Novel Uncertainty Propagation Method for Robust Aerodynamic Design

Padulo, Mattia; Campobasso, M. Sergio; Guenov, Marin D.

doi:10.2514/1.j050448

Cited by 64 publications

(62 citation statements)

References 55 publications

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“…29,30,31 Similar ideas are explored in Chen et al, who propose a method that reverses the computational flow in a design code. 32 That work builds on the univariate reduced quadrature method of Padulo et al, 33 which represents the QoI standard deviation as a function of the first four moments of a univariate input distribution.…”

Section: Variance Of Component Functions Of Hdmr Fmentioning

confidence: 99%

Sensitivity Analysis Methods for Uncertainty Budgeting in System Design

Opgenoord

Willcox

2016

AIAA Journal

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Quantification and management of uncertainty are critical in the design of engineering systems, especially in the early stages of conceptual design. This paper presents an approach to defining budgets on the acceptable levels of uncertainty in design quantities of interest, such as the allowable risk in not meeting a critical design constraint and the allowable deviation in a system performance metric. A sensitivity-based method analyzes the effects of design decisions on satisfying those budgets, and a multi-objective optimization formulation permits the designer to explore the tradespace of uncertainty reduction activities while also accounting for a cost budget. For models that are computationally costly to evaluate, a surrogate modeling approach based on high dimensional model representation (HDMR) achieves efficient computation of the sensitivities. An example problem in aircraft conceptual design illustrates the approach.

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Section: Variance Of Component Functions Of Hdmr Fmentioning

confidence: 99%

Sensitivity Analysis Methods for Uncertainty Budgeting in System Design

Opgenoord

Willcox

2016

AIAA Journal

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“…The multifidelity result is closer to the HF result with respect to the LF front: using the definition in Eq. (18), the distance d MF-HF of the MF set to the HF set is equal to 9.5, whereas the distance d LF-HF of the LF set to the HF set is 22.8 (see Table 7). Also, the MF method defines a Pareto front on the objective space, whereas the LF results are more sparse and do not present a clear trend.…”

Section: Analysis Of Pareto Frontsmentioning

confidence: 99%

“…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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“…However, even for reduced spread of the input variables, the accuracy of the method may be severely spoiled by non‐linearities in the system response. To overcome such limitations, the univariate reduced quadrature (URQ) propagation technique 1, 47 could be adopted. It estimates mean and variance of f by using the following formulas: The sampling points are found as follows: where e p is the p th vector of the identity matrix of size n and are given as follows: The weights have to be chosen as: ; ; ; ; . The URQ can be thought as a univariate version of the bivariate quadrature method proposed by Evans 48.…”

Section: Worst‐case Rdo Under Distributional Assumptionsmentioning

confidence: 99%

“…It estimates mean and variance of f by using the following formulas: The sampling points are found as follows: where e p is the p th vector of the identity matrix of size n and are given as follows: The weights have to be chosen as: ; ; ; ; . The URQ can be thought as a univariate version of the bivariate quadrature method proposed by Evans 48. Evans's method exhibits an error of in the general case, which reduces to or for symmetric input distributions 48, while the URQ error is for the general case, and if the cross derivatives of order 2 and higher are negligible 1, 47. However, Evans's method requires 2 n 2 + 1 function evaluations per iteration of optimization algorithm, while the URQ requires only 2 n + 1 of such evaluations.…”

Section: Worst‐case Rdo Under Distributional Assumptionsmentioning

confidence: 99%

Worst‐case robust design optimization under distributional assumptions

Padulo¹,

Guenov²

2011

Numerical Meth Engineering

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SUMMARYPresented in this paper is a novel robust design optimization (RDO) methodology. The problem is reformulated in order to relax, when required, the assumption of normality of objectives and constraints, which often underlies RDO. In the second place, taking into account engineering considerations concerning the risk associated with constraint violation, suitable estimates of tail conditional expectations are introduced in the set of robustness metrics. A computationally affordable yet accurate implementation of the proposed formulation is guaranteed by the adoption of a reduced quadrature technique to perform the uncertainty propagation. The methodology is successfully demonstrated with the aid of an industrial test case performing the sizing of a mid-range passenger aircraft.

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Novel Uncertainty Propagation Method for Robust Aerodynamic Design

Cited by 64 publications

References 55 publications

Sensitivity Analysis Methods for Uncertainty Budgeting in System Design

Sensitivity Analysis Methods for Uncertainty Budgeting in System Design

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

Worst‐case robust design optimization under distributional assumptions

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