Uncertainty quantification and propagation with probability boxes

Duran-Vinuesa, L.,Cuervo, D. Korean Nuclear Society 2021 Nuclear Engineering and Technology Vol.53 No.8

In the last decade, the best estimate plus uncertainty methodologies in nuclear technology and nuclear power plant design have become a trending topic in the nuclear field. Since BEPU was allowed for licensing purposes by the most important regulator bodies, different uncertainty assessment methods have become popular, overall non-parametric methods. While non-parametric tolerance regions can be well stated and used in uncertainty quantification for licensing purposes, the propagation of the uncertainty through different codes (multi-scale, multiphysics) in cascade needs a better depiction of uncertainty than the one provided by the tolerance regions or a probability distribution. An alternative method based on the parametric or distributional probability boxes is used to perform uncertainty quantification and propagation regarding statistic uncertainty from one code to another. This method is sample-size independent and allows well-defined tolerance intervals for uncertainty quantification, manageable for uncertainty propagation. This work characterizes the distributional p-boxes behavior on uncertainty quantification and uncertainty propagation through nested random sampling.

On-the-Fly Estimation Strategy for Uncertainty Propagation in Two-Step Monte Carlo Calculation for Residual Radiation Analysis

Gi Young Han,Do Hyun Kim,신창호,김송현,서보균,선광민 한국원자력학회 2016 Nuclear Engineering and Technology Vol.48 No.3

In analyzing residual radiation, researchers generally use a two-step Monte Carlo (MC) simulation. The first step (MC1) simulates neutron transport, and the second step (MC2) transports the decay photons emitted from the activated materials. In this process, the stochastic uncertainty estimated by the MC2 appears only as a final result, but it is underestimated because the stochastic error generated in MC1 cannot be directly included in MC2. Hence, estimating the true stochastic uncertainty requires quantifying the propagation degree of the stochastic error in MC1. The brute force technique is a straightforward method to estimate the true uncertainty. However, it is a costly method to obtain reliable results. Another method, called the adjoint-based method, can reduce the computational time needed to evaluate the true uncertainty; however, there are limitations. To address those limitations, we propose a new strategy to estimate uncertainty propagation without any additional calculations in two-step MC simulations. To verify the proposed method, we applied it to activation benchmark problems and compared the results with those of previous methods. The results show that the proposed method increases the applicability and user-friendliness preserving accuracy in quantifying uncertainty propagation. We expect that the proposed strategy will contribute to efficient and accurate two-step MC calculations.

Maximum Entropy를 이용한 정량적 레이더 강우추정 불확실성 분석

이재경(Jae-Kyoung Lee) 한국기상학회 2015 대기 Vol.25 No.3

Existing studies on radar rainfall uncertainties were performed to reduce the uncertainty for each stage by using bias correction during the quantitative radar rainfall estimation process. However, the studies do not provide quantitative comparison with the uncertainties for all stages. Consequently, this study proposes a suitable approach that can quantify the uncertainties at each stage of the quantitative radar rainfall estimation process. First, the new approach can present initial and final uncertainties, increasing or decreasing the uncertainty, and the uncertainty percentage at each stage. Furthermore, Maximum Entropy (ME) was applied to quantify the uncertainty in the entire process. Second, for the uncertainty quantification of radar rainfall estimation at each stage, this study used two quality control algorithms, two rainfall estimation relations, and two bias correction techniques as post-processing and progressed through all stages of the radar rainfall estimation. For the proposed approach, the final uncertainty (ME = 3.81) from the ME of the bias correction stage was the smallest while the uncertainty of the rainfall estimation stage was higher because of the use of an unsuitable relation. Additionally, the ME of the quality control was at 4.28 (112.34%), while that of the rainfall estimation was at 4.53 (118.90%), and that of the bias correction at 3.81 (100%). However, this study also determined that selecting the appropriate method for each stage would gradually reduce the uncertainty at each stage. Finally, the uncertainty due to natural variability was 93.70% of the final uncertainty. Thus, the results indicate that this new approach can contribute significantly to the field of uncertainty estimation and help with estimating more accurate radar rainfall.

