Dynamical Model of Interacting Particles for the Construction of Audze–Eglajs Designs in a Periodic Space

Dynamical Model of Interacting Particles for the Construction of Audze–Eglajs Designs in a Periodic Space

Paper in proceedings (conference paper)

The paper presents a dynamical model of mutually interacting particles in a periodic space designed to provide optimal sets of points for numerical integration. The obtained set of points is applied to Monte Carlo type integration in statistical analyses of computer models. The dynamical model mimics the behavior of charged particles with repulsive forces that are based on a selected formulation of potential. When the kinetic energy of the damped particle system approaches zero, the potential energy is reaches a local minimum. The domain within which the particles are to be distributed is a unit hypercube of a dimension equal to the number of basic variables for Monte Carlo integration. It is shown to be necessary for the design domain to be periodically repeated in order to obtain statistically uniform coverage by the points. The gained coordinates of the points in the unit hypercube are then transformed into the real space of variables in the analyzed model and used as integration points (realizations of random variables). The quality or optimality of the resulting design is dependent on the distance-based constitutive law that is derived from the assumed potential

The paper presents a dynamical model of mutually interacting particles in a periodic space designed to provide optimal sets of points for numerical integration. The obtained set of points is applied to Monte Carlo type integration in statistical analyses of computer models. The dynamical model mimics the behavior of charged particles with repulsive forces that are based on a selected formulation of potential. When the kinetic energy of the damped particle system approaches zero, the potential energy is reaches a local minimum. The domain within which the particles are to be distributed is a unit hypercube of a dimension equal to the number of basic variables for Monte Carlo integration. It is shown to be necessary for the design domain to be periodically repeated in order to obtain statistically uniform coverage by the points. The gained coordinates of the points in the unit hypercube are then transformed into the real space of variables in the analyzed model and used as integration points (realizations of random variables). The quality or optimality of the resulting design is dependent on the distance-based constitutive law that is derived from the assumed potential

Dynamical particle system, sample optimization, space filling designs

Dynamical particle system, sample optimization, space filling designs

VOŘECHOVSKÝ, M.; MAŠEK, J.; ELIÁŠ, J.

2018

10.08.2017

TU-Verlag Vienna

Vienna

978-3-903024-28-1

Proceedings of 12th Int. Conf. on Structural Safety and Reliability

1374

1383

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