Simplex-based screening designs for estimating metamodels

Pujol, Gilles

doi:10.1016/j.ress.2008.08.002

Cited by 61 publications

(25 citation statements)

References 12 publications

(21 reference statements)

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“…Morris mentioned that his method gives the total effect and it cannot distinguish between the contribution of nonlinearties and interactions. The previous statistics can be used to rank and classify the input parameters into four main categories: Inputs with insignificant effect (small

μ_{i}^{*}

). Inputs with significant effect (large

μ_{i}^{*}

) and insignificant nonlinearity and interactions (small

σ_{i}^{2}

). Inputs with significant effect (large

μ_{i}^{*}

) and significant nonlinearity and/or interactions (large

σ_{i}^{2}

). Inputs with non‐monotonic behaviour

μ_{i}^{*} \neq μ_{i}

. …”

Section: Methodsmentioning

confidence: 99%

Efficient analysis of parametric sensitivity and uncertainty of fuel cell models with application to SOFC

Radaideh

2020

Int J Energy Res

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Summary Sensitivity analysis (SA) and uncertainty quantification (UQ) are used to assess and improve engineering models. SA of fuel cell models can be challenging because of the large number of design parameters to optimize. Following the regular approach of manually testing the fuel cell outputs under changing each design parameter one at a time can be tedious. In this work, a framework of SA and UQ methods is applied with a purpose of efficiently analysing fuel cell models. The SA and UQ methods are also compared to increase the confidence in the results. In this methodology, all design parameters and their effects can be analysed in an integrated form, where model variance, sensitivity, linearity/nonlinearity, parameter interactions, and importance ranking can be assessed. This paper highlights and compares between local SA (one‐at‐a‐time linear perturbation), parameter screening (Morris screening), variance decomposition (Sobol indices), and regression‐based SA. For UQ, stochastic methods (Monte Carlo sampling) and deterministic methods (using SA profiles) are used. All methods are applied to solid oxide fuel cell (SOFC) to analyse the power output and system efficiency under 21 uncertain design parameters. Using different methods, the uncertainty in the SOFC responses (maximum power and efficiency) is about 11%, when the current density is about 13 200 A m−2. In addition, analysis shows that operating temperature (T), length of grain contact (X), grain size (Ds), porosity (ϵ), and electrolyte thickness (Le) contribute to more than 97% of the SOFC's maximum power variance, with individual contributions as follows: 63.3%, 13.1%, 12.5%, 5.4%, and 3.6%, respectively. The previous conclusions are subjective to the simplified SOFC model used in this study to demonstrate the methods. Benchmarking the UQ methods in capturing the response uncertainty and the SA methods in raking the design parameters demonstrate very good agreement between them. The methods applied in this paper can be used to achieve a comprehensive mathematical understanding of more advanced fuel cell or energy models, which can lead to better performance.

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μ_{i}^{*}

). Inputs with significant effect (large

μ_{i}^{*}

) and insignificant nonlinearity and interactions (small

σ_{i}^{2}

). Inputs with significant effect (large

μ_{i}^{*}

) and significant nonlinearity and/or interactions (large

σ_{i}^{2}

). Inputs with non‐monotonic behaviour

μ_{i}^{*} \neq μ_{i}

. …”

Section: Methodsmentioning

confidence: 99%

Efficient analysis of parametric sensitivity and uncertainty of fuel cell models with application to SOFC

Radaideh

2020

Int J Energy Res

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“…Projection of a d-dimensional OFAAT design into d − 1 dimensions reduces the number of distinct points from d + 1 to d. This is a particular issue when the projection of the screening design onto the active variables is used to estimate a detailed surrogate model. Better projection properties may be obtained by replacing an OFAAT design by a rotated simplex [86] at the cost of less precision in the estimators of the elementary effects.…”

Section: Sampling Plans For Estimating Elementary Effects (Morris' Mementioning

confidence: 99%

Design of Experiments for Screening

Woods

Lewis

2017

Handbook of Uncertainty Quantification

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The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared.

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“…The objective of this section is to suggest a common terminology on the basis of the definitions drawn from the literature (among others, Saltelli, 2000;Campolongo et al, 2007;Pujol, 2009).…”

Section: Terminologymentioning

confidence: 99%

Global sensitivity analysis for urban water quality modelling: Terminology, convergence and comparison of different methods

Vanrolleghem

Mannina

Cosenza

et al. 2015

Journal of Hydrology

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a b s t r a c tSensitivity analysis represents an important step in improving the understanding and use of environmental models. Indeed, by means of global sensitivity analysis (GSA), modellers may identify both important (factor prioritisation) and non-influential (factor fixing) model factors. No general rule has yet been defined for verifying the convergence of the GSA methods. In order to fill this gap this paper presents a convergence analysis of three widely used GSA methods (SRC, Extended FAST and Morris screening) for an urban drainage stormwater quality-quantity model. After the convergence was achieved the results of each method were compared. In particular, a discussion on peculiarities, applicability, and reliability of the three methods is presented. Moreover, a graphical Venn diagram based classification scheme and a precise terminology for better identifying important, interacting and non-influential factors for each method is proposed. In terms of convergence, it was shown that sensitivity indices related to factors of the quantity model achieve convergence faster. Results for the Morris screening method deviated considerably from the other methods. Factors related to the quality model require a much higher number of simulations than the number suggested in literature for achieving convergence with this method. In fact, the results have shown that the term ''screening'' is improperly used as the method may exclude important factors from further analysis. Moreover, for the presented application the convergence analysis shows more stable sensitivity coefficients for the Extended-FAST method compared to SRC and Morris screening. Substantial agreement in terms of factor fixing was found between the Morris screening and Extended FAST methods. In general, the water quality related factors exhibited more important interactions than factors related to water quantity. Furthermore, in contrast to water quantity model outputs, water quality model outputs were found to be characterised by high non-linearity.

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Simplex-based screening designs for estimating metamodels

Cited by 61 publications

References 12 publications

Efficient analysis of parametric sensitivity and uncertainty of fuel cell models with application to SOFC

Efficient analysis of parametric sensitivity and uncertainty of fuel cell models with application to SOFC

Design of Experiments for Screening

Global sensitivity analysis for urban water quality modelling: Terminology, convergence and comparison of different methods

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