We develop a numerical method for the computation of a minimal convex and compact set, , in the sense of mean width. This minimisation is constrained by the requirement that for all unit vectors given some Lipschitz function .
This problem arises in the construction of environmental contours under the assumption of convex failure sets. Environmental contours offer descriptions of extreme environmental conditions commonly applied for reliability analysis in the early design phase of marine structures. Usually, they are applied in order to reduce the number of computationally expensive response analyses needed for reliability estimation.
We solve this problem by reformulating it as a linear programming problem. Rigorous convergence analysis is performed, both in terms of convergence of mean widths and in the sense of the Hausdorff metric. Additionally, numerical examples are provided to illustrate the presented methods.
Keywords: Environmental Contours, Linear Programming, Structural Reliability
Åsmund Hausken Sande 1; Johan S. Wind 1
CC-BY 4.0
@article{SMAI-JCM_2024__10__55_0,
author = {\r{A}smund Hausken Sande and Johan S. Wind},
title = {Minimal {Convex} {Environmental} {Contours}},
journal = {The SMAI Journal of computational mathematics},
pages = {55--83},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {10},
year = {2024},
doi = {10.5802/smai-jcm.106},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.106/}
}
TY - JOUR AU - Åsmund Hausken Sande AU - Johan S. Wind TI - Minimal Convex Environmental Contours JO - The SMAI Journal of computational mathematics PY - 2024 SP - 55 EP - 83 VL - 10 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.106/ DO - 10.5802/smai-jcm.106 LA - en ID - SMAI-JCM_2024__10__55_0 ER -
%0 Journal Article %A Åsmund Hausken Sande %A Johan S. Wind %T Minimal Convex Environmental Contours %J The SMAI Journal of computational mathematics %D 2024 %P 55-83 %V 10 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.106/ %R 10.5802/smai-jcm.106 %G en %F SMAI-JCM_2024__10__55_0
Åsmund Hausken Sande; Johan S. Wind. Minimal Convex Environmental Contours. The SMAI Journal of computational mathematics, Volume 10 (2024), pp. 55-83. doi : 10.5802/smai-jcm.106. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.106/
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