scholarly journals Basic Framework and Main Methods of Uncertainty Quantification

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Juan Zhang ◽  
Junping Yin ◽  
Ruili Wang
Keyword(s):  
Sensitivity Analysis ◽  
Bayesian Inference ◽  
Uncertainty Quantification ◽  
Model Uncertainty ◽  
Model Calibration ◽  
Uncertainty Propagation ◽  
Propagation Model ◽  
Practical Significance ◽  
The Core ◽  
Basic Framework

Since 2000, the research of uncertainty quantification (UQ) has been successfully applied in many fields and has been highly valued and strongly supported by academia and industry. This review firstly discusses the sources and the types of uncertainties and gives an overall discussion on the goal, practical significance, and basic framework of the research of UQ. Then, the core ideas and typical methods of several important UQ processes are introduced, including sensitivity analysis, uncertainty propagation, model calibration, Bayesian inference, experimental design, surrogate model, and model uncertainty analysis.

Multiscale Variability and Uncertainty Quantification Based on a Generalized Multiscale Markov Model

2010 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Probability Theory ◽  
Bayesian Inference ◽  
Markov Model ◽  
Uncertainty Quantification ◽  
System Analysis ◽  
Scale Validation ◽  
Uncertainty Propagation ◽  
Bayes Rule ◽  
Imprecise Probability ◽  
Modal Extension

Variability is inherent randomness in systems, whereas uncertainty is due to lack of knowledge. In this paper, a generalized multiscale Markov (GMM) model is proposed to quantify variability and uncertainty simultaneously in multiscale system analysis. The GMM model is based on a new imprecise probability theory that has the form of generalized interval, which is a Kaucher or modal extension of classical set-based intervals to represent uncertainties. The properties of the new definitions of independence and Bayesian inference are studied. Based on a new Bayes’ rule with generalized intervals, three cross-scale validation approaches that incorporate variability and uncertainty propagation are also developed.

scholarly journals BETA EFFECTIVE SENSITIVITY TO NUCLEAR DATA WITHIN THE APOLLO3® NEUTRONIC PLATFORM

2021 ◽  
Vol 247 ◽  
pp. 15003
Author(s):  
G. Valocchi ◽  
P. Archier ◽  
J. Tommasi
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Uncertainty Propagation ◽  
Direct Calculation ◽  
Nuclear Data ◽  
The Core ◽  
Nuclear Data Library ◽  
Lattice Core ◽  
Effective Sensitivity ◽  
Data Library

In this paper, we present a sensitivity analysis of the beta effective to nuclear data for the UM17x17 experiment that has been performed in the EOLE reactor. This work is carried out using the APOLLO3® platform. Regarding the flux calculation, the standard two-step approach (lattice/core) is used. For what concerns the delayed nuclear data, they are processed to be directly used in the core calculation without going through the lattice one. We use the JEFF-3.1.1 nuclear data library for cross-sections and delayed data. The calculation of k-effective and beta effective is validated against a TRIPOLI4® one while the main sensitivities are validated against direct calculation. Finally, uncertainty propagation is performed using the COMAC-V2.0 covariance library.

A Spatial-Random-Process Based Multidisciplinary System Uncertainty Propagation Approach With Model Uncertainty

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Zhen Jiang ◽  
Wei Li ◽  
Daniel W. Apley ◽  
Wei Chen
Keyword(s):  
Uncertainty Quantification ◽  
Random Process ◽  
Model Uncertainty ◽  
Electronic Packaging ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Statistical Moments ◽  
Robust Design Optimization ◽  
System Uncertainty ◽  
Multidisciplinary System

