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