5,008 research outputs found
Latin hypercube sampling with inequality constraints
In some studies requiring predictive and CPU-time consuming numerical models,
the sampling design of the model input variables has to be chosen with caution.
For this purpose, Latin hypercube sampling has a long history and has shown its
robustness capabilities. In this paper we propose and discuss a new algorithm
to build a Latin hypercube sample (LHS) taking into account inequality
constraints between the sampled variables. This technique, called constrained
Latin hypercube sampling (cLHS), consists in doing permutations on an initial
LHS to honor the desired monotonic constraints. The relevance of this approach
is shown on a real example concerning the numerical welding simulation, where
the inequality constraints are caused by the physical decreasing of some
material properties in function of the temperature
mfEGRA: Multifidelity Efficient Global Reliability Analysis through Active Learning for Failure Boundary Location
This paper develops mfEGRA, a multifidelity active learning method using
data-driven adaptively refined surrogates for failure boundary location in
reliability analysis. This work addresses the issue of prohibitive cost of
reliability analysis using Monte Carlo sampling for expensive-to-evaluate
high-fidelity models by using cheaper-to-evaluate approximations of the
high-fidelity model. The method builds on the Efficient Global Reliability
Analysis (EGRA) method, which is a surrogate-based method that uses adaptive
sampling for refining Gaussian process surrogates for failure boundary location
using a single-fidelity model. Our method introduces a two-stage adaptive
sampling criterion that uses a multifidelity Gaussian process surrogate to
leverage multiple information sources with different fidelities. The method
combines expected feasibility criterion from EGRA with one-step lookahead
information gain to refine the surrogate around the failure boundary. The
computational savings from mfEGRA depends on the discrepancy between the
different models, and the relative cost of evaluating the different models as
compared to the high-fidelity model. We show that accurate estimation of
reliability using mfEGRA leads to computational savings of 46% for an
analytic multimodal test problem and 24% for a three-dimensional acoustic horn
problem, when compared to single-fidelity EGRA. We also show the effect of
using a priori drawn Monte Carlo samples in the implementation for the acoustic
horn problem, where mfEGRA leads to computational savings of 45% for the
three-dimensional case and 48% for a rarer event four-dimensional case as
compared to single-fidelity EGRA
Unlacing the lace expansion: a survey to hypercube percolation
The purpose of this note is twofold. First, we survey the study of the
percolation phase transition on the Hamming hypercube {0,1}^m obtained in the
series of papers [9,10,11,24]. Secondly, we explain how this study can be
performed without the use of the so-called "lace-expansion" technique. To that
aim, we provide a novel simple proof that the triangle condition holds at the
critical probability. We hope that some of these techniques will be useful to
obtain non-perturbative proofs in the analogous, yet much more difficult study
on high-dimensional tori.Comment: 19 pages. arXiv admin note: text overlap with arXiv:1201.395
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
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