Open Access

REVIEW

Optimization-Based Approaches to Uncertainty Analysis of Structures Using Non-Probabilistic Modeling: A Review

Yoshihiro Kanno^1,*, Izuru Takewaki²

1 Mathematics and Informatics Center, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-8656, Japan
2 Department of Architecture, Kyoto Arts and Crafts University, Kawabata-Shichijo-Agaru, Higashiyama-Ku, Kyoto, 605-0991, Japan

* Corresponding Author: Yoshihiro Kanno. Email: -tokyo.ac.jp

Computer Modeling in Engineering & Sciences 2025, 143(1), 115-152. https://doi.org/10.32604/cmes.2025.061551

Received 27 November 2024; Accepted 18 February 2025; Issue published 11 April 2025

Abstract

Response analysis of structures involving non-probabilistic uncertain parameters can be closely related to optimization. This paper provides a review on optimization-based methods for uncertainty analysis, with focusing attention on specific properties of adopted numerical optimization approaches. We collect and discuss the methods based on nonlinear programming, semidefinite programming, mixed-integer programming, mathematical programming with complementarity constraints, difference-of-convex programming, optimization methods using surrogate models and machine learning techniques, and metaheuristics. As a closely related topic, we also overview the methods for assessing structural robustness using non-probabilistic uncertainty modeling. We conclude the paper by drawing several remarks through this review.

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Keywords

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