LMS Transfer path analysis

1. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 1
Transfer path analysis
P

2. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 2
Transfer path analysis
Application background
 Structureborne noise - structural path between source and receiver
 from engine
 from suspension
 from exhaust, gearbox, drive-line
 Airborne noise - no structural path between source and receiver
 engine noise
 aerodynamic noise
 radiated noise from panels
 What are the main contributors, the important transfer paths ?
Treated in ASQ

3. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 3
Transfer path analysis
Principles
 Simplify noise/vibration path into source-receiver-transfer system
Transfer
- structure
- sound field
Receiver
- human ear
- steering wheel
Source
- connection between
excitation source and
target structure

4. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 4
 Quantification of source-receiver-transfer system
Transfer path analysis
Principles
Transfer
- vibro-(acoustic) FRF
- Pa/N or (m2/s)/N
Receiver
- pressure or acceleration
- Pa or m2/s
Source
- force
- N

5. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 5
Transfer path analysis
Principles
 Structure-borne noise/vibration breakdown and ranking
 Preceiver =  Pi
 Partial contribution Pi
 Pi = Fi . Hi
PF
Source : N Transfer : Pa/N
 Xreceiver =  Xi
 Xi = Fi . Hi
XF
Source : N Transfer : (m/s2)/N
:
:
:
:

6. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 6
Transfer path analysis
Two applications
 Transfer path ranking, contribution analysis
 Preceiver =  FiHi
PF
 source or transfer problem ?
 post processing for FBS, ASQ, FE calculations
 Multiple force estimation methods
Fi ?

7. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 7
Transfer path analysis
Source identification
 Complex dynamic stiffness method
 Acceleration measurements
 Mount rates
 Full matrix inversion
 Acceleration measurements
 FRF measurements (full matrix)
 Driving point inversion
 Acceleration measurements
 Driving point FRF
measurements

8. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 8
Transfer path analysis
Complex dynamic stiffness method
t
x


s
x


       
 



 t
s X
X
K
F 


 Acceleration measurements on both sides of
mount
 Stiffness characteristics of mount

9. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 9
Transfer path analysis
Complex dynamic stiffness determination

 determination of stiffness in three direction
 rotational degrees of freedom neglected
 cross-coupling effects neglected
 Automatic integration/differentiation of mount stiffness data
 Behavior of mounts is not very linear
 apply correct pre-load
 temperature effects may be important
 adapt excitation according to actual operational conditions
 
 



X
F
K 
)
(

10. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 10
Transfer path analysis
Complex dynamic stiffness determination
Mount
Ground
Mass (pre-load)
F
vert
x

 hor
x



11. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 11
Transfer path analysis
Inverse method
F1
x4
x3
T14
T13
F2
T24
T23
 
  2
24
1
14
2
1
4
2
23
1
13
2
1
3
.
.
,
.
.
,
F
T
F
T
F
F
f
x
F
T
F
T
F
F
f
x






F : excitation
X : response
T : transfer function



















2
1
24
14
23
13
4
3
F
F
T
T
T
T
x
x




















4
3
1
24
14
23
13
2
1
x
x
T
T
T
T
F
F

12. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 12
Transfer path analysis
Inverse method : example
Operational measurements
 acceleration at three points
Laboratory measurements
 full FRF matrix between
excitation at point 1 and
response at the other points
1
x


1001
x


1002
x


1
1001
1002
Finput

13. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 13
1001
1002
F1
oper ?
Transfer path analysis
Inverse method : example






























oper
oper
oper
oper
x
x
x
F
x
F
x
F
x
F
1002
1001
1
1
1
1002
1
1001
1
1
1













14. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 14
Transfer path analysis
Singular value decomposition
 Singular value decomposition of transfer function matrix
       
   





n
i
n
i
i
m
i
nxn
mxn
mxm
mxn
V
U
V
U
H
1
*
*

 
















0
0
0
0
0
0
0
2
1
n
mxn













M : number of responses
N : number of sources
M  N

15. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 15
Transfer path analysis
Singular value decomposition
 Example : 28x15 accelerance FRF matrix

16. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 16
Transfer path analysis
Singular value decomposition
   
