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Generation of non-gaussian tensor-valued random fields using an isde-based algorithm

Publication ,  Conference
Guilleminot, J; Soize, C
Published in: Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013
December 1, 2013

This work is concerned with the construction of a random generator for non-Gaussian tensorvalued random fields. Specifically, it focuses on the generation of the class of Prior Algebraic Stochastic Models associated with elliptic operators, for which the family of first-order marginal probability distributions is constructed using the MaxEnt principle. The strategy essentially relies on the definition of a family of diffusion processes, the invariant measures of which coincide with the target system of first-order marginal probability distributions. Those processes are classically defined as the unique stationary solutions of a family of Itô stochastic differential equations, the definition of which involves the construction of a family of normalized Wiener processes. The definition of the later allows spatial dependencies to be generated and the algorithm turns out to be very efficient for high probabilistic dimensions - it does not suffer from the curse of dimensionnality that is inherently exhibited by Gaussian chaos expansions, for instance. The algorithm is finally exemplified through the generation of a matrix-valued non-Gaussian random field. © 2013 Taylor & Francis Group, London.

Duke Scholars

Published In

Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013

Publication Date

December 1, 2013

Start / End Page

2793 / 2798
 

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Guilleminot, J., & Soize, C. (2013). Generation of non-gaussian tensor-valued random fields using an isde-based algorithm. In Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013 (pp. 2793–2798).
Guilleminot, J., and C. Soize. “Generation of non-gaussian tensor-valued random fields using an isde-based algorithm.” In Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013, 2793–98, 2013.
Guilleminot J, Soize C. Generation of non-gaussian tensor-valued random fields using an isde-based algorithm. In: Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013. 2013. p. 2793–8.
Guilleminot, J., and C. Soize. “Generation of non-gaussian tensor-valued random fields using an isde-based algorithm.” Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013, 2013, pp. 2793–98.
Guilleminot J, Soize C. Generation of non-gaussian tensor-valued random fields using an isde-based algorithm. Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013. 2013. p. 2793–2798.

Published In

Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013

Publication Date

December 1, 2013

Start / End Page

2793 / 2798