use of multi-input single-output methods to improve measurement repeatability for road noise in...

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

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.

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

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

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

vii

LIST OF TABLES

No Tables Provided.

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.

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-

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

So

nes (

dif

fuse)

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

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

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

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

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.

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.

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.

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. Itis assumed similar results would be achieved if damping material was placed on the inside of the vehicle.

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.

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.

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

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

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.

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

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.

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

A verage 1Hz c oherenc e A verage 4Hz c oherenc e 4Hz max4 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 A verage 1Hz c oherenc e With Damper A verage 4Hz c oherenc e4Hz max 4 Hz min1Hz 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.

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 D am per D OE frontleftx

No D am per D OE frontlefty

No D am per D OE frontleftz

No D am per D OE frontrightx

No D am per D OE frontrighty

No D am per D OE frontrightz

No D am per D OE rearleftx

No D am per D OE rearlefty

No D am per D OE rearleftz

No D am per D OE rearrightx

No D am per D OE rearrighty

No D am per D OE rearrightz

No D am per D OE rearrightz

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 D am per D OE frontleftx

with D am per D OE frontlefty

with D am per D OE frontleftz

with D am per D OE frontrightx

with D am per D OE frontrighty

with D am per D OE frontrightz

with D am per D OE rearleftx

with D am per D OE rearlefty

with D am per D OE rearleftz

with D am per D OE rearrightx

with D am per D OE rearrighty

with D am per D OE rearrightz

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

21

396

616

288 280 300368

195 209 204 218335

20595

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

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 es t F iltered front left Y T rans fer function delta

-2

-1.5

-1

-0.5

0

0.5

1

1.5

10 100 1000 10000

Damper improved

Baseline better

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.

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

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 Settings\rschube1\My Documents\D219-258\RoadNoise\Multi-input\baseD-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

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) & "}"



ID={0}

Else

InputSignals = fle & Z & ".dac{" & B(Y) & "}," & fle & Z &".dac{" & B(X) & "}"

OutputSignals = fle & "-CSDs" & Z & ".dac{" & B(X) & "+" & B(Y) & "}"



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 Settings\rschube1\My Documents\D219-258\RoadNoise\Multi-input\masticD-r"

totB=12

totRun=6

Z = 5

InputSignals = fle & Z & ".dac{" & A & "}"

OutputSignals = fle & "-CSDs" & Z & ".dac{" & A & "+" & A & "}"



ID={0}

26

For X = 1 To totB

InputSignals = fle & Z & ".dac{" & A & "}," & fle & Z &".dac{" & B(X) & "}"

OutputSignals = fle & "-CSDs" & Z & ".dac{" & A & "+" & B(X) & "}"



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) & "}"



ID={0}

Else

InputSignals = fle & Z & ".dac{" & B(Y) & "}," & fle & Z &".dac{" & B(X) & "}"

OutputSignals = fle & "-CSDs" & Z & ".dac{" & B(X) & "+" & B(Y) & "}"



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

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).';

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).';

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.'

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

Appendix B

Raw data and information

A. Named Elements for Door Mastic case

%%%%%%%%%%HEADER%%%%%%%%%%

signal name DOE

file name C:\Documents and Settings\rschube1\My Documents\D219-

258\RoadNoise\Multi-input\masticD-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

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

33

B. Time series of DOE and 12 inputs:

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