Uncertainty Qualification Research Articles

Use of forward sensitivity analysis method to improve code scaling, applicability, and uncertainty (CSAU) methodology

Abstract Since the code scaling, applicability, and uncertainty (CSAU) methodology was proposed about two decades ago, it has been widely used for new reactor designs and existing LWRs power uprates. In spite of these huge successes, CSAU has been criticized for the need of further improvement, focusing on two main issues – lack of objectiveness and high cost. With the effort to develop next generation safety analysis codes, new opportunities appear to take advantage of new numerical methods, better physical models, and modern uncertainty qualification methods. Forward sensitivity (FS) analysis directly solves the partial differential equations for parameter sensitivities. Moreover, our work shows that time and space steps can be treated as special sensitivity parameters so that numerical errors can be directly compared with physical uncertainties. It should be noted that FS analysis is an intrusive uncertainty quantification method that requires the user of the method to be familiar with the simulation code structure including numerical spatial and temporal integration techniques. When the FS analysis is implemented in a new advanced system analysis code, CSAU could be significantly improved by quantifying numerical errors and allowing a quantitative PIRT (Q-PIRT) to reduce subjective judgment and improve efficiency. This paper will review the issues related to the current CSAU implementations, introduce FS analysis, show a simple example to perform FS analysis, and discuss potential improvements on CSAU with FS analysis. Finally, the general research direction and requirements to use FS analysis in an advanced system analysis code will be discussed.

Application of multiscale finite element method in the uncertainty qualification of large-scale groundwater flow

In this article, we discuss the application of multiscale finite element method (MsFEM) to groundwater flow in heterogeneous porous media. We investigate the ability of MsFEM in qualifying the flow uncertainty. Monte Carlo simulation is employed to implement the stochastic analysis, and MsFEM is used to avoid a full resolution to the spatial variable conductivity field. Large-scale flow with high variability is investigated by inspecting the single realization as well as the probability distribution functions of head and velocity. The numerical results show that the performance of MsFEM depends on the ratio between the correlation length and the coarse element size. An accurate prediction to the velocity requires a much lower ratio than the head. The MsFEM has different convergence rates for the head and the velocity, while the convergence rates do not deteriorate as the variance grows.

Evaluating the uncertainty of Darcy velocity with sparse grid collocation method

Spatial variability of Darcy velocity is presented due to the heterogeneity of aquifer parameters. The uncertainty qualification of velocity suffers great challenge in the complex porous media. This work focuses on the use of sparse grid collocation method in velocity simulation. Since the sparse grid collocation method provides a non-intrusive way to incorporate any existing deterministic solver, the mixed finite element method is combined as the deterministic solver to retain the local continuity of Darcy velocity. We decompose the error of the velocity into three components, and illustrate that the Karhunen-Loeve truncation brings more error into velocity approximation than into head. The convergence properties of velocity moments restrict the application of sparse grid collocation method in the problems with small correlation lengths. This work provides insights towards the application of sparse grid collocation method to velocity modeling. It is demonstrated that for which problems the sparse grid collocation method is expected to be competitive with the Monte Carlo simulation. Further work about the anisotropic sparse grid collocation method should be extended to circumvent the obstacle of dimensionality.

The Measurement of Real-Asset Determinants of Systematic Risk and the Likelihood of Receipt of Uncertainty Qualifications1

The findings of prior research have been inconsistent about the use of systematic risk (beta) as a surrogate for those aspects of the audit environment related to the likelihood of an uncertainty qualification. The purpose of this study is to refine the theoretical framework and measurement issues of this topic through an examination of the association between two real-asset determinants of systematic risk (the degree of operating leverage and the degree of financial leverage) and the likelihood of receipt of an uncertainty qualification. The results indicate that these two leverage measures are not significantly associated with the receipt of uncertainty qualifications in auditing practice.