Domenico Quagliarella

Aerodynamic shape optimization via non-intrusive POD-based surrogate modelling

A surrogate-based optimization framework is proposed to exploit a reduced order model (ROM) as surrogate evaluator in aerodynamic design based on computational fluid dynamics (CFD) methods. The model is based on the Proper Orthogonal Decomposition (POD) of an ensemble of CFD solutions. Full POD and zonal POD models performances are analysed with respect to their suitability to find the global optimum in an evolutionary optimization frame. Indeed, reduced order models are used as fitness evaluator to improve the aerodynamic performances of a two-dimensional airfoil. Finally, the performances of various surrogate-based shape optimization (SBSO) methods are compared to the efficiency of data-fit assisted optimization and to the accuracy of a plain optimization, where, instead, each aerodynamic evaluation is performed with the high-fidelity model.

Constraint handling in efficient global optimization

Real-world optimization problems are often subject to several constraints which are expensive to evaluate in terms of cost or time. Although a lot of effort is devoted to make use of surrogate models for expensive optimization tasks, not many strong surrogate-assisted algorithms can address the challenging constrained problems. Efficient Global Optimization (EGO) is a Kriging-based surrogate-assisted algorithm. It was originally proposed to address unconstrained problems and later was modified to solve constrained problems. However, these type of algorithms still suffer from several issues, mainly: (1) early stagnation, (2) problems with multiple active constraints and (3) frequent crashes. In this work, we introduce a new EGO-based algorithm which tries to overcome these common issues with Kriging optimization algorithms. We apply the proposed algorithm on problems with dimension d ≤ 4 from the G-function suite [16] and on an airfoil shape example.

Design of a Supersonic Natural Laminar Flow Wing-Body

The present investigation has been carried out within the SUPERTRAC project funded by the European Community in the 6th Framework Programme and aimed at investigating various techniques within laminar flow technology applied to supersonic drag reduction. In particular, this work deals with natural laminar flow shape design of a supersonic high-sweep wing–body configuration. The reference geometry has been provided by Dassault Aviation, one of the two industrial partners together with Airbus. Two different design are presented, produced by the Italian Aerospace Research Center and ONERA, respectively, using numerical optimization procedures based on evolutionary computing techniques and robust aerodynamic analysis tools. Results show how shape optimization can be effective in changing the boundary-layer characteristics of a supersonic high-swept wing and enhancing natural laminar flow on the wing surface.

Aerodynamic Design with Physics-Based Surrogates

Details, references and guidelines are given about the adoption of surrogate models and reduced-order models within the aerodynamic shape optimization context. The aerodynamic design problem and its approximated version are introduced and discussed and then, an overview of various surrogate models and surrogate-based optimization methods is given. Subsequently, the concept of model order reduction is recalled, and the performance analysis of reduced-order models based on proper orthogonal decomposition (POD ) is discussed. Within this context, some techniques to adaptively and globally improve the accuracy of POD-based surrogates are illustrated. Finally, an aerodynamic shape design problem of a transonic airfoil is used to practically analyze and compare the performances of various surrogate-based optimization methods.

Efficient aerodynamic optimization of a very light jet aircraft using evolutionary algorithms and RANS flow models

The challenging problem of wing design for small business aircraft configurations is here explored using evolutionary computing. The activity focuses on the aerodynamic analysis and optimization of a laminar wing in cruise and high lift conditions. The main feature of the work is the application of natural laminar flow technology which in turn implies pressure gradient optimization. The optimization study is performed by using chained CFD based aerodynamic numerical methods in an evolutionary optimization framework. A major issue is the simulation of the rear-mounted engine mass flow inlet in cruise conditions, which introduces a remarkable geometry complication and computational time increase into the optimization process. The first section gives some details about the design and analysis system. The reference configuration is analyzed to show the starting point of the aerodynamic design. Then the optimization problem definition and the adopted strategy is discussed. The final section is devoted to the aerodynamic analysis of the obtained optimal configuration.

