Efficient shape optimization for certain and uncertain aerodynamic design

Schillings, Claudia; Schmidt, Stephan; Schulz, Volker

doi:10.1016/j.compfluid.2010.12.007

Cited by 63 publications

(40 citation statements)

References 36 publications

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“…One classical approach is to propagate the randomness into the whole chain and get a noisy functional. And then assimilate this functional by a low-complexity model and design for this new functional [3,8,12]. This approach demands for a priori regularity hypothesis for the reduced-order model and trust regions definition.…”

Section: Simulation Under Uncertaintymentioning

confidence: 99%

“…Recent works, however, show ways to include these. In [3], authors, after making a priori hypothesis on shape uncertainties, use proper orthogonal decomposition together with sparse grid sampling [4] to reduce the probability space and a polynomial chaos propagation method [5] to evaluate the effect of the uncertainties on the functional in a nonintrusive way. Minimization can then be performed involving different functional momentums.…”

Section: Introductionmentioning

confidence: 99%

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Value at risk for confidence level quantifications in robust engineering optimization

Mohammadi

2013

Optim Control Appl Methods

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Abstract. We show how to introduce the Value at Risk (VaR) concept in optimization algorithms with emphasis in calculation complexity issues. To do so we assume known the PDF of the uncertainties. Our aim is to quantify our confidence on the optimal solution at low complexity without a sampling of the control space. The notion of over-solving appears naturally where it becomes useless to solve accurately near an optimum when the variations in control parameters fall below the uncertainties. Examples show the behavior of this VaR-based correction and link the approach to momentum-based optimization where the mean and variance of a functional are considered. The approach is then applied to an inverse problem with fluids with uncertainties in the definition of the injection devices. It is shown that an optimization problem with an admissible solution in the control space in the deterministic case can lose its solution in the presence of uncertainties on the control parameters which suggests that the control space itself should be redefined in such a situation to recover an admissible problem. This permits to evaluate the cost of making reliable a system which has been deterministically designed, but which has uncertain parameters. A shape optimization problem closes the paper showing the importance of including VaR information during the design iterations and not only at the end.

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Section: Simulation Under Uncertaintymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Value at risk for confidence level quantifications in robust engineering optimization

Mohammadi

2013

Optim Control Appl Methods

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“…These questions are important as today industrial robust design mainly relies on reduced order modelling and intelligent sampling [2,3,4,6] which either does not use high-fidelity simulations during design or uses lower accuracy than what would be affordable in a mono-point optimization. Our aim is to propose a plausible alternative.…”

Section: Introductionmentioning

confidence: 99%

Reduced sampling and incomplete sensitivity for low‐complexity robust parametric optimization

Mohammadi

2013

Numerical Methods in Fluids

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To cite this version:Bijan Mohammadi. Reduced sampling and incomplete sensitivity for low-complexity robust parametric optimization. International Journal for Numerical Methods in Fluids, Wiley, 2013, 73 (4) Abstract. The paper considers robust parametric optimization problems using multi-point formulations and makes the link with momentum based formulations. Optimal sampling issues are discussed and a procedure is proposed to quantify the confidence level on the robustness of the design. We also discuss incomplete sensitivity evaluations to take into account the computational complexity constraint. This permits to take advantage of what was previously developed for efficient mono-point design where the cost of the optimization is comparable to one state evaluations. The proposed algorithm is fully parallel and the time-to-solution is comparable to mono-point situations. Concepts are introduced through simple examples and the paper ends with the design of the shape of an aircraft robust over a range of transverse winds.

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“…e(s) = 0. Random fields have previously been used to model geometric variability in airfoils [9,10]. This approach is closely related to PCA based models of geometric variability [1,4].…”

Section: Modelling Geometric Variabilitymentioning

confidence: 99%

Simultaneous Robust Design and Tolerancing of Compressor Blades

Dow

Wang

2014

Volume 2B: Turbomachinery

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The manufacturing processes used to create compressor blades inevitably introduce geometric variability to the blade surface. In addition to increasing the performance variability, it has been observed that introducing geometric variability tends to reduce the mean performance of compressor blades. For example, the mean adiabatic efficiency observed in compressor blades with geometric variability are typically lower than the efficiency in the absence of variability [?]. This "mean-shift" in performance leads to increased operating costs over the life of the compressor blade. These detrimental effects can be reduced by using robust optimization techniques to optimize the blade geometry. The impact of geometric variability can also be reduced by imposing stricter tolerances, thereby directly reducing the allowable level of variability. However, imposing stricter manufacturing tolerances increases the cost of manufacturing. Thus, the blade design and tolerances must be chosen with both performance and manufacturing cost in mind.This paper presents a computational framework for performing simultaneous robust design and tolerancing of compressor blades subject to manufacturing variability. The manufacturing variability is modelled as a Gaussian random field with non-stationary variance to simulate the effects of spatially varying manufacturing tolerances. The statistical performance of the compressor blade system is evaluated using the Monte Carlo method. A gradient based optimization scheme is used to deter- * Corresponding author mine the optimal blade geometry and distribution of manufacturing tolerances. NOMENCLATUREA You may include nomenclature here. α There are two arguments for each entry of the nomemclature environment, the symbol and the definition.The spacing between abstract and the text heading is two line spaces. The primary text heading is boldface in all capitals, flushed left with the left margin. The spacing between the text and the heading is also two line spaces. INTRODUCTIONThis article illustrates preparation of ASME paper using L A T E X2 ε . The L A T E X macro asme2e.cls, the BIBT E X style file asmems4.bst, and the template asme2e.tex that create this article are available on the WWW at the URL address http://iel.ucdavis.edu/code/. To ensure compliance with the 2003 ASME MS4 style guidelines [?], you should modify neither the L A T E X macro asme2e.cls nor the BIBT E X style file asmems4.bst. By comparing the output generated by typesetting this file and the L A T E X2 ε source file, you should find everything you need to help you through the preparation of ASME paper using L A T E X2 ε . Details on

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Efficient shape optimization for certain and uncertain aerodynamic design

Cited by 63 publications

References 36 publications

Value at risk for confidence level quantifications in robust engineering optimization

Value at risk for confidence level quantifications in robust engineering optimization

Reduced sampling and incomplete sensitivity for low‐complexity robust parametric optimization

Simultaneous Robust Design and Tolerancing of Compressor Blades

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