Visualization tools for uncertainty and sensitivity analyses on thermal-hydraulic transients

Popelin, Anne-Laure; Iooss, Bertrand

doi:10.1051/snamc/201403403

Cited by 6 publications

(6 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In our method, the functional curves are handled by reducing their dimension via projection, using PCA as in [12] (which is limited to the two first components). [13] has introduced this PCA-based approach for visualizing (but noninteractively) functional outputs of computer experiments. Later, [14] has extended the technique to selecting and modeling more than two PCA components by advanced statistical techniques.…”

Section: Background and Related Workmentioning

confidence: 99%

“… Are there some clusters, which correspond to different behaviors of the physical model that generated these outputs? These questions can be answered by methods found in the recent technical literature by the way of Principal Component Analysis (PCA) methods, with a statistical viewpoint [12][13][14] or with a visualization viewpoint [15][16][17]. However, for augmented ensembles new challenges arise because a member of such ensemble consists of a set of input parameters (which drove a numerical simulation) and its associated functional output.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Visual Sensitivity Analysis for Parameter-Augmented Ensembles of Curves

Ribés

Pouderoux²,

Iooss³

2019

Journal of Verification, Validation and Uncertainty Quantification

Self Cite

View full text Add to dashboard Cite

Engineers and computational scientists often study the behavior of their simulations by repeated solutions with variations in their parameters, which can be for instance boundary values or initial conditions. Through such simulation ensembles, uncertainty in a solution is studied as a function of the various input parameters. Solutions of numerical simulations are often temporal functions, spatial maps or spatio-temporal outputs. The usual way to deal with such complex outputs is to limit the analysis to several probes in the temporal/spatial domain. This leads to smaller and more tractable ensembles of functional outputs (curves) with their associated input parameters: augmented ensembles of curves. This article describes a system for the interactive exploration and analysis of such augmented ensembles. Descriptive statistics on the functional outputs are performed by Principal Component Analysis projection, kernel density estimation and the computation of High Density Regions. This makes possible the calculation of functional quantiles and outliers. Brushing and linking the elements of the system allows in-depth analysis of the ensemble. The system allows for functional descriptive statistics, cluster detection and finally for the realization of a visual sensitivity analysis via cobweb plots. We present two synthetic examples and then validate our approach in an industrial use-case concerning a marine current study using a hydraulic solver.

show abstract

Section: Background and Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Visual Sensitivity Analysis for Parameter-Augmented Ensembles of Curves

Ribés

Pouderoux²,

Iooss³

2019

Journal of Verification, Validation and Uncertainty Quantification

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, its shape (as in the boxplot bivariate extension) is very different to the one of boxplot. It is worth noting that it has already been applied in the context of nuclear reliability study in Popelin and Iooss (2013). The method of Hyndman and Shang (2010) is based on the uncertainty characterization of the functional variables.…”

Section: Nuclear Reliability Applicationmentioning

confidence: 99%

Uncertainty quantification for functional dependent random variables

et al. 2016

View full text Add to dashboard Cite

This paper proposes a new methodology to model uncertainties associated with functional random variables. This methodology allows to deal simultaneously with several dependent functional variables and to address the specific case where these variables are linked to a vectorial variable, called covariate. In this case, the proposed uncertainty modelling methodology has two objectives: to retain both the most important features of the functional variables and their features which are the most correlated to the covariate. This methodology is composed of two steps. First, the functional variables are decomposed on a functional basis. To deal simultaneously with several dependent functional variables, a Simultaneous Partial Least Squares algorithm is proposed to estimate this basis. Second, the joint probability density function of the coefficients selected in the decomposition is modelled by a Gaussian mixture model. A new sparse method based on a Lasso penalization algorithm is proposed to estimate the Gaussian mixture model parameters and reduce their number. Several criteria are introduced to assess the methodology performance: its ability to approximate the functional variables probability distribution, their dependence structure and their features which explain the covariate. Finally, the whole methodology is applied on a simulated example and on a nuclear reliability test case.

show abstract

“…Each curve represents either a realization within the data set or an additional realization sampled in the reduced space; thus functional characteristics such as spatial or temporal correlation are preserved. From (Popelin and Iooss 2013;Ribés et al 2015), the HDR method is more robust to outlier detection than other methods such as functional boxplot (Sun and Genton 2011). This article proposes a solution to visualize high input and output dimensions.…”

Section: Introductionmentioning

confidence: 99%

Sounding Spider: An Efficient Way for Representing Uncertainties in High Dimensions

Roy¹,

Ricci²,

Cuenot³

et al. 2018

Preprint

View full text Add to dashboard Cite

This article proposes a visualization method for multidimensional data based on: (i) Animated functional Hypothetical Outcome Plots (f-HOPs); (ii) 3-dimensional Kiviat plot; and (iii) data sonification. In an Uncertainty Quantification (UQ) framework, such analysis coupled with standard statistical analysis tools such as Probability Density Functions (PDF) can be used to augment the understanding of how the uncertainties in the numerical code inputs translate into uncertainties in the quantity of interest (QoI).In contrast with static representation of most advanced techniques such as functional Highest Density Region (HDR) boxplot or functional boxplot, f-HOPs is a dynamic visualization that enables the practitioners to infer the dynamics of the physics and enables to see functional correlations that may exist. While this technique only allows to represent the QoI, we propose a 3-dimensional version of the Kiviat plot to encode all input parameters. This new visualization takes advantage of information from f-HOPs through data sonification. All in all, this allows to analyse large datasets within a high-dimensional parameter space and a functional QoI in the same canvas. The proposed method is assessed and showed its benefits on two related environmental datasets.

show abstract

Visualization tools for uncertainty and sensitivity analyses on thermal-hydraulic transients

Cited by 6 publications

References 12 publications

A Visual Sensitivity Analysis for Parameter-Augmented Ensembles of Curves

A Visual Sensitivity Analysis for Parameter-Augmented Ensembles of Curves

Uncertainty quantification for functional dependent random variables

Sounding Spider: An Efficient Way for Representing Uncertainties in High Dimensions

Contact Info

Product

Resources

About