_SENS 49.7099990845
$dB_TYPE Linear

41. 33
B. Time series of DOE and 12 inputs:

42. 34

43. 35

44. 36

45. 37

46. 38
C. Example of Auto Spectral density: DOE in (Pa)²/Hz
D. Example of Cross Spectral Density: DOE and front left wheel input X in
((Pa)*(m/sec²))/Hz