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Distance-based optimal sampling in a hypercube: Analogies to N-body systems

Identifikátory výsledku

  • Kód výsledku v IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F19%3APU134106" target="_blank" >RIV/00216305:26110/19:PU134106 - isvavai.cz</a>

  • Výsledek na webu

    <a href="http://www.sciencedirect.com/science/article/pii/S0965997819301164" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0965997819301164</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.advengsoft.2019.102709" target="_blank" >10.1016/j.advengsoft.2019.102709</a>

Alternativní jazyky

  • Jazyk výsledku

    angličtina

  • Název v původním jazyce

    Distance-based optimal sampling in a hypercube: Analogies to N-body systems

  • Popis výsledku v původním jazyce

    A method is proposed for the construction of uniformly distributed point sets within a design domain using an analogy to a dynamical system of interacting particles. The possibility of viewing various distance-based optimality criteria as formulas representing the potential energy of a system of charged particles is discussed. The potential energy is employed in deriving the equations of motion of the particles. The particles are either attracted or repelled and dissipative dynamical systems can be simulated to achieve optimal and near-optimal arrangements of points. The design domain is set up as an Nvar-dimensional unit hypercube, with Nvar being the number of variables (factors). The number of points is equal to the number of simulations (levels). The periodicity assumption of the design domain is shown to be an elegant way to obtain statistically uniform coverage of the design domain. The ϕp criterion, which is a generalization of the Maximin criterion, is selected in order to demonstrate its analogy with an N-body system. This criterion guarantees that the points are spread uniformly within the design domain. The solution to such an N-body system is presented. The obtained designs are shown to outperform the existing optimal designs in various types of applications: multidimensional numerical integration, statistical exploration of computer models, reliability analyses of engineering systems, and screenings or exploratory designs for the global optimization/minimization of functions.

  • Název v anglickém jazyce

    Distance-based optimal sampling in a hypercube: Analogies to N-body systems

  • Popis výsledku anglicky

    A method is proposed for the construction of uniformly distributed point sets within a design domain using an analogy to a dynamical system of interacting particles. The possibility of viewing various distance-based optimality criteria as formulas representing the potential energy of a system of charged particles is discussed. The potential energy is employed in deriving the equations of motion of the particles. The particles are either attracted or repelled and dissipative dynamical systems can be simulated to achieve optimal and near-optimal arrangements of points. The design domain is set up as an Nvar-dimensional unit hypercube, with Nvar being the number of variables (factors). The number of points is equal to the number of simulations (levels). The periodicity assumption of the design domain is shown to be an elegant way to obtain statistically uniform coverage of the design domain. The ϕp criterion, which is a generalization of the Maximin criterion, is selected in order to demonstrate its analogy with an N-body system. This criterion guarantees that the points are spread uniformly within the design domain. The solution to such an N-body system is presented. The obtained designs are shown to outperform the existing optimal designs in various types of applications: multidimensional numerical integration, statistical exploration of computer models, reliability analyses of engineering systems, and screenings or exploratory designs for the global optimization/minimization of functions.

Klasifikace

  • Druh

    J<sub>imp</sub> - Článek v periodiku v databázi Web of Science

  • CEP obor

  • OECD FORD obor

    20101 - Civil engineering

Návaznosti výsledku

  • Projekt

    <a href="/cs/project/GA16-22230S" target="_blank" >GA16-22230S: Rozvoj pokročilých simulačních metod pro statistickou analýzu konstrukcí</a><br>

  • Návaznosti

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Ostatní

  • Rok uplatnění

    2019

  • Kód důvěrnosti údajů

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Údaje specifické pro druh výsledku

  • Název periodika

    ADVANCES IN ENGINEERING SOFTWARE

  • ISSN

    0965-9978

  • e-ISSN

    1873-5339

  • Svazek periodika

    137

  • Číslo periodika v rámci svazku

    102709

  • Stát vydavatele periodika

    GB - Spojené království Velké Británie a Severního Irska

  • Počet stran výsledku

    16

  • Strana od-do

    1-16

  • Kód UT WoS článku

    000489017800001

  • EID výsledku v databázi Scopus

    2-s2.0-85071721151