Data analysis techniques: Difference between revisions
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=== Linear analysis === | === Linear analysis === | ||
* Correlation | * [[:Wikipedia:Correlation|Correlation]] analysis | ||
* [[:Wikipedia:Fourier transform|Fourier]] analysis | * [[:Wikipedia:Fourier transform|Fourier]] analysis | ||
* [[:Wikipedia:Wavelet|Wavelet]] analysis | * [[:Wikipedia:Wavelet|Wavelet]] analysis | ||
* Conditional analysis | * Conditional analysis <ref>I. Teliban, D. Block, A. Piel and F. Greiner, ''Improved conditional averaging technique for plasma fluctuation diagnostics'', [[doi:10.1088/0741-3335/49/4/011|Plasma Phys. Control. Fusion '''49'''(2007) 485–497]]</ref> | ||
* Probability | * Probability distribution, [[:Wikipedia:Cumulative distribution function|Cumulative distribution function]] (rank) | ||
=== Non-linear analysis === | === Non-linear analysis === | ||
* [[ | * [[Bicoherence]], bispectrum | ||
* Chaos analysis ([[:Wikipedia:Attractor|Strange attractor]], [[:Wikipedia:Fractal dimension|Fractal dimension]], [[:Wikipedia:Mutual information|Mutual information]]) | * Chaos analysis ([[:Wikipedia:Attractor|Strange attractor]], [[:Wikipedia:Fractal dimension|Fractal dimension]], [[:Wikipedia:Mutual information|Mutual information]], [[:Wikipedia:Lyapunov exponent|Lyapunov exponent]], [[Intermittence]]) | ||
* [[:Wikipedia:Hilbert-Huang transform|Hilbert-Huang transform]] | * [[:Wikipedia:Hilbert-Huang transform|Hilbert-Huang transform]] <ref>N. Huang and S. Shen, ''Hilbert-Huang transform and its applications'' (World Scientific, London, 2005) {{ISBN|978-9812563767}}</ref><ref>B.A. Carreras et al., ''Reconstruction of intermittent waveforms associated with the zonal flow at the transition leading to the edge shear flow layer'', [[doi:10.1088/0029-5515/51/5/053022|Nucl. Fusion '''51''' (2011) 053022]]</ref> | ||
=== Self-similarity === | |||
* [[:Wikipedia:Rescaled range|Rescaled range]] or [[:Wikipedia:Hurst exponent|Hurst]] analysis; Structure functions | |||
* Waiting times, quiet times <ref>R. Sánchez et al., ''Quiet-time statistics: A tool to probe the dynamics of self-organized-criticality systems from within the strong overlapping regime'', [[doi:10.1103/PhysRevE.66.036124|Phys. Rev. E '''66''', 036124 (2002)]]</ref> | |||
=== Causality === | |||
* [[Causality detection]]<ref>B.Ph. van Milligen, G. Birkenmeier, M. Ramisch, T. Estrada, C. Hidalgo, and A. Alonso, ''Causality detection and turbulence in fusion plasmas'', [[doi:10.1088/0029-5515/54/2/023011|Nucl. Fusion '''54''' (2014), 023011]]</ref>: the determination of a causal interaction between two fluctuating variables, based on, e.g., the Transfer Entropy | |||
== Spatial analysis == | == Spatial analysis == | ||
| Line 25: | Line 33: | ||
== Spatio-temporal analysis == | == Spatio-temporal analysis == | ||
* [[Biorthogonal decomposition]] | * [[Biorthogonal decomposition]] <ref>B.Ph. van Milligen, E. Sánchez, A. Alonso, M.A. Pedrosa, C. Hidalgo, A. Martín de Aguilera, A. López Fraguas, ''The use of the Biorthogonal Decomposition for the identification of zonal flows at TJ-II'', [[doi:10.1088/0741-3335/57/2/025005|Plasma Phys. Control. Fusion '''57''', 2 (2015) 025005]]</ref> | ||
== Image analysis == | == Image analysis == | ||
| Line 43: | Line 51: | ||
[[Error propagation]] | [[Error propagation]] | ||
== References == | |||
<references /> | |||
Latest revision as of 12:11, 21 April 2024
This page collects information on data analysis techniques used in fusion research.
Temporal analysis
Linear analysis
- Correlation analysis
- Fourier analysis
- Wavelet analysis
- Conditional analysis [1]
- Probability distribution, Cumulative distribution function (rank)
Non-linear analysis
- Bicoherence, bispectrum
- Chaos analysis (Strange attractor, Fractal dimension, Mutual information, Lyapunov exponent, Intermittence)
- Hilbert-Huang transform [2][3]
Self-similarity
- Rescaled range or Hurst analysis; Structure functions
- Waiting times, quiet times [4]
Causality
- Causality detection[5]: the determination of a causal interaction between two fluctuating variables, based on, e.g., the Transfer Entropy
Spatial analysis
Most of the techniques listed under 'temporal analysis' can of course be applied to spatial data.
- Tomography (cf. TJ-II:Tomography)
Spatio-temporal analysis
Image analysis
- Twodimensional Fourier analysis
- Twodimensional wavelet analysis
- Event detection using thresholding
- Optical flow (for movies)
Integrated data analysis
The goal of integrated data analysis is to combine the information from a set of diagnostics providing complementary information in order to recover the best possible reconstruction of the actual state of the system subjected to measurement.
See also
References
- ↑ I. Teliban, D. Block, A. Piel and F. Greiner, Improved conditional averaging technique for plasma fluctuation diagnostics, Plasma Phys. Control. Fusion 49(2007) 485–497
- ↑ N. Huang and S. Shen, Hilbert-Huang transform and its applications (World Scientific, London, 2005) ISBN 978-9812563767
- ↑ B.A. Carreras et al., Reconstruction of intermittent waveforms associated with the zonal flow at the transition leading to the edge shear flow layer, Nucl. Fusion 51 (2011) 053022
- ↑ R. Sánchez et al., Quiet-time statistics: A tool to probe the dynamics of self-organized-criticality systems from within the strong overlapping regime, Phys. Rev. E 66, 036124 (2002)
- ↑ B.Ph. van Milligen, G. Birkenmeier, M. Ramisch, T. Estrada, C. Hidalgo, and A. Alonso, Causality detection and turbulence in fusion plasmas, Nucl. Fusion 54 (2014), 023011
- ↑ B.Ph. van Milligen, E. Sánchez, A. Alonso, M.A. Pedrosa, C. Hidalgo, A. Martín de Aguilera, A. López Fraguas, The use of the Biorthogonal Decomposition for the identification of zonal flows at TJ-II, Plasma Phys. Control. Fusion 57, 2 (2015) 025005