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

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. W...

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Bibliographic Details
Published in:Computer modeling in engineering & sciences Vol. 143; no. 1; pp. 115 - 152
Main Authors: Kanno, Yoshihiro, Takewaki, Izuru
Format: Journal Article
Language:English
Published: Henderson Tech Science Press 2025
Subjects:
Algorithms
Convexity
Design optimization
Design specifications
Fuzzy sets
Heuristic methods
Integer programming
Machine learning
Mathematical programming
Mixed integer
Nonlinear programming
Optimization
Parameter uncertainty
Probabilistic models
Probability theory
Random variables
Semidefinite programming
Uncertainty analysis
ISSN:1526-1506, 1526-1492, 1526-1506
Online Access:Get full text
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Summary: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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ISSN:1526-1506
1526-1492
1526-1506
DOI:10.32604/cmes.2025.061551