   
   
     
   













n
i
m
i
i
n
i
T
mxm
nxm
nxn
mxm
mxn
T
nxn
nxm
U
V
U
V
U
V
H
1
*
1
1
1
1
1
1

 Matrix inversion by singular value decomposition
 




















0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
1
n
nxm











17. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 17
 Matrix inversion by singular value decomposition
Over determination allowed (M  N)
 Least squares estimate
 Calculation of condition number : upper bound for
multiplication coefficient of relative error
Transfer path analysis
Singular value decomposition
n
number
condition

1
_ 

18. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 18
 Improving the matrix condition
 Delete p singular values : condition number drops
 Three possibilities : number, relative, absolute
 Overdetermination : 2/1
Transfer path analysis
Singular value decomposition
p
n
number
condition



1
_ n-p > n

19. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 19
Transfer path analysis
Number criterium

20. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 20
Transfer path analysis
Relative criterium

21. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 21
Transfer path analysis
Relation condition number / overdetermination

22. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 22
Transfer path analysis
Selection of overdetermination points
 Overdetermination : 2n responses to estimate n forces
 Location of OD points
 good coherence with signal in transfer path
 not to close to transfer path : no extra information
 3 extra points in one direction better then 1point measured in 3
directions
 Pressure response can be included in matrix inversion

23. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 23
Transfer path analysis
SVD example : fully trimmed car
Original FRFs + condition number Elements from inverted matrix

24. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 24
Transfer path analysis
SVD example : body in white
Original FRFs + condition number Elements from inverted matrix

25. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 25
Transfer path analysis
Transfer functions
 Measured in uncoupled condition
 engine, drive-line removed
 suspension removed
 Follows from substructuring formulation
 P=HA+BFi=HB([HA+HB+K-1]-1HAFi)=HBFc
HA HB
K
source target
Fc
Fi P
TPA

26. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 26
Transfer path analysis
Transfer functions
 Always check
 Linearity
 Coherence
 Reciprocity
 Impact or shaker testing
 Coherence with hammer excitation
 Misalignment of shaker
 Small errors become important after matrix inversion
Excitation
direction

27. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 27
Transfer path analysis
Vibro-acoustic reciprocity
i
j
j
i
PF
F
P
Q
x
H 


F1
F2
Pj
1
x


2
x


Qj
 Reduction of measurement effort
j
i
Q
x
unit
define )
(

28. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 28
Transfer path analysis
Volume velocity source
 Volume velocity sources
 Sufficiently excite cavity and/or structure : high power
 Not influenced by acoustic boundary
 Ease of use : constant calibration factor
 Omni-directional

29. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 29
Transfer path analysis
Features : easy model definition
 Model definition based on PID and SID annotations
mic:1:S
body:2
body:1
Data type Primary ID Secondary ID
Force body:1:+Z -
body:2:+Z -
Pressure mic:1:S -
FRF mic:1:S body:1:+Z
mic:1:S body:2:+Z

30. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 30
x1 x2 ... xr
x11…x21…xr1
PCA
Force
id.
TPA
x12…x22…xr2 x1m…x2m…xrm
x11…x21…xr1 x12…x22…xr2 x1m…x2m…xrm
f11…f21…fn1 f12…f22…fn2 f1m…f2m…fnm
phenomenon 1 phenomenon 2 phenomenon m
Transfer path analysis
Features: support of multi-reference problems
 Support of single
reference problems :
engine noise e.g.
 Multi-reference
problems (road
noise e.g.) require
Principal
Component Analysis

31. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 31
Transfer path analysis
Features : structure and air-borne problems
 Study contribution of structure and air-borne noise in one
analysis : Preceiver =  Fi . Hi
PF+  Qi’ . Hi’
AA
 Pre-processor required for Panel Contribution Analysis

32. LMS
INTERNATIONAL
CMC - TPA training - May, 2005 32
Transfer path analysis
Extensions to TPA
 Easy data grouping mechanism in post-processing
 grouping based on PID
 simplifying visualization
 Frequency spectra, ordercuts and autopowers (new) supported
 Automatic squaring of FRFs in case of autopowers
 Condition calculation : specify frequency range