Offline and Real-time signal processing on fusion signals

pancakesbootΤεχνίτη Νοημοσύνη και Ρομποτική

24 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

53 εμφανίσεις

Signal processing tools Lisbon 18/02/09


R Coelho

1
/29

Offline and Real
-
time signal processing on fusion signals

Outline


1


The Fourier space methods

2


Empirical mode decomposition

3


(k,ω) space methods
-

Coherency spectrum and SVD

4


Beyond the Fourier paradigm


剥慬
-
瑩t攠扡b敤e瑥捨t楱略i.





Motional Stark Effect data processing.

R. Coelho, D. Alves

Associação EURATOM/IST, Instituto de Plasmas e Fusão Nuclear

Signal processing tools Lisbon 18/02/09


R Coelho

2
/29

1.
Fourier space methods (time dual)



Eigenmode decomposition providing signal support (even for
discontinuous signals)











continuous










discrete


Some Useful Properties


If







h(ω)=f(ω)g(ω)


If h(x)=f(x)g(x) then h(ω)=f(ω)*g(ω)



Signal processing tools Lisbon 18/02/09


R Coelho

3
/29

1.
Fourier space methods (time dual)


Some Useful Properties


If







h(ω)=f(ω)g(ω)





FILTERING in time !


If h(x)=f(x)g(x) then h(ω)=f(ω)*g(ω)






FILTERING in frequency !

Signal processing tools Lisbon 18/02/09


R Coelho

4
/29

1.
Fourier space methods


Time
-
frequency analysis


Sliding FFT method

: S(t,ω) where midpoint of time window
corresponds to a FFT.


Windowed spectrogram

: same as above but with window
function to reduce noise and enhance time localization


Spectrogram with zero padding

: same as above but zero
padding to each time window


shadow frequency

resolution
enhancement




Signal processing tools Lisbon 18/02/09


R Coelho

5
/29

2. Empirical mode decomposition








N
j
j
j
N
j
j
t
t
A
t
IMF
t
S
1
1
))
(
cos(
).
(
)
(
)
(

Signal processing tools Lisbon 18/02/09


R Coelho

6
/29

2. Empirical mode decomposition

Mirnov signal spectra, # 11672 using
EMD 3 dominant IMF (signals +
frequencies)

Signal processing tools Lisbon 18/02/09


R Coelho

7
/29

3. (k,ω) space methods
-

Coherency spectrum
and SVD


Coherency
-
Spectrum



standard tool for mode number analysis of





fluctuation spectra


Formal definition





,
-

auto
-
spectrums



-

cross
-
spectrum densities of two signals




Coherency






Phase









2
/
1
2
1
12
1
2
)
(
S
)
(
S
)
(
S
)
(
C






)
(
S
1

)
(
S
2

)
(
S
12

2
1
2
)
(
C




)
(
C
Arg
1
2


Signal processing tools Lisbon 18/02/09


R Coelho

8
/29

Singular value decomposition (SVD)




SVD is a decomposition of an array in time and space,
finding the most significant time and space characteristics.



The SVD of an
NxM

matrix
A

is
A=UWV
T





W

-

MxM

diagonal matrix with the singular values




Columns of
matrix
V
give the principal spatial modes and
the product
UW

the principal time components.




Signal processing tools Lisbon 18/02/09


R Coelho

9
/29

Mode number analysis by coherence spectrum


Cross
-
Spectrum



standard tool for mode number analysis of





MHD fluctuation spectra



Formal definition





,
-

auto
-
spectrums



-

cross
-
spectrum densities of two signals




Coherency






Phase









2
/
1
2
1
12
1
2
)
(
S
)
(
S
)
(
S
)
(
C






)
(
S
1

)
(
S
2

)
(
S
12

2
1
2
)
(
C




)
(
C
Arg
1
2


Signal processing tools Lisbon 18/02/09


R Coelho

10
/29

Background





With



m

is the mode number and


瑨t⁦牥qen捹





Phase difference between signals :





Generalisation of full coil array naturally leads to a
linear fit of
entire coil set




t
2
m
cos
)
r
(
B
B






1
2
1
2
1
2
m
m
m













2
/
1
2
1
12
1
2
)
(
S
)
(
S
)
(
S
)
(
C






Signal processing tools Lisbon 18/02/09


R Coelho

11
/29

Time/frequency constraints




Ensemble averaging is in practice replaced by time averaging



Spectral estimation done usually with FFT




…FFT Coherency spectrum drawbacks…







Each FFT (N
-
samples) gives
ONE

estimate for
AMPLITUDE

and


PHASE

for each frequency component.





