# Investigation of advanced UQ for CRUD prediction with VIPRE.

## Abstract

This document summarizes the results from a level 3 milestone study within the CASL VUQ effort. It demonstrates the application of 'advanced UQ,' in particular dimension-adaptive p-refinement for polynomial chaos and stochastic collocation. The study calculates statistics for several quantities of interest that are indicators for the formation of CRUD (Chalk River unidentified deposit), which can lead to CIPS (CRUD induced power shift). Stochastic expansion methods are attractive methods for uncertainty quantification due to their fast convergence properties. For smooth functions (i.e., analytic, infinitely-differentiable) in L{sup 2} (i.e., possessing finite variance), exponential convergence rates can be obtained under order refinement for integrated statistical quantities of interest such as mean, variance, and probability. Two stochastic expansion methods are of interest: nonintrusive polynomial chaos expansion (PCE), which computes coefficients for a known basis of multivariate orthogonal polynomials, and stochastic collocation (SC), which forms multivariate interpolation polynomials for known coefficients. Within the DAKOTA project, recent research in stochastic expansion methods has focused on automated polynomial order refinement ('p-refinement') of expansions to support scalability to higher dimensional random input spaces [4, 3]. By preferentially refining only in the most important dimensions of the input space, the applicability of these methods can be extended frommore »

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Laboratories

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1029759

- Report Number(s):
- SAND2011-7193

TRN: US201201%%169

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ANISOTROPY; CALCITE; CONVERGENCE; DIMENSIONS; FORECASTING; INTERPOLATION; POLYNOMIALS; PROBABILITY; REFINING; ROUGHNESS; SIMULATION; STATISTICS

### Citation Formats

```
Eldred, Michael Scott.
```*Investigation of advanced UQ for CRUD prediction with VIPRE.*. United States: N. p., 2011.
Web. doi:10.2172/1029759.

```
Eldred, Michael Scott.
```*Investigation of advanced UQ for CRUD prediction with VIPRE.*. United States. doi:10.2172/1029759.

```
Eldred, Michael Scott. Thu .
"Investigation of advanced UQ for CRUD prediction with VIPRE.". United States. doi:10.2172/1029759. https://www.osti.gov/servlets/purl/1029759.
```

```
@article{osti_1029759,
```

title = {Investigation of advanced UQ for CRUD prediction with VIPRE.},

author = {Eldred, Michael Scott},

abstractNote = {This document summarizes the results from a level 3 milestone study within the CASL VUQ effort. It demonstrates the application of 'advanced UQ,' in particular dimension-adaptive p-refinement for polynomial chaos and stochastic collocation. The study calculates statistics for several quantities of interest that are indicators for the formation of CRUD (Chalk River unidentified deposit), which can lead to CIPS (CRUD induced power shift). Stochastic expansion methods are attractive methods for uncertainty quantification due to their fast convergence properties. For smooth functions (i.e., analytic, infinitely-differentiable) in L{sup 2} (i.e., possessing finite variance), exponential convergence rates can be obtained under order refinement for integrated statistical quantities of interest such as mean, variance, and probability. Two stochastic expansion methods are of interest: nonintrusive polynomial chaos expansion (PCE), which computes coefficients for a known basis of multivariate orthogonal polynomials, and stochastic collocation (SC), which forms multivariate interpolation polynomials for known coefficients. Within the DAKOTA project, recent research in stochastic expansion methods has focused on automated polynomial order refinement ('p-refinement') of expansions to support scalability to higher dimensional random input spaces [4, 3]. By preferentially refining only in the most important dimensions of the input space, the applicability of these methods can be extended from O(10{sup 0})-O(10{sup 1}) random variables to O(10{sup 2}) and beyond, depending on the degree of anisotropy (i.e., the extent to which randominput variables have differing degrees of influence on the statistical quantities of interest (QOIs)). Thus, the purpose of this study is to investigate the application of these adaptive stochastic expansion methods to the analysis of CRUD using the VIPRE simulation tools for two different plant models of differing random dimension, anisotropy, and smoothness.},

doi = {10.2172/1029759},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2011},

month = {9}

}