# Data analysis techniques

From FusionWiki

This page collects information on data analysis techniques used in fusion research.

## Contents

## 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)
- 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

- Biorthogonal decomposition
^{[6]}

## 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