Comparative Evaluation of Probabilistic Uncertainty-Propagations to Seismic Collapse Capacity of Low-Rise Steel Moment-Resisting Frames

Dong-Hyeon Shin,양원직,김형준 한국강구조학회 2016 International Journal of Steel Structures Vol.16 No.3

The collapse capacity of a structure employing hysteretic energy dissipating devices (HEDDs) is considerably influenced by the uncertainties which are categorized to the aleatory and epistemic uncertainties. This study aims to comparatively evaluate uncertainty-propagations to the seismic collapse performance of the low-rise steel moment-resisting frames (SMRFs) with and without HEDDs, and to investigate on the effects of HEDDs to the failure modes of damped structures when the uncertainties are collectively propagated to the seismic response. In order to achieve this, incremental dynamic analyses are carried out to assess the collapse capacities of typical low-rise SMRFs with and without HEDDs. The Monte-Carlo simulation adopting a Latin hypercube sampling method is then performed to reflect the probabilistic uncertainty-propagation to the collapse capacities of structures. The analysis results show that the collapse capacities of low-rise SMRFs are considerably changed due to the uncertainty-propagation and HEDDs decrease the uncertainty-propagation to the collapse capacities of low-rise SMRFs because they induces a constant collapse mode with relatively low variation.

Simplifi ed Estimation Method for Collective Uncertainty-Propagations of Hysteretic Energy Dissipating Device’s Properties

신동현,김형준 한국강구조학회 2018 International Journal of Steel Structures Vol.18 No.5

Hysteretic energy dissipating devices (HEDDs) have been increasingly applied to building construction to improve the seismic performance. The seismic responses of such damped structures are signifi cantly aff ected by HEDD’s structural properties. An accurate investigation on the propagation of HEDD’s structural properties is required for reasonable evaluation of the seismic performance of a structure. This study aims to develop simplifi ed methods that can estimate the collective uncertainty-propagation to the seismic response of damped structures employing HEDDs. To achieve this, three- and six-story steel moment-resisting frames were selected and the propagations of the individual HEDD’s property-uncertainties were evaluated when they are subjected to various levels of seismic demand. Based on the result of individual uncertainty-propagations, a simplifi ed method is proposed to evaluate the variation of seismic response collectively propagated by HEDD’s property-uncertainties and is verifi ed by comparing with the exact collective uncertainty-propagation calculated using the Monte Carlo simulation method. The proposed method, called as a modifi ed SRSS method in this study, is established from a conventional square root of the sum of the squares (SRSS) method with the relative contributions of the individual HEDD’s property-uncertainty propagations. This study shows that the modifi ed SRSS method provides a better estimation than the conventional SRSS method and can signifi cantly reduce computational time with reasonable accuracy compared with the Monte Carlo simulation method.

Application case for phase III of UAM-LWR benchmark: Uncertainty propagation of thermal-hydraulic macroscopic parameters

Mesado C.,Miró R.,Verdú G. 한국원자력학회 2020 Nuclear Engineering and Technology Vol.52 No.8

This work covers an important point of the benchmark released by the expert group on Uncertainty Analysis in Modeling of Light Water Reactors. This ambitious benchmark aims to determine the uncertainty in light water reactors systems and processes in all stages of calculation, with emphasis on multiphysics (coupled) and multi-scale simulations. The Gesellschaft für Anlagen und Reaktorsicherheit methodology is used to propagate the thermal-hydraulic uncertainty of macroscopic parameters through TRACE5.0p3/PARCSv3.0 coupled code. The main innovative points achieved in this work are i) a new thermal-hydraulic model is developed with a highly-accurate 3D core discretization plus an iterative process is presented to adjust the 3D bypass flow, ii) a control rod insertion occurrence ewhich data is obtained from a real PWR teste is used as a transient simulation, iii) two approaches are used for the propagation process: maximum response where the uncertainty and sensitivity analysis is performed for the maximum absolute response and index dependent where the uncertainty and sensitivity analysis is performed at each time step, and iv) RESTING MATLAB code is developed to automate the model generation process and, then, propagate the thermal-hydraulic uncertainty. The input uncertainty information is found in related literature or, if not found, defined based on expert judgment. This paper, first, presents the Gesellschaft für Anlagen und Reaktorsicherheit methodology to propagate the uncertainty in thermalhydraulic macroscopic parameters and, then, shows the results when the methodology is applied to a PWR reactor