Average over N
w

windows


N

N
w

samples to

ONE

Coherency


spectrum




Trade
-
off Time/frequency resolution

Signal processing tools Lisbon 18/02/09


R Coelho

12
/29

Beyond FFT paradigm...



State variable recursive estimation according to linear model +
measurements













F


process matrix





K


filter gain








z


measurements






R,Q


noise covariances



The process matrix





R.Coelho, D.Alves, RSI08

1
k
k
x
ˆ
F
x
ˆ










k
k
k
k
k
x
ˆ
H
z
K
x
ˆ
x
ˆ













N
2
1
N
F
F
F
F
h

















)
cos(
)
sin(
)
sin(
)
cos(
F
i
i
i
i
i
s
i
i
/
2





Signal processing tools Lisbon 18/02/09


R Coelho

13
/29

Kalman filter based spectrogram



Real
-
time replacement of spectrogram.


Amplitude, at a given time sample, estimated as












2
i
2
2
1
i
2
i
x
ˆ
x
ˆ
A





df=5kHz




s
=
2MHz

Signal processing tools Lisbon 18/02/09


R Coelho

14
/29

Kalman coherence spectrum



Real
-
time estimation of in
-
phase and quadratures of each

-
component allows for cross
-
spectrum estimation :












Two coil signals (labelled
a

and
b
)





in
-
phase ( )





quadrature ( )



ADVANTAGE





Streaming estimation of phase difference.




Much less “sample consuming” than FFT.




Effective filtering of estimates “sharpens” coherency.

cos
x
ˆ
sin
x
ˆ
Signal processing tools Lisbon 18/02/09


R Coelho

15
/29

Synthetised results








FFT algorithm







Coherency (12 eq.spaced tor.coils)













n=
-
3,4


s
=100kHz

375 pt for averaging (3.75ms)

125pt/FFT

50pt overlap (0.5ms)

Signal processing tools Lisbon 18/02/09


R Coelho

16
/29

Synthetised results








KCS algorithm







Coherency (12 eq.spaced tor.coils)













n=
-
3,4


s
=100kHz

50 pt for averaging


=
800Hz

Signal processing tools Lisbon 18/02/09


R Coelho

17
/29

Experimental results


#68202 (n=1 ST precursor)








FFT algorithm







Coherency (first 5 tor.coils only)













n=1


s
=1MHz

1500 pt for averaging (1.5ms)

1000pt/FFT

100pt overlap

Signal processing tools Lisbon 18/02/09


R Coelho

18
/29

Experimental results









KCS algorithm







Coherency (first 5 tor.coils only)















s
=1MHz

100 pt for averaging


=
1000Hz

Signal processing tools Lisbon 18/02/09


R Coelho

19
/29

Experimental results


#72689 (m=3,n=2 NTM)








FFT algorithm







Coherency (first 5 tor.coils only)













n=1

s
=1MHz

1500 pt for averaging (1.5ms)

1000pt/FFT

100pt overlap

Signal processing tools Lisbon 18/02/09


R Coelho

20
/29

Experimental results









KCS algorithm







Coherency (first 5 tor.coils only)















s
=1MHz

100 pt for averaging


=
1000Hz

n=3, IDL “fake contouring”

Earlier detection in coherency (threshold effect)

Signal processing tools Lisbon 18/02/09


R Coelho

21
/29

Conclusions



A novel method for space
-
frequency MHD analysis using Mirnov
data was developed.



A Kalman filter lock
-
in amplifier implementation is used to
replace the FFT in the coherence function calculation.



Particularly suited technique for real
-
time analysis with limited
number of streaming data



Saving in data samples arises from the streaming estimation of
in
-
phase and quadrature components of any given frequency
mode existent in the data, not possible in a FFT based
algorithm.



Ongoing work…better candidates will be targeted !




Signal processing tools Lisbon 18/02/09


R Coelho

22
/29