# Uncertainty Analysis in 3D Equilibrium Reconstruction

## Abstract

Reconstruction is an inverse process where a parameter space is searched to locate a set of parameters with the highest probability of describing experimental observations. Due to systematic errors and uncertainty in experimental measurements, this optimal set of parameters will contain some associated uncertainty. This uncertainty in the optimal parameters leads to uncertainty in models derived using those parameters. V3FIT is a three-dimensional (3D) equilibrium reconstruction code that propagates uncertainty from the input signals, to the reconstructed parameters, and to the final model. Here in this paper, we describe the methods used to propagate uncertainty in V3FIT. Using the results of whole shot 3D equilibrium reconstruction of the Compact Toroidal Hybrid, this propagated uncertainty is validated against the random variation in the resulting parameters. Two different model parameterizations demonstrate how the uncertainty propagation can indicate the quality of a reconstruction. As a proxy for random sampling, the whole shot reconstruction results in a time interval that will be used to validate the propagated uncertainty from a single time slice.

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Auburn Univ., AL (United States). Allison Lab.

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

- OSTI Identifier:
- 1423072

- Grant/Contract Number:
- AC05-00OR22725; FG02-03ER54692

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Fusion Science and Technology

- Additional Journal Information:
- Journal Volume: 73; Journal Issue: 3; Journal ID: ISSN 1536-1055

- Publisher:
- American Nuclear Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Bayesian inference; equilibrium reconstruction

### Citation Formats

```
Cianciosa, Mark R., Hanson, James D., and Maurer, David A..
```*Uncertainty Analysis in 3D Equilibrium Reconstruction*. United States: N. p., 2018.
Web. doi:10.1080/15361055.2017.1392819.

```
Cianciosa, Mark R., Hanson, James D., & Maurer, David A..
```*Uncertainty Analysis in 3D Equilibrium Reconstruction*. United States. doi:10.1080/15361055.2017.1392819.

```
Cianciosa, Mark R., Hanson, James D., and Maurer, David A.. Wed .
"Uncertainty Analysis in 3D Equilibrium Reconstruction". United States.
doi:10.1080/15361055.2017.1392819.
```

```
@article{osti_1423072,
```

title = {Uncertainty Analysis in 3D Equilibrium Reconstruction},

author = {Cianciosa, Mark R. and Hanson, James D. and Maurer, David A.},

abstractNote = {Reconstruction is an inverse process where a parameter space is searched to locate a set of parameters with the highest probability of describing experimental observations. Due to systematic errors and uncertainty in experimental measurements, this optimal set of parameters will contain some associated uncertainty. This uncertainty in the optimal parameters leads to uncertainty in models derived using those parameters. V3FIT is a three-dimensional (3D) equilibrium reconstruction code that propagates uncertainty from the input signals, to the reconstructed parameters, and to the final model. Here in this paper, we describe the methods used to propagate uncertainty in V3FIT. Using the results of whole shot 3D equilibrium reconstruction of the Compact Toroidal Hybrid, this propagated uncertainty is validated against the random variation in the resulting parameters. Two different model parameterizations demonstrate how the uncertainty propagation can indicate the quality of a reconstruction. As a proxy for random sampling, the whole shot reconstruction results in a time interval that will be used to validate the propagated uncertainty from a single time slice.},

doi = {10.1080/15361055.2017.1392819},

journal = {Fusion Science and Technology},

number = 3,

volume = 73,

place = {United States},

year = {Wed Feb 21 00:00:00 EST 2018},

month = {Wed Feb 21 00:00:00 EST 2018}

}