Preliminary Research on the Uncertainty Estimation in the Probabilistic Designs

Youn Byung D.,Lee Jae-Hwan The Society of Naval Architects of Korea 2005 Journal of ship and ocean technology Vol.9 No.1

In probabilistic design, the challenge is to estimate the uncertainty propagation, since outputs of subsystems at lower levels could constitute inputs of other systems or at higher levels of the multilevel systems. Three uncertainty propagation estimation techniques are compared in this paper in terms of numerical efficiency and accuracy: root sum square (linearization), distribution-based moment approximation, and Taguchi-based integration. When applied to reliability-based design optimization (RBDO) under uncertainty, it is investigated which type of applications each method is best suitable for. Two nonlinear analytical examples and one vehicle crashworthiness for side-impact simulation example are employed to investigate the unique features of the presented techniques for uncertainty propagation. This study aims at helping potential users to identify appropriate techniques for their applications in the multilevel design.

A Formal Guidance for Handling Different Uncertainty Sources Employed in the Level 2 PSA

Ahn Kwang-Il,Yang Joon-Eon,Ha Jae-Joo Korean Nuclear Society 2004 Nuclear Engineering and Technology Vol.36 No.1

The methodological framework of the Level 2 PSA appears to be currently standardized in a formalized fashion, but there have been different opinions on the way the sources of uncertainty are characterized and treated. This is primarily because the Level 2 PSA deals with complex phenomenological processes that are deterministic in nature rather than random processes, and there are no probabilistic models characterizing them clearly. As a result, the probabilistic quantification of the Level 2 PSA CET / APET is often subjected to two sources of uncertainty: (a) incomplete modeling of accident pathways or different predictions for the behavior of phenomenological events and (b) expert-to-expert variation in estimating the occurrence probability of phenomenological events. While a clear definition of the two sources of uncertainty involved in the Level 2 PSA makes it possible to treat an uncertainty in a consistent manner, careless application of these different sources of uncertainty may produce different conclusions in the decision-making process. The primary purpose of this paper is to characterize typical sources of uncertainty that would often be addressed in the Level 2 PSA and to provide a formal guidance for quantifying their impacts on the PSA Level 2 risk results. An additional purpose of this paper is to give a formal approach on how to combine random uncertainties addressed in the Level 1 PSA with subjectivistic uncertainties addressed in the Level 2 PSA.

PROPAGATION OF NUCLEAR DATA UNCERTAINTIES FOR PWR CORE ANALYSIS

Cabellos, O.,Castro, E.,Ahnert, C.,Holgado, C. Korean Nuclear Society 2014 Nuclear Engineering and Technology Vol.46 No.3

An uncertainty propagation methodology based on the Monte Carlo method is applied to PWR nuclear design analysis to assess the impact of nuclear data uncertainties. The importance of the nuclear data uncertainties for $^{235,238}U$, $^{239}Pu$, and the thermal scattering library for hydrogen in water is analyzed. This uncertainty analysis is compared with the design and acceptance criteria to assure the adequacy of bounding estimates in safety margins.

Propagation of Nuclear Data Uncertainties for PWR Core Analysis

O. CABELLOS,E. CASTRO,C. AHNERT,C. HOLGADO 한국원자력학회 2014 Nuclear Engineering and Technology Vol.46 No.3

An uncertainty propagation methodology based on the Monte Carlo method is applied to PWR nuclear design analysis toassess the impact of nuclear data uncertainties. The importance of the nuclear data uncertainties for 235,238U, 239Pu, and thethermal scattering library for hydrogen in water is analyzed. This uncertainty analysis is compared with the design andacceptance criteria to assure the adequacy of bounding estimates in safety margins.