122,455 research outputs found
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
Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis
In this paper, we consider a regression model built on dependent variables.
This regression modelizes an input output relationship. Under boundedness
assumptions on the joint distribution function of the input variables, we show
that a generalized Hoeffding-Sobol decomposition is available. This leads to
new indices measuring the sensitivity of the output with respect to the input
variables. We also study and discuss the estimation of these new indices
Model updating using uncertain experimental modal data
The propagation of parameter uncertainty in structural dynamics has become a feasible method to determine the probabilistic description of the vibration response of industrial scale �nite element models. Though methods for uncertainty propagation have been developed extensively, the quanti�cation of parameter uncertainty has been neglected in the past. But a correct assumption for the parameter variability is essential for the estimation of the uncertain vibration response. This paper shows how to identify model parameter means and covariance matrix from uncertain experimental modal test data. The common gradient based approach from deterministic computational model updating was extended by an equation that accounts for the stochastic part. In detail an inverse approach for the identi�cation of statistical parametric properties will be presented which will be applied on a numerical model of a replica of the GARTEUR SM-AG19 benchmark structure. The uncertain eigenfrequencies and mode shapes have been determined in an extensive experimental modal test campaign where the aircraft structure was tested repeatedly while it was 130 times dis- and reassembled in between each experimental modal analysis
The role of learning on industrial simulation design and analysis
The capability of modeling real-world system operations has turned simulation into an indispensable problemsolving methodology for business system design and analysis. Today, simulation supports decisions ranging
from sourcing to operations to finance, starting at the strategic level and proceeding towards tactical and
operational levels of decision-making. In such a dynamic setting, the practice of simulation goes beyond
being a static problem-solving exercise and requires integration with learning. This article discusses the role
of learning in simulation design and analysis motivated by the needs of industrial problems and describes
how selected tools of statistical learning can be utilized for this purpose
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 for stochastic simulators based on generalized lambda surrogate models
Global sensitivity analysis aims at quantifying the impact of input
variability onto the variation of the response of a computational model. It has
been widely applied to deterministic simulators, for which a set of input
parameters has a unique corresponding output value. Stochastic simulators,
however, have intrinsic randomness due to their use of (pseudo)random numbers,
so they give different results when run twice with the same input parameters
but non-common random numbers. Due to this random nature, conventional Sobol'
indices, used in global sensitivity analysis, can be extended to stochastic
simulators in different ways. In this paper, we discuss three possible
extensions and focus on those that depend only on the statistical dependence
between input and output. This choice ignores the detailed data generating
process involving the internal randomness, and can thus be applied to a wider
class of problems. We propose to use the generalized lambda model to emulate
the response distribution of stochastic simulators. Such a surrogate can be
constructed without the need for replications. The proposed method is applied
to three examples including two case studies in finance and epidemiology. The
results confirm the convergence of the approach for estimating the sensitivity
indices even with the presence of strong heteroskedasticity and small
signal-to-noise ratio
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