Uncertainty based robust optimization method for drag minimization problems in aerodynamics

Tang, Zhili; Périaux, Jacques

doi:10.1016/j.cma.2011.12.011

Cited by 26 publications

(9 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, following Taguchi's definition, one can look for minimal-variance design or only a given level for the variance. Indeed, a classical approach to extend single point design and improve off-design points is to control mean performance and variance of the functional [6]. One can also look for information about the tails of the distributions which can be linked to the variance in the Gaussian framework (we will use this relationship in section 3 in quantile-based extreme scenarios).…”

Section: Parametric Optimizationmentioning

confidence: 99%

Ensemble Kalman Filters and geometric characterization of sensitivity spaces for uncertainty quantification in optimization

Mohammadi

2015

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

We present an original framework for uncertainty quantification (UQ) in optimization. It is based on a cascade of ingredients with growing computational complexity for both forward and reverse uncertainty propagation. The approach is merely geometric. It starts with a complexity-based splitting of the independent variables and the definition of a parametric optimization problem. Geometric characterization of global sensitivity spaces through their dimensions and relative positions by the principal angles between global search subspaces bring a first set of information on the impact of uncertainties on the functioning parameters on the optimal solution. Joining the multi-point descent direction and the quantiles on the optimization parameters permits to define the notion of Directional Extreme Scenarios (DES) without sampling of large dimension design spaces. One goes beyond DES with Ensemble Kalman Filters (EnKF) after the multi-point optimization algorithm is cast into an ensemble simulation environment. This formulation accounts for the variability in large dimension. The UQ cascade ends with the joint application of the EnKF and DES leading to the concept of Ensemble Directional Extreme Scenarios (EDES) which provides more exhaustive possible extreme scenarios knowing the Probability Density Function of our optimization parameters. A final interest of the approach is that it provides an indication of the size of the ensemble which must be considered in the EnKF. These ingredients are illustrated on an history matching problem.

show abstract

Section: Parametric Optimizationmentioning

confidence: 99%

Ensemble Kalman Filters and geometric characterization of sensitivity spaces for uncertainty quantification in optimization

Mohammadi

2015

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…These 2 clear trends make the flow around the blade more uncertain and make the performance requirements of the blade more complex and comprehensive. Considerable investigations have been conducted on robust design to find both high performance and low sensitivity solutions to uncertain operation conditions in aviation engineering . Detailed reviews on robust design can be found in the literature .…”

Section: Introductionmentioning

confidence: 99%

Overall design optimization of dedicated outboard airfoils for horizontal axis wind turbine blades

Yang

Liao

et al. 2018

Wind Energy

View full text Add to dashboard Cite

Designing the primary airfoils for the outboard part of wind turbine blades is a complicated problem of balancing structural, aerodynamic, and acoustic requirements. This paper presents an optimization method for the overall performance of outboard wind turbine airfoils. Based on the complex flow characteristics of the rotor blades and the varying requirements along the span of a blade, the design principles of outboard airfoils were investigated. The requirements for improving the structural performance and reducing the aerodynamic noise were combined with the following aerodynamic design considerations: high efficiency, low extreme loads, stability, and a wide operating region. Thus, this paper proposes a new mathematical model for overall airfoil optimization using the airfoil performance evaluation indicators. Then, an integrated optimization design platform is established for outboard airfoils. Through 2 design cases, new airfoils with desirable aerodynamic characteristics and improved overall performance were obtained.Comparisons between the new airfoils and reference airfoils based on numerical predictions indicate that the proposed method with the newly established mathematical model can effectively balance the complex requirements of the airfoil and improve its overall performance. More notably, the design cases also indicate that the established optimization design method can be used to address special designs of outboard airfoils for different blade requirements. KEYWORDS evaluation parameters, horizontal axis wind turbine, integrated design platform, numerical optimization method, outboard airfoils, overall performance 1 | INTRODUCTION Dedicated airfoils for horizontal axis wind turbines (HAWTs) have evolved over the past several decades and have received increasing attention in recent years because of the increasingly complex aerodynamic and structural requirements of the rotor blades. The airfoil is the profile of the blade cross section, and its performance determines the energy capture performance of the blade. Special airfoils for wind turbines were initially designed in the 1980s. 1 Later, they were intensively developed by the National Renewable Energy Laboratory (NREL), 2 TU Delft, 3 and RISØ, 4 and they have recently nearly replaced traditional aviation airfoils in blade designs. However, with the development of upscaling rotor blades and regional wind farms, the efficient design of special blades operating in different conditions requires advanced airfoils with improved overall performance.Specifically, design methods for improving the overall airfoil performance need to be developed.The early airfoils specially created for wind turbines were designed using the inverse method. 5,6 With the help of subsonic, low Re flow solvers, 7-9 researchers developed some commonly used wind turbine airfoils. However, the inverse design method cannot effectively address the multiobjective design problem. The objectives mainly focused on several aerodynamic force coefficients, such as c l,design or l/d max ...

show abstract

“…Fisher [1] started working on robust design method in early 1920s with the development of statistical design of experiments (DoE) approach to improve the yield of agricultural crops. Taguchi [2], a Japanese engineer, also known as father of robust design, developed the foundation of robust design during 1950's [3,4]. Aerodynamic shape optimization has become integral part in the design of aerodynamic components such as aircraft wing.…”

mentioning

confidence: 99%

Surrogate-based robust design optimization of airfoil using inexpensive Monte Carlo method

Shahbaz

Han

Song

et al. 2016

2016 13th International Bhurban Conference on Applied Sciences and Technology (IBCAST)

View full text Add to dashboard Cite

This paper presents an efficient robust design optimization under the uncertainty quantification (UQ) of aleatory flight conditions using inexpensive Monte Carlo (IMC) method. Robust design optimization (RDO) technique is used to reduce the statistical moments of drag coefficient of an airfoil subject to some aerodynamic and geometric constraints. IMC approach with kriging surrogate model has been utilized to evaluate the robustness of a candidate design for prediction of statistical parameters and probability density functions of output response quantities. CFD calculations of RAE2822 airfoil have been evaluated using in-house code, PMNS2D. Combination of CFD input flight parameters such as free stream Mach number and angle of attack are varied and the propagation of their corresponding aleatory uncertainties on output properties of interest is studied. The reduction in objective function (C d ) is about 37.48% and 39.19% for combination of Mach and alpha uncertainties under Gaussian and LHS distributions respectively. Probability density function (PDF) of an output uncertainty is also compared with real PDF and found in good agreement with each other.

show abstract

Uncertainty based robust optimization method for drag minimization problems in aerodynamics

Cited by 26 publications

References 15 publications

Ensemble Kalman Filters and geometric characterization of sensitivity spaces for uncertainty quantification in optimization

Ensemble Kalman Filters and geometric characterization of sensitivity spaces for uncertainty quantification in optimization

Overall design optimization of dedicated outboard airfoils for horizontal axis wind turbine blades

Surrogate-based robust design optimization of airfoil using inexpensive Monte Carlo method

Contact Info

Product

Resources

About