258,206 research outputs found
Computing derivative-based global sensitivity measures using polynomial chaos expansions
In the field of computer experiments sensitivity analysis aims at quantifying
the relative importance of each input parameter (or combinations thereof) of a
computational model with respect to the model output uncertainty. Variance
decomposition methods leading to the well-known Sobol' indices are recognized
as accurate techniques, at a rather high computational cost though. The use of
polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to
alleviate the computational burden though. However, when dealing with large
dimensional input vectors, it is good practice to first use screening methods
in order to discard unimportant variables. The {\em derivative-based global
sensitivity measures} (DGSM) have been developed recently in this respect. In
this paper we show how polynomial chaos expansions may be used to compute
analytically DGSMs as a mere post-processing. This requires the analytical
derivation of derivatives of the orthonormal polynomials which enter PC
expansions. The efficiency of the approach is illustrated on two well-known
benchmark problems in sensitivity analysis
Sensitivity analysis of expensive black-box systems using metamodeling
Simulations are becoming ever more common as a tool for designing complex
products. Sensitivity analysis techniques can be applied to these simulations
to gain insight, or to reduce the complexity of the problem at hand. However,
these simulators are often expensive to evaluate and sensitivity analysis
typically requires a large amount of evaluations. Metamodeling has been
successfully applied in the past to reduce the amount of required evaluations
for design tasks such as optimization and design space exploration. In this
paper, we propose a novel sensitivity analysis algorithm for variance and
derivative based indices using sequential sampling and metamodeling. Several
stopping criteria are proposed and investigated to keep the total number of
evaluations minimal. The results show that both variance and derivative based
techniques can be accurately computed with a minimal amount of evaluations
using fast metamodels and FLOLA-Voronoi or density sequential sampling
algorithms.Comment: proceedings of winter simulation conference 201
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
Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations
To perform uncertainty, sensitivity or optimization analysis on scalar
variables calculated by a cpu time expensive computer code, a widely accepted
methodology consists in first identifying the most influential uncertain inputs
(by screening techniques), and then in replacing the cpu time expensive model
by a cpu inexpensive mathematical function, called a metamodel. This paper
extends this methodology to the functional output case, for instance when the
model output variables are curves. The screening approach is based on the
analysis of variance and principal component analysis of output curves. The
functional metamodeling consists in a curve classification step, a dimension
reduction step, then a classical metamodeling step. An industrial nuclear
reactor application (dealing with uncertainties in the pressurized thermal
shock analysis) illustrates all these steps
Derivative based global sensitivity measures
The method of derivative based global sensitivity measures (DGSM) has
recently become popular among practitioners. It has a strong link with the
Morris screening method and Sobol' sensitivity indices and has several
advantages over them. DGSM are very easy to implement and evaluate numerically.
The computational time required for numerical evaluation of DGSM is generally
much lower than that for estimation of Sobol' sensitivity indices. This paper
presents a survey of recent advances in DGSM concerning lower and upper bounds
on the values of Sobol' total sensitivity indices . Using these
bounds it is possible in most cases to get a good practical estimation of the
values of . Several examples are used to illustrate an
application of DGSM
Reliability-based design optimization using kriging surrogates and subset simulation
The aim of the present paper is to develop a strategy for solving
reliability-based design optimization (RBDO) problems that remains applicable
when the performance models are expensive to evaluate. Starting with the
premise that simulation-based approaches are not affordable for such problems,
and that the most-probable-failure-point-based approaches do not permit to
quantify the error on the estimation of the failure probability, an approach
based on both metamodels and advanced simulation techniques is explored. The
kriging metamodeling technique is chosen in order to surrogate the performance
functions because it allows one to genuinely quantify the surrogate error. The
surrogate error onto the limit-state surfaces is propagated to the failure
probabilities estimates in order to provide an empirical error measure. This
error is then sequentially reduced by means of a population-based adaptive
refinement technique until the kriging surrogates are accurate enough for
reliability analysis. This original refinement strategy makes it possible to
add several observations in the design of experiments at the same time.
Reliability and reliability sensitivity analyses are performed by means of the
subset simulation technique for the sake of numerical efficiency. The adaptive
surrogate-based strategy for reliability estimation is finally involved into a
classical gradient-based optimization algorithm in order to solve the RBDO
problem. The kriging surrogates are built in a so-called augmented reliability
space thus making them reusable from one nested RBDO iteration to the other.
The strategy is compared to other approaches available in the literature on
three academic examples in the field of structural mechanics.Comment: 20 pages, 6 figures, 5 tables. Preprint submitted to Springer-Verla
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