6533b839fe1ef96bd12a6479

RESEARCH PRODUCT

General framework for testing Poisson-Voronoi assumption for real microstructures

Jilt SietsmaGeurt JongbloedMartina VittoriettiWei LiPiet Kok

subject

FOS: Computer and information sciencesreal microstructuresPoisson-Voronoi diagrams0211 other engineering and technologies02 engineering and technologyManagement Science and Operations ResearchPoisson distribution01 natural sciencesStatistics - ApplicationsMethodology (stat.ME)Set (abstract data type)010104 statistics & probabilitysymbols.namesakehypothesis testingPeriodic boundary conditionsApplied mathematicsApplications (stat.AP)0101 mathematicsStatistics - MethodologyStatistical hypothesis testing021103 operations researchCumulative distribution functionDiagramscalingGeneral Business Management and Accounting62P30 62-00 62-01 62G10persistence landscapeModeling and SimulationsymbolsTopological data analysiscumulative distribution functionVoronoi diagram

description

Modeling microstructures is an interesting problem not just in Materials Science but also in Mathematics and Statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single phase steel microstructures. The aim of this paper is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson-Voronoi assumption based on images of 2D sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, three different model tests are proposed. The first two are based on the coefficient of variation and the cumulative distribution function of the cells area. The third exploits tools from to Topological Data Analysis, such as persistence landscapes.

yearjournalcountryeditionlanguage
2020-02-11Applied Stochastic Models in Business and Industry
10.1002/asmb.2517http://resolver.tudelft.nl/uuid:397d7b83-633b-4da6-9605-088fe3fefc95