Value-at-Risk and Conditional Value-at-Risk in Optimization Under Uncertainty

This work is related to the use of various risk measures in the context of robust- and reliability-based optimization. We start from the definition of risk measure and its formal setting, and then, we show how different risk functional definitions can lead to different approaches to the problem of optimization under uncertainty. In particular, the application of value-at-risk (VaR) and conditional value-at-risk (CVaR), also called quantiles and superquantiles, is here illustrated. These risk measures originated in the area of financial engineering, but they are very well and naturally suited to reliability-based design optimization problems and they represent a possible alternative to more traditional robust design approaches. We will then discuss the implementation of an efficient risk measure-based optimization algorithm based on the introduction of the weighted empirical cumulative distribution function (WECDF) and on the use of methods for changing the probability measure. Subsequently, we will discuss the problems related to the error in the estimation of the risk function and we will illustrate the “bootstrap” computational statistics technique to get an estimate of the standard error on VaR and CVaR. Finally, we will report some simple application examples of this approach to robust and reliability-based optimization.

UQ Sensitivity Analysis and Robust Design Optimization of a Supersonic Natural Laminar Flow Wing-Body

The robust design optimization of a natural laminar flow wing for a supersonic business jet is the objective of the reported research work. In particular, the pursued goal is to obtain a wing shape whose performance is influenced as least as possible by geometrical uncertainties. The starting point is a supersonic business jet wing-body that was already optimized for natural laminar flow using a deterministic approach within the EU funded SUPERTRAC Project. This configuration was firstly analyzed to identify the main dependencies, and interactions of the parameters that describe the uncertainty sources in the robust design problem, and in a second step, a robust design optimization algorithm was used to obtain an optimal solution less sensible to geometrical perturbation with respect to the baseline. The optimization algorithm is an evolutionary one and its principal requirement is the resilience to noise in the objective function values. The objective function that defines the goal of the optimization is based on special risk functions, namely value-at-risk (VaR) and conditional value-at-risk (CVaR), that are widely used in financial engineering community and that offer interesting advantages with respect to more classical approaches based on expectation or variance risk functions. The initial part of the optimization task is based on VaR risk function computed using a very coarse sample set. In a second step, the CVaR function, computed over a finer sample is used to further improve the results. The confidence intervals of VaR and CVaR estimations are computed using the bootstrap computational statistics technique. The results illustrate the feasibility of such a robust optimization approach for the application to industrial class robust design optimization techniques.

Application of Surrogate-Based Optimization Techniques to Aerodynamic Design Cases

The paper proposes the application of evolutionary-based optimization coupled with physics-based and adaptively-trained surrogate model to the solution of both two- and three-dimensional aerodynamic optimization problems. The shape parameterization approach consists of the Class-Shape Transformation (CST) method with a sufficient degree of Bernstein polynomials to cover a wide range of shapes. The in-house ZEN flow solver is used for RANS aerodynamic solution. Results show that, thanks to the combined usage of surrogate models and smart training, optimal candidates may be located in the design space even with limited computational resources with respect to standard global optimization approaches.

Augmented Lagrangian Approach for Constrained Potential Nash Games

An approach to the resolution of inequality constrained potential games based on a dual problem is here presented. The dual problem is solved by using a two-level optimization iterative scheme based on a linear program for the dual problem and a classical hybrid evolutionary approach for the primal problem. An application to a facility location problem in presence of obstacles is described.

Uncertainty Sources in the Baseline Configuration for Robust Design of a Supersonic Natural Laminar Flow Wing-Body

An aerodynamic configuration of a supersonic business jet wing-body is proposed as baseline for a robust aerodynamic shape design problem. This configuration has been analyzed to identify the main dependencies and interactions of the parameters that describe the uncertainty sources in the robust design problem. Subsequent steps of the research activity will be related to the robust natural laminar flow design optimization of this configuration.