968 research outputs found
Global Sensitivity Analysis of Stochastic Computer Models with joint metamodels
The global sensitivity analysis method, used to quantify the influence of
uncertain input variables on the response variability of a numerical model, is
applicable to deterministic computer code (for which the same set of input
variables gives always the same output value). This paper proposes a global
sensitivity analysis methodology for stochastic computer code (having a
variability induced by some uncontrollable variables). The framework of the
joint modeling of the mean and dispersion of heteroscedastic data is used. To
deal with the complexity of computer experiment outputs, non parametric joint
models (based on Generalized Additive Models and Gaussian processes) are
discussed. The relevance of these new models is analyzed in terms of the
obtained variance-based sensitivity indices with two case studies. Results show
that the joint modeling approach leads accurate sensitivity index estimations
even when clear heteroscedasticity is present
Global sensitivity analysis of stochastic computer models with joint metamodels
The global sensitivity analysis method used to quantify the influence of uncertain input variables on the variability in numerical model responses has already been applied to deterministic computer codes; deterministic means here that the same set of input variables gives always the same output value. This paper proposes a global sensitivity analysis methodology for stochastic computer codes, for which the result of each code run is itself random. The framework of the joint modeling of the mean and dispersion of heteroscedastic data is used. To deal with the complexity of computer experiment outputs, nonparametric joint models are discussed and a new Gaussian process-based joint model is proposed. The relevance of these models is analyzed based upon two case studies. Results show that the joint modeling approach yields accurate sensitivity index estimatiors even when heteroscedasticity is strong
Global sensitivity analysis of computer models with functional inputs
Global sensitivity analysis is used to quantify the influence of uncertain
input parameters on the response variability of a numerical model. The common
quantitative methods are applicable to computer codes with scalar input
variables. This paper aims to illustrate different variance-based sensitivity
analysis techniques, based on the so-called Sobol indices, when some input
variables are functional, such as stochastic processes or random spatial
fields. In this work, we focus on large cpu time computer codes which need a
preliminary meta-modeling step before performing the sensitivity analysis. We
propose the use of the joint modeling approach, i.e., modeling simultaneously
the mean and the dispersion of the code outputs using two interlinked
Generalized Linear Models (GLM) or Generalized Additive Models (GAM). The
``mean'' model allows to estimate the sensitivity indices of each scalar input
variables, while the ``dispersion'' model allows to derive the total
sensitivity index of the functional input variables. The proposed approach is
compared to some classical SA methodologies on an analytical function. Lastly,
the proposed methodology is applied to a concrete industrial computer code that
simulates the nuclear fuel irradiation
Metamodel variability analysis combining bootstrapping and validation techniques
Research on metamodel-based optimization has received considerably increasing interest in recent years, and has found successful applications in solving computationally expensive problems. The joint use of computer simulation experiments and metamodels introduces a source of uncertainty that we refer to as metamodel variability. To analyze and quantify this variability, we apply bootstrapping to residuals derived as prediction errors computed from cross-validation. The proposed method can be used with different types of metamodels, especially when limited knowledge on parameters’ distribution is available or when a limited computational budget is allowed. Our preliminary experiments based on the robust version of
the EOQ model show encouraging results
Uncertainty and sensitivity analysis of functional risk curves based on Gaussian processes
A functional risk curve gives the probability of an undesirable event as a
function of the value of a critical parameter of a considered physical system.
In several applicative situations, this curve is built using phenomenological
numerical models which simulate complex physical phenomena. To avoid cpu-time
expensive numerical models, we propose to use Gaussian process regression to
build functional risk curves. An algorithm is given to provide confidence
bounds due to this approximation. Two methods of global sensitivity analysis of
the models' random input parameters on the functional risk curve are also
studied. In particular, the PLI sensitivity indices allow to understand the
effect of misjudgment on the input parameters' probability density functions
Sensitivity analysis and related analysis: A survey of statistical techniques
This paper reviews the state of the art in five related types of analysis, namely (i) sensitivity or what-if analysis, (ii) uncertainty or risk analysis, (iii) screening, (iv) validation, and (v) optimization. The main question is: when should which type of analysis be applied; which statistical techniques may then be used? This paper distinguishes the following five stages in the analysis of a simulation model. 1) Validation: the availability of data on the real system determines which type of statistical technique to use for validation. 2) Screening: in the simulation's pilot phase the really important inputs can be identified through a novel technique, called sequential bifurcation, which uses aggregation and sequential experimentation. 3) Sensitivity analysis: the really important inputs should be This approach with its five stages implies that sensitivity analysis should precede uncertainty analysis. This paper briefly discusses several case studies for each phase.Experimental Design;Statistical Methods;Regression Analysis;Risk Analysis;Least Squares;Sensitivity Analysis;Optimization;Perturbation;statistics
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