An efficient sampling scheme: Updated Latin Hypercube Sampling

Florian, Aleš

doi:10.1016/0266-8920(92)90015-a

Cited by 190 publications

(101 citation statements)

References 6 publications

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“…The second pair of box plots indicates that modifying these randomly generated LH designs to obtain the desired levels for the limited-level factors in S 1 , and S 9 has little impact on the respective ρ map values. The third pair of box plots shows that ρ map drops dramatically when the method of Florian (1992) is applied to the initial, randomly generated, continuous-valued designs. This approach yields designs that meet our near-orthogonality criterion of ρ map < 0.05 roughly 96% of the time when K = 135; the minimum ρ map was 0.057 when K = 15.…”

Section: Modifying Continuous-factor Designs For Use With Discrete Famentioning

confidence: 99%

Efficient, nearly orthogonal-and-balanced, mixed designs: an effective way to conduct trade-off analyses via simulation

Vieira

Sanchez

Kienitz

et al. 2013

Journal of Simulation

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Designed experiments are powerful methodologies for gaining insights into the behaviour of complex simulation models. In recent years, many new designs have been created to address the large number of factors and complex response surfaces that often arise in simulation studies, but handling discrete-valued or qualitative factors remains problematic. We propose a framework for generating a design, of specified size, that is nearly orthogonal and nearly balanced for any mix of factor types (categorical, numerical discrete, and numerical continuous) and mix of factor levels. These new designs allow decision makers structured methods for trade-off analyses in situations that are not necessarily amenable to other methods for choosing alternatives, such as simulation optimization or ranking and selection approaches. These new designs also compare well to existing approaches for constructing custom designs for smaller experiments, and may also be of interest for exploring computer models in domains where fewer factors are involved.

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Section: Modifying Continuous-factor Designs For Use With Discrete Famentioning

confidence: 99%

Efficient, nearly orthogonal-and-balanced, mixed designs: an effective way to conduct trade-off analyses via simulation

Vieira

Sanchez

Kienitz

et al. 2013

Journal of Simulation

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“…The random elements in the construction of LHs means that any given realization may have poor design properties, for example, a high Pmax· This is particularly likely when k and n are small. A common solution is to generate many random LHs and select the one with the best properties, such as the minimum Pmax· Others (e.g., Florian 1992;Owen 1994) have developed algorithms that may reduce the off-diagonal correlations of a LH design matrix. Ye ( l 998a) went farther, deriving a method that generates OLHs …”

Section: Orthogonal Latin Hypercubes With Additional Variablesmentioning

confidence: 99%

“…In brief, Florian's (1992) method is as follows. For each column of a design matrix X, each element is replaced with its…”

Section: Acknowledgmentsmentioning

confidence: 99%

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Efficient Nearly Orthogonal and Space-Filling Latin Hypercubes

2007

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“…The present paper describes a complete methodology for uncertainty propagation which combines: (a) a threelayer sandwich plate stochastic viscoelastic finite element, previously described in reference [14], for which a parameterization approach has been suggested in such a way to enable the introduction of parametric variations in a straightforward manner; (b) a model condensation strategy specially adapted to viscoelastic systems, in which the dynamic response of the damped system is projected on a truncated modal basis of the associated undamped system, such basis being enriched by static residual vectors; (c) MCS combined with Latin Hypercube (LHC) sampling [15] as the stochastic solver used to evaluate the response variability.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Modeling of Surface Viscoelastic Treatments Combined with Model Condensation Procedures

Lima

Rade

Bouhaddi

2010

Shock and Vibration

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Abstract. Engineering structures incorporating viscoelastic materials are characterized by inherent uncertainties affecting the parameters that control the efficiency of the viscoelastic dampers. In this context, the handling of variability in viscoelastic systems is a natural and necessary extension of the modeling capability of the present techniques of deterministic analysis. Among the various methods devised for uncertainty modeling, the stochastic finite element method has received major attention, as it is well adapted for applications to complex engineering systems. In this paper, the stochastic finite element method applied to a structural three-layer sandwich plate finite element containing a viscoelastic layer, with random parameters modelled as random fields, is presented. Accounting for the dependence of the behaviour of the viscoelastic materials with respect to frequency and temperature, using the concepts of complex modulus and shift factor, the uncertainties are modelled as homogeneous Gaussian stochastic fields and are discretized according to the spectral method, using Karhunen-Loève expansions. The modeling procedure is confined to the frequency domain, and the dynamic responses are characterized by frequency response functions (FRF's). Monte Carlo Simulation (MCS) combined with Latin Hypercube Sampling is used as the stochastic solver. The typically high dimensions of finite element models of viscoelastic systems combined with the large number of Monte Carlo samples to be computed make the evaluation of the FRF's variability computer intensive. Those difficulties motivate the use of condensation methods specially adapted for viscoelastic systems, in order to alleviate the computational cost. After the presentation of the underlying formulation, numerical applications of moderate complexity are presented and discussed aiming at demonstrating the main features and, particularly, the computation cost savings provided by the association of MCS with the suggested condensation procedure.

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An efficient sampling scheme: Updated Latin Hypercube Sampling

Cited by 190 publications

References 6 publications

Efficient, nearly orthogonal-and-balanced, mixed designs: an effective way to conduct trade-off analyses via simulation

Efficient, nearly orthogonal-and-balanced, mixed designs: an effective way to conduct trade-off analyses via simulation

Efficient Nearly Orthogonal and Space-Filling Latin Hypercubes

Stochastic Modeling of Surface Viscoelastic Treatments Combined with Model Condensation Procedures

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