The performance of a multidisciplinary system is inevitably affected by various sources of uncertainties, usually categorized as aleatory (e.g., input variability) or epistemic (e.g., model uncertainty) uncertainty. In the framework of design under uncertainty, all sources of uncertainties should be aggregated to assess the uncertainty of system quantities of interest (QOIs). In a multidisciplinary design system, uncertainty propagation (UP) refers to the analysis that quantifies the overall uncertainty of system QOIs resulting from all sources of aleatory and epistemic uncertainty originating in the individual disciplines. However, due to the complexity of multidisciplinary simulation, especially the coupling relationships between individual disciplines, many UP approaches in the existing literature only consider aleatory uncertainty and ignore the impact of epistemic uncertainty. In this paper, we address the issue of efficient uncertainty quantification of system QOIs considering both aleatory and epistemic uncertainties. We propose a spatial-random-process (SRP) based multidisciplinary uncertainty analysis (MUA) method that, subsequent to SRP-based disciplinary model uncertainty quantification, fully utilizes the structure of SRP emulators and leads to compact analytical formulas for assessing statistical moments of uncertain QOIs. The proposed method is applied to a benchmark electronic packaging design problem. The estimated low-order statistical moments of the QOIs are compared to the results from Monte Carlo simulations (MCSs) to demonstrate the effectiveness of the method. The UP result is then used to facilitate the robust design optimization of the electronic packaging system.

A System Uncertainty Propagation Approach With Model Uncertainty Quantification in Multidisciplinary Design

2014 ◽  
Author(s):  
Zhen Jiang ◽  
Wei Li ◽  
Daniel W. Apley ◽  
Wei Chen
Keyword(s):  
Uncertainty Quantification ◽  
Model Uncertainty ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Statistical Moments ◽  
Multidisciplinary Design ◽  
Design System ◽  
System Uncertainty ◽  
The Impact ◽  
Multidisciplinary System

The performance of a multidisciplinary system is inevitably affected by various sources of uncertainties, usually categorized as aleatory (e.g. input variability) or epistemic (e.g. model uncertainty) uncertainty. In the framework of design under uncertainty, all sources of uncertainties should be aggregated to assess the uncertainty of system quantities of interest (QOIs). In a multidisciplinary design system, uncertainty propagation refers to the analysis that quantifies the overall uncertainty of system QOIs resulting from all sources of aleatory and epistemic uncertainty originating in the individual disciplines. However, due to the complexity of multidisciplinary simulation, especially the coupling relationships between individual disciplines, many uncertainty propagation approaches in the existing literature only consider aleatory uncertainty and ignore the impact of epistemic uncertainty. In this paper, we address the issue of efficient uncertainty quantification of system QOIs considering both aleatory and epistemic uncertainties. We propose a spatial-random-process (SRP) based multidisciplinary uncertainty analysis (MUA) method that, subsequent to SRP-based disciplinary model uncertainty quantification, fully utilizes the structure of SRP emulators and leads to compact analytical formulas for assessing statistical moments of uncertain QOIs. The proposed method is applied to a benchmark electronics packaging problem. To demonstrate the effectiveness of the method, the estimated low-order statistical moments of the QOIs are compared to the results from Monte Carlo simulations.

scholarly journals Best-Estimate Plus Uncertainty Framework for Multiscale, Multiphysics Light Water Reactor Core Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Jason Hou ◽  
Maria Avramova ◽  
Kostadin Ivanov
Keyword(s):  
Uncertainty Quantification ◽  
Phase Ii ◽  
Uncertainty Propagation ◽  
Nuclear Data ◽  
Light Water Reactor ◽  
Phase Iii ◽  
Core Analysis ◽  
Light Water ◽  
The Core ◽  
Phase Phase

