To establish confidence in the results of computerized physics models, a key regulatory requirement is to develop a scientifically defendable process. The methods employed for confidence, characterization, and consolidation, or C³, are statistically involved and are often accessible only to avid statisticians. This manuscript serves as a pedagogical presentation of the C³ process to all stakeholders—including researchers, industrial practitioners, and regulators—to impart an intuitive understanding of the key concepts and mathematical methods entailed by C³. The primary focus is on calculation of tolerance limits, which is the overall goal of the C³ process. Tolerance limits encode the confidence in the calculation results as communicated to the regulator. Understanding the C³ process is especially critical today, as the nuclear industry is considering more innovative ways to assess new technologies, including new reactor and fuel concepts, via an integrated approach that optimally combines modeling and simulation and minimal targeted validation experiments. This manuscript employs intuitive, analytical, numerical, and visual representations to explain how tolerance limits may be calculated for a wide range of configurations, and it also describes how their values may be interpreted. Various verification tests have been developed to test the calculated tolerance limits and to help delineate their values. The manuscript demonstrates the calculation of tolerance limits for TSURFER, a computer code developed by the Oak Ridge National Laboratory for criticality safety applications. The goal is to evaluate the tolerance limit for TSURFER-determined criticality biases to support the determination of upper, subcritical limits for regulatory purposes.

The current regulatory process allows for the use of models employing realistic assumptions as opposed to conservative bounding approaches, requiring a concerted use of best-estimate modeling and comprehensive estimation of uncertainties, collectively referred to as best-estimate-plus-uncertainty methods. This necessitates access to an integrated and automated procedure for the propagation and understanding of key sources of uncertainties. Focusing on neutronic reactor core simulation, this paper lays the theoretical foundations for an uncertainty characterization framework that is comprehensive, informative, and efficient, implying its ability to propagate all sources of uncertainties and identify key contributors in a computationally efficient manner. This paper represents the overarching objective of our work to propagate multigroup (MG) cross section uncertainties through lattice physics calculations and core-wide simulation. This requires the evaluation of few-group parameters uncertainties in terms of a wide range of local conditions, e.g., burnup, fuel temperature, etc., which results in a very high dimensional uncertainty space. The first strategy employed to compress the few-group uncertainties is the physics-guided coverage mapping (PCM) methodology developed to assess the similarity between the branch and base uncertainties in lattice calculation. To further compress the uncertainty propagated, this paper employs an accuracy-preserving reduced order modeling (ROM) technique relying on the use of range finding algorithms to construct all few-group parameters variations to a very small preset tolerance. In a separate cosubmitted paper, this framework is demonstrated to thermal reactors including both light and heavy water systems using a number of computer codes, including NESTLE-C, SERPENT, SCALE's NEWT, and SAMPLER codes.

Uncertainty quantification has been recognized by the community as an essential component of best-estimate reactor analysis simulation because it provides a measure by which the credibility of the simulation can be assessed. In a companion paper, a framework for the propagation of nuclear data uncertainties from the multigroup level through lattice physics and core calculations and ultimately to core responses of interest has been developed. The overarching goal of this framework is to automate the propagation, prioritization, mapping, and reduction of uncertainties for reactor analysis core simulation. This paper employs both heavy and light water reactor systems to exemplify the application of this framework. Specifically, the paper is limited to the propagation of the nuclear data starting with the multigroup cross section covariance matrix and down to core responses, e.g., eigenvalue and power distribution, in steady-state core wide calculations. The goal is to demonstrate how the framework employs reduction techniques to compress the uncertainty space into a very small number of active degrees-of-freedom (DOFs), which renders the overall process computationally feasible for day-to-day engineering evaluations.

This paper reports on the development and testing of a comprehensive few-group cross section input uncertainty library for the NESTLE-C nodal diffusion-based nuclear reactor core simulator. This library represents the first milestone of a first-of-a-kind framework for the integrated characterization of uncertainties in steady-state and transient CANDU reactor simulations. The objective of this framework is to propagate, prioritize and devise a mapping capability for uncertainties in support of model validation of best-estimate calculations. A complete framework would factor both input and modeling uncertainty contributions. The scope of the present work is limited to the propagation of multi-group cross-section uncertainties through lattice physics calculations down to the few-group format, representing the input to the NESTLE-C core simulator, and finally to core responses of interest.