Optimizations Under Uncertainty Using Gradients, Hessians, and Surrogate Models

Rumpfkeil, Markus P.

doi:10.2514/1.j051847

Cited by 31 publications

(11 citation statements)

References 52 publications

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“…The steps involved in robust optimization under mixed uncertainties [20][21][22]25 are detailed here (see Figure 5). Surrogate models are built to propagate aleatory uncertainties and bound-constrained optimizations are used to propagate epistemic uncertainties.…”

Section: Iic3 Robust Optimization Frameworkmentioning

confidence: 99%

“…The employed IMCS-BCO framework has been developed by Lockwood et al [20][21][22] and Rumpfkeil. 25 A detailed discussion of all the steps involved is given in Section II.C.3. The computational requirements in Table 1 are given for just one iteration of the numerical solution of the robust optimization problem.…”

Section: Iib3 Propagation Of Mixed Uncertaintiesmentioning

confidence: 99%

“…In comparison, the aleatory gradient was easy to obtain because the same surrogate model is used and only the change in sample points (random realizations) has to be accounted for. In this work the following approximations are used: 25 dµ…”

Section: Iic4 Gradient Evaluationmentioning

confidence: 99%

See 2 more Smart Citations

Robust Optimizations of Structural and Aerodynamic Designs

Boopathy

Rumpfkeil

2014

15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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This paper demonstrates the use of polynomial chaos and kriging surrogate models, which are enhanced with a dynamic training point selection framework, for the propagation of mixed epistemic and aleatory uncertainties in robust optimization problems. The selection of training points for the two surrogate models is guided by local surrogate models (multivariate interpolation and regression) which are built using a subset of the available training data. The aleatory uncertainties are propagated via extensive sampling of the surrogate models, whereas the epistemic uncertainties are propagated using a box-constrained optimization approach. Robust optimizations are demonstrated for two structural and one aerodynamic test problem. The structural test cases include designing a three-bar truss and a cantilever beam, whereas the aerodynamic test case involves the robust lift-constrained drag minimization of an airfoil under transonic flow conditions.

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Section: Iic3 Robust Optimization Frameworkmentioning

confidence: 99%

Section: Iib3 Propagation Of Mixed Uncertaintiesmentioning

confidence: 99%

See 1 more Smart Citation

Robust Optimizations of Structural and Aerodynamic Designs

Boopathy

Rumpfkeil

2014

15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

Self Cite

View full text Add to dashboard Cite

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“…For instance, uncertainties on the geometric parameters [17][18][19] and on the operating conditions [20,21] fall into this category. Other research focused more on epistemic uncertainties, which represent a lack of knowledge associated with the modeling process, that are reducible through the introduction of additional information [22].…”

Section: Introductionmentioning

confidence: 99%

Multifidelity Physics-Based Method for Robust Optimization Applied to a Hovering Rotor Airfoil

et al. 2015

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The paper presents a multifidelity robust optimization technique with application to the design of rotor blade airfoils in hover. A genetic algorithm is coupled with a non-intrusive uncertainty propagation technique based on polynomial chaos expansion to determine the robust optimal airfoils that maximize the mean value of the lift-to-drag ratio while minimizing the variance, under uncertain operating conditions. Uncertainties on the blade pitch angle and induced velocity are considered. To deal with the variable operating conditions induced by the considered uncertainties and to alleviate the computational cost of the optimization procedure, a multifidelity strategy is developed that exploits two aerodynamic models of different fidelity. The two models correspond to different physical descriptions of the flowfield around the airfoil; thus, the multifidelity method employs the low-fidelity model in regions of the stochastic space where the physics of the problem is well captured by the model, and it switches to high-fidelity estimates only where needed. The proposed robust optimization technique is compared with the robust optimization based on the high-fidelity aerodynamic model and the deterministic optimization, to assess the capability of finding a consistent Pareto set and to evaluate the numerical efficiency. The results obtained show how the robust multifidelity approach is effective in reducing the sensitivity of the designed airfoils with respect to variation in the operating conditions

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“…These discrepancies can for instance be caused by manufacturing tolerances [77] or approximations in the numerical model. The existence of these discrepancies can be taken into account by applying an optimization under uncertainty [87,149] approach. By using such an approach, the result of solving an optimization problem is more likely to show optimal performance in reality as well.…”

Section: Optimization Methodsmentioning

confidence: 99%

O a method for simulation-based wind turbine blade design

Jongsma¹

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SummaryW ind turbines are an important means for the production of renewable energy. This energy, commonly referred to as wind energy, is produced by extracting the kinetic energy from the wind and to subsequently convert it, usually via a rotational motion, to electrical energy. Wind conditions vary from one site to another and the design of a horizontal axis wind turbine depends on these local wind conditions. One of the important aspects of the design of a wind turbine concerns the aerodynamic shape of the rotor blades. The research presented in this thesis focusses on the development of a computational method that can be used for aerodynamic shape optimization.Other aspects -apart from the aerodynamic shape of a wind turbine rotor bladeare also important in the design of a wind turbine, for instance the structural design of the blade. To take this multidisciplinary character of wind turbine design into account, one of the aims of the research presented in this thesis has been that the aerodynamic shape optimization method seamlessly fits into the design process. Moreover, the optimization method is required to be efficient and fully automatic.A suitable method for the parametrization of the wind turbine blade geometry has been investigated. This investigation lead to the choice to use a non-uniform rational basis spline (NURBS) surface for representing the aerodynamic shape of the wind turbine blade. Such a description of the parametrization of the geometry is compatible with computer aided design methods, which eases the incorporation of the aerodynamic shape optimization method in the multidisciplinary design process. A model optimization problem has been considered to determine the relation between the number of design variables that is required to sufficiently accurately represent the design space for solving an aerodynamic shape optimization problem to the number of design variables that is required to realize an accurate NURBS representation of an aerodynamic shape. For the purpose of obtaining a NURBS surface representation of a wind turbine rotor blade, a fitting procedure has been developed. The accuracy of the resulting fit for two representative wind turbine blades is presented. It has been found that sufficient accuracy can be achieved with a NURBS surface described by 13 chordwise sections with 13 control points each.In the present research, objective functions are considered for which the evaluation requires the solution of partial differential equations that govern flow: the Euler equations. Since only for very particular flow configurations an analytical solution of these equations can be found, an approximate solution is computed by solving the discretized equations. Solving the discretized Euler equations requires the discretization of the whole flow domain. During the optimization procedure, the geometry of the rotor blade adapts, i Summary requiring a discrete representation of the new flow domain. To accommodate the change in shape during the optimization, a hyperbolic grid generation me...

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Optimizations Under Uncertainty Using Gradients, Hessians, and Surrogate Models

Cited by 31 publications

References 52 publications

Robust Optimizations of Structural and Aerodynamic Designs

Robust Optimizations of Structural and Aerodynamic Designs

Multifidelity Physics-Based Method for Robust Optimization Applied to a Hovering Rotor Airfoil

O a method for simulation-based wind turbine blade design

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