Tremendous work has been done in the Light Water Reactor (LWR) Modelling and Simulation (M&S) uncertainty quantification (UQ) within the framework of the Organization for Economic Cooperation and Development (OECD)/Nuclear Energy Agency (NEA) LWR Uncertainty Analysis in Modelling (UAM) benchmark, which aims to investigate the uncertainty propagation in all M&S stages of the LWRs and to guide uncertainty and sensitivity analysis methodology development. The Best-Estimate Plus Uncertainty (BEPU) methodologies have been developed and implemented within the framework of the LWR UAM benchmark to provide a realistic predictive simulation capability without compromising the safety margins. This paper describes the current status of the methodological development, assessment, and integration of the BEPU methodology to facilitate the multiscale, multiphysics LWR core analysis. The comparative analysis of the results in the stand-alone multiscale neutronics phase (Phase I) is first reported for understanding the general trend of the uncertainty of core parameters due to the nuclear data uncertainty. It was found that the predicted uncertainty of the system eigenvalue is highly dependent on the choice of the covariance libraries used in the UQ process and is less sensitive to the solution method, nuclear data library, and UQ method. High-to-Low (Hi2Lo) model information approaches for multiscale M&S are introduced for the core single physics phase (Phase II). In this phase, the other physics (fuel and moderator), providing feedback to neutronics M&S in a LWR core, and time-dependent phenomena are considered. Phase II is focused on uncertainty propagation in single physics models which are components of the LWR core coupled multiphysics calculations. The paper discusses the link and interactions between Phase II to the multiphysics core and system phase (Phase III), that is, the link between uncertainty propagation in single physics on local scale and multiphysics uncertainty propagation on the core scale. Particularly, the consistency in uncertainty assessment between higher-fidelity models implemented in fuel performance codes and the rather simplified models implemented in thermal-hydraulics codes, to be used for coupling with neutronics in Phase III is presented. Similarly, the uncertainty quantification on thermal-hydraulic models is established on a relatively small scale, while these results will be used in Phase III at the core scale, sometimes with different codes or models. Lastly, the up-to-date UQ method for the coupled multiphysics core calculation in Phase III is presented, focusing on the core equilibrium cycle depletion calculation with associated uncertainties.

Sensitivity Analysis and Selection of Check Index of Signal Intersection Simulation Model Based on VISSIM

2019 ◽  
Vol 2 (5) ◽  
Author(s):  
Mengda Zhang ◽  
Chenjing Zhou ◽  
Tian-tian Zhang ◽  
Yan Han
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Model ◽  
Optimal Process ◽  
Parameter Calibration ◽  
Index Set ◽  
The Core ◽  
Core Module ◽  
Simulation Parameter ◽  
Simulation Parameters ◽  
Selection Of

Selecting check index quantitatively is the core of the calibration of micro traffic simulation parameters at signal intersection. Five indexes in the node (intersection) module of VISSIM were selected as the check index set. Twelve simulation parameters in the core module were selected as the simulation parameters set. Optimal process of parameter calibration was proposed and model of the intersection of Huangcun west street and Xinghua street in Beijing was built in VISSIM to verify it. The sensitivity analysis between each check index and simulation parameter in their own set was conducted respectively. Sensitive parameter sets of different check indices were obtained and compared. The results show that different indexes have different size of set, and average vehicle delay's is maximum, so it's necessary to select index quantitatively. The results can provide references for scientific selection of the check indexes and improve the study efficiency of parameter calibration.

Sensitivity analysis of sandwich beams and plates accounting for variable support conditions

2013 ◽  
Vol 61 (1) ◽  
pp. 201-210 ◽  
Author(s):  
R. Studziński ◽  
Z. Pozorski ◽  
A. Garstecki
Keyword(s):  
Sensitivity Analysis ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Practical Applications ◽  
The Core ◽  
State Of Stress ◽  
Thin Steel ◽  
Influence Of Temperature On ◽  
Support Conditions ◽  
Variable Support

Abstract The paper addresses the problems of the sensitivity analysis and optimal design of multi-span sandwich panels with a soft core and flat thin steel facings. The response functional is formulated in a general form allowing wide practical applications. Sensitivity gradients of this functional with respect to dimensional, material and support parameters are derived using adjoint variable method. These operators account for the jump of the slope of a Timoshenko beam or a Reissner plate at the position of concentrated active load or reaction, thus extending the sensitivity operators known in literature. The jump of slope is the effect of shear deformation of the core. Special attention is focussed on sensitivity and optimisation allowing for variable support position and stiffness, because local phenomena observed in supporting area of sandwich plates often initiate failure mechanisms. Introducing optimally located elastic supports allows to reduce the unfavourable influence of temperature on the state of stress. Several examples illustrate the application of derived sensitivity operators and demonstrate their exactness

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