Identification of random shapes from images through polynomial chaos expansion of random level set functions

• Published in: International journal for numerical methods in engineering Vol. 79; no. 2; pp. 127 - 155
• Main Authors: Stefanou, G., Nouy, A., Clement, A.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 09.07.2009; Wiley
• Subjects: Applied sciences; Artificial intelligence; Chaos theory; Computer science; control theory; systems; Computer simulation; Engineering Sciences; Equivalence; Exact sciences and technology; extended stochastic finite element method; level set method; Mathematical analysis; Mathematical models; Mathematics; maximum likelihood; Mechanics; Numerical Analysis; Pattern recognition. Digital image processing. Computational geometry; Polycarbonates; polynomial chaos; probabilistic identification; random geometry; Strategy; Chaos; Probabilistic approach; Image databank; Contour line; Shape detection; Modeling; Orthogonal polynomial; polynomial chaos; Image segmentation; Uncertain system; extended stochastic finite element method; level set method; Random set; Random function; Maximum likelihood; random geometry; probabilistic identification; Structural analysis; eXtended Finite Element Method; Random geometry; Extended stochastic finite element method; Polynomial chaos; Level-set method; Probabilistic identification
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2546

In this paper, an efficient method is proposed for the identification of random shapes in a form suitable for numerical simulation within the extended stochastic finite element method (X‐SFEM). The method starts from a collection of images representing different outcomes of the random shape to identify. The key point of the method is to represent the random geometry in an implicit manner using the level set technique. In this context, the problem of random geometry identification is equivalent to the identification of a random level set function, which is a random field. This random field is represented on a polynomial chaos (PC) basis and various efficient numerical strategies are proposed in order to identify the coefficients of its PC decomposition. The performance of these strategies is evaluated through some ‘manufactured’ problems and useful conclusions are provided. The propagation of geometrical uncertainties in structural analysis using the X‐SFEM is finally examined. Copyright © 2009 John Wiley & Sons, Ltd.