scholarly journals A methodology for performing sensitivity analysis in dynamic fuel cycle simulation studies applied to a PWR fleet simulated with the CLASS tool

2018 ◽  
Vol 4 ◽  
pp. 13 ◽  
Author(s):  
Nicolas Thiollière ◽  
Jean-Baptiste Clavel ◽  
Fanny Courtin ◽  
Xavier Doligez ◽  
Marc Ernoult ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Fuel Cycle ◽  
Minor Actinide ◽  
Cycle Simulation ◽  
Mox Fuel ◽  
Sensitivity Indices ◽  
Standard Scenario ◽  
Plutonium Production ◽  
Input Variables ◽  
Scenario Study

Fuel cycle simulators are used worldwide to provide scientific assessment to fuel cycle future strategies. Those tools help understanding the fuel cycle physics and determining the most impacting drivers at the cycle scale. A standard scenario calculation is usually based on a set of operational assumptions, such as reactor Burn-Up, deployment history, cooling time, etc. Scenario output is then the evolution of isotopes mass in the facilities that composes the nuclear fleet. The increase of computing capacities and the use of neutron data fast predictors provide new opportunities in nuclear scenario studies. Indeed, a very high number of calculations is possible, which allows testing a high number of operational assumptions combinations. The global sensitivity analysis (GSA) formalism is specifically well adapted for this kind of problem. In this new framework, a scenario study is based on the sampling of operational data, which become input variables. A first result of a scenario study is the highlight of relations between operational input data and outputs. Input variable subspace that satisfy optimization criteria on an output, such as plutonium incineration or stabilization, can also be determined. In this paper, a focus is made on the methodology based on GSA. This innovative methodology is presented and applied to a simple fleet simulation composed of a PWR-UOx fuel and a PWR-MOx fuel. Calculations are done with the fuel cycle simulator CLASS developed by the CNRS/IN2P3 in collaboration with IRSN. The design of experiment is built from five fuel cycle input sampled variables. Sensitivity indices have been calculated on plutonium and minor actinide (MA) production. It shows that the PWR-UOx Burn-Up and the fraction of PWR-MOx fuel are the most important input variables that explain the plutonium production. For the MA production, main drivers depend strongly on isotopes. Sensitivity analysis also reveals input variable subspace responsible of simulation crash, what led to an important improvement of the model algorithms. An equilibrium condition on the plutonium mass in the stockpile used for building MOx fuel has been applied. The solution is represented as a subspace in the PWR-UOx Burn-Up and PWR-MOx fraction input space. For instance, achieving a plutonium equilibrium in a stockpile fed by a PWR-UOx that operates at 40 GWd/t requires a PWR-MOx fraction between 9 and 14%. This study also provides data related to plutonium incineration induced by the utilization of the MOx.

scholarly journals Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single-Loop Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Cheng ◽  
Zhenzhou Lu ◽  
Luyi Li
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Single Loop ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Distribution Parameters ◽  
Input Variables ◽  
Sampling Probability

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.

Moment Matching for Sensitivity Analysis of Probabilistic Model Output

2004 ◽  
Author(s):  
Mahmoud Awad ◽  
Agus Sudjianto ◽  
Nanua Singh
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Models ◽  
Moment Matching ◽  
Model Output ◽  
Sensitivity Indices ◽  
Variance Contribution ◽  
Complex Engineering ◽  
Input Variables ◽  
The Relationship ◽  
Effective Sensitivity

With the advent of highly complex engineering simulation models that describe the relationship between input variables and output response, the need for an efficient and effective sensitivity analysis is more demanding. In this article, a generalized approach that can provide efficient as well as accurate global sensitivity indices is developed. The approach consists of two steps: running an orthogonal array based experiment using moment-matched levels of the input variables and followed by a variance contribution analysis. The benefits of the approach are demonstrated through three different examples.

scholarly journals New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2425
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Binary Outcome ◽  
Global Sensitivity ◽  
First Order ◽  
Sensitivity Measure ◽  
Sensitivity Indices ◽  
Alternative Measures ◽  
Input Variables ◽  
Dome Shape

This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1 − Pf) and discrete entropy—Pfln(Pf) − (1 − Pf)ln(1 − Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.

scholarly journals A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2489
Author(s):  
Zhiwei Bai ◽  
Hongkui Wei ◽  
Yingying Xiao ◽  
Shufang Song ◽  
Sergei Kucherenko
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Joint Probability ◽  
Copula Functions ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Sensitivity Analysis Method ◽  
Input Variables ◽  
Vine Copula ◽  
Bivariate Copula

