Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
On combining feasibility, descent and superlinear convergence in inequality constrained optimization
Mathematical Programming: Series A and B
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Computational Statistics & Data Analysis
Dimension reduction method for reliability-based robust design optimization
Computers and Structures
Efficient uncertainty quantification with the polynomial chaos method for stiff systems
Mathematics and Computers in Simulation
Approximate confidence interval for standard deviation of nonnormal distributions
Computational Statistics & Data Analysis
Design optimization for robustness in multiple performance functions
Structural and Multidisciplinary Optimization
On robust design optimization of truss structures with bounded uncertainties
Structural and Multidisciplinary Optimization
Robust design optimization by polynomial dimensional decomposition
Structural and Multidisciplinary Optimization
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This paper proposes formulations and algorithms for design optimization under both aleatory (i.e., natural or physical variability) and epistemic uncertainty (i.e., imprecise probabilistic information), from the perspective of system robustness. The proposed formulations deal with epistemic uncertainty arising from both sparse and interval data without any assumption about the probability distributions of the random variables. A decoupled approach is proposed in this paper to un-nest the robustness-based design from the analysis of non-design epistemic variables to achieve computational efficiency. The proposed methods are illustrated for the upper stage design problem of a two-stage-to-orbit (TSTO) vehicle, where the information on the random design inputs are only available as sparse point data and/or interval data. As collecting more data reduces uncertainty but increases cost, the effect of sample size on the optimality and robustness of the solution is also studied. A method is developed to determine the optimal sample size for sparse point data that leads to the solutions of the design problem that are least sensitive to variations in the input random variables.