Efficient multi-objective shape optimization using proper orthogonal decomposition with variable fidelity concept

Abstract

A variable fidelity concept is introduced in a re-parameterization approach based on the proper orthogonal decomposition (POD) to efficiently solve multi-objective aerodynamic shape optimization problems. The re-parameterization approach enables to extract dominant shape deformation modes from a database of good designs and to reduce the number of design variables. The present variable fidelity approach is proposed by utilizing low-fidelity functional evaluations to select the good designs. The proposed approach is investigated in two multi-objective aerodynamic shape optimization problems of 2D airfoil in which the combinations of viscous/inviscid simulations or fine/coarse grid simulations are treated as the high/low-fidelity evaluation methods. It can be confirmed that dominant POD modes obtained from low-fidelity evaluations are qualitatively equivalent with that obtained from high-fidelity evaluations. Non-dominated solutions obtained from a conventional optimization approach can be reproduced with smaller numbers of design variables using the dominant POD modes. The computational costs to solve the multi-objective aerodynamic shape optimization problems can be dramatically reduced by introducing the variable fidelity concept.

Comparative study of dimension reduction methods for efficient design optimization

“…Furthermore, at the stage of obtaining the approximate Pareto optimal solutions, the strict accuracy is not required for performance evaluation, so that a variable fidelity (VF) method can be introduced in this stage corresponding to the pre-process of dimension reduction. The VF method is to utilize high and low fidelity performance evaluations simultaneously to efficiently solve an optimization problem, which have been widely investigated in literature (Kennedy and O'Hagan, 2000;Alexandrov et al, 2001;Forrester et al, 2007;Han and Görtz, 2012;Yamazaki and Mavriplis, 2013;Ariyarit and Kanazaki, 2017;Yamazaki, 2017;Yamazaki, 2020). Figure 1 shows the flowchart of the present method with the VF concept.…”

“…The authors have also investigated a method to reduce the dimensionality of the design variables space by utilizing POD in multi-objective optimization problems (Yamazaki, 2020). Beneficial results have been obtained in which the number of design variables as well as total computational cost could be reduced.…”

Shape Optimization under Stochastic Conditions by Design-space Augmented Dimensionality Reduction

“…2 can be consequently transformed as shown in Fig. 12 POD/PCA have been crucial in enhancing the design of airfoils and wings, streamlining external aerodynamic optimizations for both subsonic [35,36,24] and transonic [37,38,39,40,41,42,24,43,44,45,46] regimes of airfoils and wings, as well as for internal aerodynamics of compressors [47,48], turbines [49], and nozzles [50]. These methods have facilitated efficient parameterization and reduced drag, optimizing aerodynamic performance for aircraft, including underwater autonomous vehicles [51].…”

Efficient Multi-objective Aerodynamic Shape Optimization of 3D Supersonic Transport Using Proper Orthogonal Decomposition

“…There are various kinds of geometry parametrization methods such as the Hicks-Henne approach, 1) parametric section airfoil approach, 2) the Bezier curve, 3) free-form deformation (FFD), 4) and proper orthogonal decomposition (POD). 5,6) The shape parameterization methods can be classified into two types: constructive methods and deformative methods. The deformative methods of Hicks and Henne, 1) Désidéri et al, 3) Samareh, 4) Jichao et al, 5) and Yamazaki 6) deform the shape of a baseline model while the constructive method of Sobieczky 2) directly defines new shapes using design parameters.…”