For multidimensional dependent cases with incomplete probability information of random variables, global sensitivity analysis (GSA) theory is not yet mature. The joint probability density function (PDF) of multidimensional variables is usually unknown, meaning that the samples of multivariate variables cannot be easily obtained. Vine copula can decompose the joint PDF of multidimensional variables into the continuous product of marginal PDF and several bivariate copula functions. Based on Vine copula, multidimensional dependent problems can be transformed into two-dimensional dependent problems. A novel Vine copula-based approach for analyzing variance-based sensitivity measures is proposed, which can estimate the main and total sensitivity indices of dependent input variables. Five considered test cases and engineering examples show that the proposed methods are accurate and applicable.

scholarly journals From Probabilistic to Quantile-Oriented Sensitivity Analysis: New Indices of Design Quantiles

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1720 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Structural Reliability ◽  
Building Design ◽  
Design Standards ◽  
Average Value ◽  
Sensitivity Indices ◽  
Before And After ◽  
Input Variables ◽  
Total Sensitivity

In structural reliability analysis, sensitivity analysis (SA) can be used to measure how an input variable influences the failure probability Pf of a structure. Although the reliability is usually expressed via Pf, Eurocode building design standards assess the reliability using design quantiles of resistance and load. The presented case study showed that quantile-oriented SA can provide the same sensitivity ranking as Pf-oriented SA or local SA based on Pf derivatives. The first two SAs are global, so the input variables are ranked based on total sensitivity indices subordinated to contrasts. The presented studies were performed for Pf ranging from 9.35 × 10−8 to 1–1.51 × 10−8. The use of quantile-oriented global SA can be significant in engineering tasks, especially for very small Pf. The proposed concept provided an opportunity to go much further. Left-right symmetry of contrast functions and sensitivity indices were observed. The article presents a new view of contrasts associated with quantiles as the distance between the average value of the population before and after the quantile. This distance has symmetric hyperbola asymptotes for small and large quantiles of any probability distribution. Following this idea, new quantile-oriented sensitivity indices based on measuring the distance between a quantile and the average value of the model output are formulated in this article.

scholarly journals A Sampling-Based Sensitivity Analysis Method Considering the Uncertainties of Input Variables and Their Distribution Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1095
Author(s):  
Xiang Peng ◽  
Xiaoqing Xu ◽  
Jiquan Li ◽  
Shaofei Jiang
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Method ◽  
Transformation Method ◽  
Unscented Transformation ◽  
Performance Function ◽  
Gaussian Integration ◽  
Sensitivity Indices ◽  
Sensitivity Analysis Method ◽  
Distribution Parameters ◽  
Input Variables

For engineering products with uncertain input variables and distribution parameters, a sampling-based sensitivity analysis methodology was investigated to efficiently determine the influences of these uncertainties. In the calculation of the sensitivity indices, the nonlinear degrees of the performance function in the subintervals were greatly reduced by using the integral whole domain segmentation method, while the mean and variance of the performance function were calculated using the unscented transformation method. Compared with the traditional Monte Carlo simulation method, the loop number and sampling number in every loop were decreased by using the multiplication approximation and Gaussian integration methods. The proposed algorithm also reduced the calculation complexity by reusing the sample points in the calculation of two sensitivity indices to measure the influence of input variables and their distribution parameters. The accuracy and efficiency of the proposed algorithm were verified with three numerical examples and one engineering example.

scholarly journals Global Sensitivity Analysis of Ultimate Limit States of Stainless Steel Structural Members

2021 ◽  
Vol 1203 (2) ◽  
pp. 022142
Author(s):  
Abayomi Omishore
Keyword(s):  
Sensitivity Analysis ◽  
Stainless Steel ◽  
Yield Strength ◽  
Higher Order ◽  
Carbon Steels ◽  
Sensitivity Analyses ◽  
Statistical Characteristics ◽  
Limit States ◽  
Sensitivity Indices ◽  
Input Variables

