# An EPGPT-based approach for uncertainty quantification

## Abstract

Generalized Perturbation Theory (GPT) has been widely used by many scientific disciplines to perform sensitivity analysis and uncertainty quantification. This manuscript employs recent developments in GPT theory, collectively referred to as Exact-to-Precision Generalized Perturbation Theory (EPGPT), to enable uncertainty quantification for computationally challenging models, e.g. nonlinear models associated with many input parameters and many output responses and with general non-Gaussian parameters distributions. The core difference between EPGPT and existing GPT is in the way the problem is formulated. GPT formulates an adjoint problem that is dependent on the response of interest. It tries to capture via the adjoint solution the relationship between the response of interest and the constraints on the state variations. EPGPT recasts the problem in terms of a smaller set of what is referred to as the 'active' responses which are solely dependent on the physics model and the boundary and initial conditions rather than on the responses of interest. The objective of this work is to apply an EPGPT methodology to propagate cross-sections variations in typical reactor design calculations. The goal is to illustrate its use and the associated impact for situations where the typical Gaussian assumption for parameters uncertainties is not valid and when nonlinearmore »

- Authors:

- Dept. of Nuclear Engineering, North Caroline State Univ., Raleigh, NC 27695 (United States)

- Publication Date:

- Research Org.:
- American Nuclear Society, Inc., 555 N. Kensington Avenue, La Grange Park, Illinois 60526 (United States)

- OSTI Identifier:
- 22105785

- Resource Type:
- Conference

- Resource Relation:
- Conference: PHYSOR 2012: Conference on Advances in Reactor Physics - Linking Research, Industry, and Education, Knoxville, TN (United States), 15-20 Apr 2012; Other Information: Country of input: France; 18 refs.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; ALGORITHMS; COMPUTERIZED SIMULATION; CROSS SECTIONS; DATA COVARIANCES; DESIGN; NONLINEAR PROBLEMS; PERTURBATION THEORY; REACTOR CORES; SENSITIVITY ANALYSIS; VARIATIONS

### Citation Formats

```
Wang, C., and Abdel-Khalik, H. S.
```*An EPGPT-based approach for uncertainty quantification*. United States: N. p., 2012.
Web.

```
Wang, C., & Abdel-Khalik, H. S.
```*An EPGPT-based approach for uncertainty quantification*. United States.

```
Wang, C., and Abdel-Khalik, H. S. Sun .
"An EPGPT-based approach for uncertainty quantification". United States.
```

```
@article{osti_22105785,
```

title = {An EPGPT-based approach for uncertainty quantification},

author = {Wang, C. and Abdel-Khalik, H. S.},

abstractNote = {Generalized Perturbation Theory (GPT) has been widely used by many scientific disciplines to perform sensitivity analysis and uncertainty quantification. This manuscript employs recent developments in GPT theory, collectively referred to as Exact-to-Precision Generalized Perturbation Theory (EPGPT), to enable uncertainty quantification for computationally challenging models, e.g. nonlinear models associated with many input parameters and many output responses and with general non-Gaussian parameters distributions. The core difference between EPGPT and existing GPT is in the way the problem is formulated. GPT formulates an adjoint problem that is dependent on the response of interest. It tries to capture via the adjoint solution the relationship between the response of interest and the constraints on the state variations. EPGPT recasts the problem in terms of a smaller set of what is referred to as the 'active' responses which are solely dependent on the physics model and the boundary and initial conditions rather than on the responses of interest. The objective of this work is to apply an EPGPT methodology to propagate cross-sections variations in typical reactor design calculations. The goal is to illustrate its use and the associated impact for situations where the typical Gaussian assumption for parameters uncertainties is not valid and when nonlinear behavior must be considered. To allow this demonstration, exaggerated variations will be employed to stimulate nonlinear behavior in simple prototypical neutronics models. (authors)},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {7}

}