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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.

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Offline and Real-time signal processing on fusion signals

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  1. 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

  2. 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)

  3. 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 !

  4. 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

  5. 2. Empirical mode decomposition

  6. 2. Empirical mode decomposition Mirnov signal spectra, # 11672 using EMD 3 dominant IMF (signals + frequencies)

  7. 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

  8. 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.

  9. 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

  10. 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

  11. 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

  12. 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

  13. Kalman filter based spectrogram Real-time replacement of spectrogram. Amplitude, at a given time sample, estimated as • df=5kHz • s=2MHz

  14. 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.

  15. 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)

  16. Synthetised results KCS algorithm Coherency (12 eq.spaced tor.coils) n=-3,4 s=100kHz 50 pt for averaging =800Hz

  17. 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

  18. Experimental results KCS algorithm Coherency (first 5 tor.coils only) s=1MHz 100 pt for averaging =1000Hz

  19. 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

  20. 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)

  21. 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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