Offline and real time signal processing on fusion signals
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Outline 1 – The Fourier space methods 2 – Empirical mode decomposition 3 – (k,ω) space methods - Coherency spectrum and SVD 4 – Beyond the Fourier paradigm  Real-time based techniques. – Motional Stark Effect data processing. Offline and Real-time signal processing on fusion signals.

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Offline and Real-time signal processing on fusion signals

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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  Real-time based techniques.

– Motional Stark Effect data processing.

Offline and Real-time signal processing on fusion signals

R. Coelho, D. Alves

Associação EURATOM/IST, Instituto de Plasmas e Fusão Nuclear


Offline and real time signal processing on fusion signals

  • 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)


Offline and real time signal processing on fusion signals

  • 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 !


Offline and real time signal processing on fusion signals

  • 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 frequencyresolution enhancement


Offline and real time signal processing on fusion signals

2. Empirical mode decomposition


Offline and real time signal processing on fusion signals

2. Empirical mode decomposition

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


Offline and real time signal processing on fusion signals

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


Offline and real time signal processing on fusion signals

  • 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=UWVT

  •  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.


Offline and real time signal processing on fusion signals

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


Offline and real time signal processing on fusion signals

Background

 With

m is the mode number and  the frequency

 Phase difference between signals :

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


Offline and real time signal processing on fusion signals

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 Nw windows  NNw samples to ONE Coherency

spectrum

Trade-off Time/frequency resolution


Offline and real time signal processing on fusion signals

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 matrixR.Coelho, D.Alves, RSI08


Offline and real time signal processing on fusion signals

Kalman filter based spectrogram

Real-time replacement of spectrogram.

Amplitude, at a given time sample, estimated as

  • df=5kHz

  • s=2MHz


Offline and real time signal processing on fusion signals

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.


Offline and real time signal processing on fusion signals

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)


Offline and real time signal processing on fusion signals

Synthetised results

KCS algorithm

Coherency (12 eq.spaced tor.coils)

n=-3,4

s=100kHz

50 pt for averaging

=800Hz


Offline and real time signal processing on fusion signals

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


Offline and real time signal processing on fusion signals

Experimental results

KCS algorithm

Coherency (first 5 tor.coils only)

s=1MHz

100 pt for averaging

=1000Hz


Offline and real time signal processing on fusion signals

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


Offline and real time signal processing on fusion signals

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)


Offline and real time signal processing on fusion signals

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 !


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