Doctoral Dissertations

Date of Award

12-1998

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Nuclear Engineering

Major Professor

Laurence F. Miller

Committee Members

James S. Bogard, Peter G. Groer, Rafael B. Perez, Lawrence W. Townsend

Abstract

The purpose of this research is to improve the computational efficiency of the Limit State method for uncertainty analysis. The viability of using the improved Limit State method with radiological and environmental assessment computer codes is investigated. The uncertainty results are compared against that obtained using Monte Carlo methods.

There are several methods available for evaluating uncertainty using the probability-distribution approach. Of these methods, the more common approaches are to use response surface analysis, differential analysis, and Monte Carlo. The Limit State method has been introduced as an alternative approach for performing uncertainty analysis. One of the problems encountered with the Limit State method is the efficient generation of a Limit State function (approximating function) for computer codes that are implicit.

In this research, automatic differentiation is utilized to improve the computational efficiency of the Limit State method. An iteration routine based on automatic differentiation can also be used to obtain more accurate results with a first order function. A groundwater pollutant transport model was selected to test the efficiency improvements to the Limit State method.

Cumulative Distribution Functions (CDF) of groundwater transport test cases using Limit State were generated. These CDFs required approximately 20 computer model runs. These CDFs are more accurate than the CDFs generated using 50 runs from Latin Hypercube sampling. The Limit State CDFs compare favorably with the CDFs generated using 100, and 500 Latin Hypercube samples. A CDF computed using 10,000 Monte Carlo runs is used as the benchmark for accuracy. The computational efficiency of the automatic differentiation approach for Limit State uncertainty analysis was compared with that using conventional numerical differentiation schemes (for computing sensitivities). Computer time savings on the order of a factor of ten can be realized using the improved Limit State approach. Automatic differentiation requires a precompilation step, which requires some effort. However, the Monte Carlo method requires large amounts of data handling, which is time consuming as well.

This research shows that the Limit State method, augmented with automatic differentiation, is a viable approach for efficiently performing uncertainty analysis of computationally intensive computer models.

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