Abstract The article presents global Sobol sensitivity analysis of a rolled member in tension made from austenitic chromium-nickel stainless steel of type 1.4307/AISI 304 L. The statistical characteristics of yield strength and of the geometry of the rolled steel IPE cross-section are presented on the basis of published experimental research. The sensitivity analysis showed the dominant effect of the yield strength on the static resistance. The second dominant variable is the flange thickness. Higher-order sensitivity indices oriented at detecting the presence of interaction effects between input variables are very small. The characteristics of other types of sensitivity analyses oriented at quantiles or the probability of failure are discussed, especially in terms of a higher proportion of higher-order sensitivity indices. The results of Sobol sensitivity analysis of stainless steel are compared with similar results of carbon steels.

scholarly journals Sensitivity Analysis in Probabilistic Structural Design: A Comparison of Selected Techniques

2020 ◽  
Vol 12 (11) ◽  
pp. 4788 ◽  
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Structural Reliability ◽  
Limit State ◽  
Information Value ◽  
Ultimate Limit State ◽  
State Function ◽  
Sensitivity Indices ◽  
Small Failure Probability ◽  
Input Variables

Although more and more reliability-oriented sensitivity analysis (ROSA) techniques are now available, review and comparison articles of ROSA are absent. In civil engineering, many of the latest indices have never been used to analyse structural reliability for very small failure probability. This article aims to analyse and compare different sensitivity analysis (SA) techniques and discusses their strengths and weaknesses. For this purpose, eight selected sensitivity indices are first described and then applied in two different test cases. Four ROSA type indices are directly oriented on the failure probability or reliability index beta, and four other indices (of a different type) are oriented on the output of the limit state function. The case study and results correspond to cases under common engineering assumptions, where only two independent input variables with Gaussian distribution of the load action and the resistance are applied in the ultimate limit state. The last section of the article is dedicated to the analysis of the different results. Large differences between first-order sensitivity indices and very strong interaction effects obtained from ROSA are observed for very low values of failure probability. The obtained numerical results show that ROSA methods lack a common platform that clearly interprets the relationship of indices to their information value. This paper can help orientate in the selection of which sensitivity measure to use.

scholarly journals An Application of Monte-Carlo-Based Sensitivity Analysis on the Overlap in Discriminant Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
S. Razmyan ◽  
F. Hosseinzadeh Lotfi
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Discriminant Analysis ◽  
Uncertain Variable ◽  
Model Parameters ◽  
Sampled Data ◽  
First Order ◽  
Sensitivity Indices ◽  
Input Variables

Discriminant analysis (DA) is used for the measurement of estimates of a discriminant function by minimizing their group misclassifications to predict group membership of newly sampled data. A major source of misclassification in DA is due to the overlapping of groups. The uncertainty in the input variables and model parameters needs to be properly characterized in decision making. This study combines DEA-DA with a sensitivity analysis approach to an assessment of the influence of banks’ variables on the overall variance in overlap in a DA in order to determine which variables are most significant. A Monte-Carlo-based sensitivity analysis is considered for computing the set of first-order sensitivity indices of the variables to estimate the contribution of each uncertain variable. The results show that the uncertainties in the loans granted and different deposit variables are more significant than uncertainties in other banks’ variables in decision making.

Global Sensitivity Analysis for Field Response Based on the Manifold of Feature Covariance Matrix

2021 ◽  
Author(s):  
Zhouzhou Song ◽  
Zhao Liu ◽  
Can Xu ◽  
Ping Zhu
Keyword(s):  
Sensitivity Analysis ◽  
Covariance Matrix ◽  
Computational Models ◽  
Global Sensitivity Analysis ◽  
Feature Selection Method ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Field Response ◽  
Input Variables ◽  
The Impact

Abstract In real-world applications, it is commonplace that the computational models have field responses, i.e., the temporal or spatial fields. It has become a critical task to develop global sensitivity analysis (GSA) methods to measure the effect of each input variable on the full-field. In this paper, a new sensitivity analysis method based on the manifold of feature covariance matrix (FCM) is developed for quantifying the impact of input variables on the field response. The method firstly performs feature extraction on the field response to obtain a low-dimensional FCM. An adaptive feature selection method is proposed to avoid the FCM from singularity. Thereby, the field response is represented by a FCM, which lies on a symmetric positive-definite matrix manifold. Then, the GSA technique based on the Cramér-von Mises distance for output valued on the Riemannian manifold is introduced for estimating the sensitivity indices for field response. An example of a temporal field and an example of a 2-D displacement field are introduced to demonstrate the applicability of the proposed method in estimating global sensitivity indices for field solution. Results show that the proposed method can distinguish the important input variables correctly and can yield robust index values. Besides, the proposed method can be implemented for GSA for field responses of different dimensionalities.

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