Optimization Using Multiple Dominance Criteria for Aerospace Design Under Uncertainty

Cook, Laurence W.; Jarrett, Jerome P.

doi:10.2514/1.j056951

Cited by 8 publications

(7 citation statements)

References 40 publications

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“…This has motivated the development of several optimization formulations that consider the probability distribution in its entirety . Similarly in Reference , where we used multiple dominance criteria whose optimal sets were guaranteed to have a nonempty intersection, giving a trivial overall preorder over design space to use in optimization.…”

Section: Design Under Uncertaintymentioning

confidence: 99%

“…Illustration of Pareto dominance of moments and stochastic dominance of corresponding CDFs for hypothetical designs (adapted from Reference ). A, Pareto dominance.…”

Section: Design Under Uncertaintymentioning

confidence: 99%

“…We cannot formulate this problem using the approaches of Reference , but can using the approach developed in this article. To demonstrate, we consider the following test problem:

g (x, u) = 9 + 2 (5 u_{1} u_{2} x_{1} + x_{2} u_{2}^{2} + x_{2} u_{2}^{3} + 2.5 ‖ x - [0.1, 0.4] ‖^{2}),

where x ∈[−0.5,0.5] 2 is the vector of design variables that can be controlled, and u is the realization of an uncontrollable random input, denoted U , which is uniformly distributed over [−1,1] 2 .…”

Section: Design Under Uncertaintymentioning

confidence: 99%

“…A design should be both robust (often quantified by low variance of the quantity of interest) but also give a high probability of good performance. In many cases, minimizing variance can result in designs that are robust, but whose CDFs lie entirely at worse values than other designs; such designs are said to be stochastically dominated . Therefore, we would be interested in obtaining the most robust design that is not stochastically dominated, which is equivalent to finding the design with the lowest variance within the set of stochastically nondominated designs.…”

Section: Introductionmentioning

confidence: 99%

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Design optimization using multiple dominance relations

Cook

Willcox

Jarrett

2020

Numerical Meth Engineering

Self Cite

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A challenge in engineering design is to choose suitable objectives and constraints from many quantities of interest, while ensuring an optimization is both meaningful and computationally tractable. We propose an optimization formulation that can take account of more quantities of interest than existing formulations, without reducing the tractability of the problem. This formulation searches for designs that are optimal with respect to a binary relation within the set of designs that are optimal with respect to another binary relation. We then propose a method of finding such designs in a single optimization by defining an overall ranking function to use in optimizers, reducing the cost required to solve this formulation. In a design under uncertainty problem, our method obtains the most robust design that is not stochastically dominated faster than a multiobjective optimization. In a car suspension design problem, our method obtains superior designs according to a k-optimality condition than previously suggested multiobjective approaches to this problem. In an airfoil design problem, our method obtains designs closer to the true lift/drag Pareto front using the same computational budget as a multiobjective optimization. K E Y W O R D Saerodynamics, engineering design, optimization, probabilistic methods, shape design, suspension design, transonic *A binary relation is a comparison of two designs that determines whether one is better than the other, and for an optimal design no better design exists with respect to the relation. 3 Int J Numer Methods Eng. 2020;121:2481-2502.wileyonlinelibrary.com/journal/nme

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Section: Design Under Uncertaintymentioning

confidence: 99%

“…Illustration of Pareto dominance of moments and stochastic dominance of corresponding CDFs for hypothetical designs (adapted from Reference ). A, Pareto dominance.…”

Section: Design Under Uncertaintymentioning

confidence: 99%

“…We cannot formulate this problem using the approaches of Reference , but can using the approach developed in this article. To demonstrate, we consider the following test problem:

g (x, u) = 9 + 2 (5 u_{1} u_{2} x_{1} + x_{2} u_{2}^{2} + x_{2} u_{2}^{3} + 2.5 ‖ x - [0.1, 0.4] ‖^{2}),

Section: Design Under Uncertaintymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design optimization using multiple dominance relations

Cook

Willcox

Jarrett

2020

Numerical Meth Engineering

Self Cite

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show abstract

“…Dynamic disturbances and unmodeled dynamics widely exist in many physical systems, such as power industries [17,18] and aerospace systems [19,20]. Inherently, nonlinear and uncertainty characteristics of system dynamics are difficult to model.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Platoon Control for Marine Surface Vehicles in the Presence of Constraints

Liang

Wang

2020

Complexity

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This paper presents the platoon formation control design for unmanned surface vehicles with input and output constraints. First, Barrier Lyapunov Function (BLF) is employed to ensure the desired line-of-sight (LOS) range. The LOS range should be maintained within the predefined regions between each marine vehicle and its predecessor while the connected platoons track the trajectory. Next, to handle the model uncertainties and unknown external disturbance, we propose an adaptive neural network controller that approximates the unknown nonlinearities. Furthermore, the Nussbaum function is applied to compensate for input saturations. In addition, formation errors can be guaranteed by stability analysis. The distance between two consecutive agents does not violate collision avoidance and connectivity in the presence of input saturation. Finally, the feasibility of the theoretical results is illustrated through the simulation results.

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Optimum aerodynamic shape design under uncertainty by utility theory and metamodeling

Leifsson

2019

Aerospace Science and Technology

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Optimization Using Multiple Dominance Criteria for Aerospace Design Under Uncertainty

Cited by 8 publications

References 40 publications

Design optimization using multiple dominance relations

Design optimization using multiple dominance relations

Adaptive Platoon Control for Marine Surface Vehicles in the Presence of Constraints

Optimum aerodynamic shape design under uncertainty by utility theory and metamodeling

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