Surrogate-based optimisation using adaptively scaled radial basis functions
Artikel i vetenskaplig tidskrift, 2020

Aerodynamic shape optimisation is widely used in several applications, such as road vehicles, aircraft and trains. This paper investigates the performance of two surrogate-based optimisation methods; a Proper Orthogonal Decomposition-based method and a force-based surrogate model. The generic passenger vehicle DrivAer is used as a test case where the predictive capability of the surrogate in terms of aerodynamic drag is presented. The Proper Orthogonal Decomposition-based method uses simulation results from topologically different meshes by interpolating all solutions to a common mesh for which the decomposition is calculated. Both the Proper Orthogonal Decomposition- and force-based approaches make use of Radial Basis Function interpolation. The Radial Basis Function hyperparameters are optimised using differential evolution. Additionally, the axis scaling is treated as a hyperparameter, which reduces the interpolation error by more than 50% for the investigated test case. It is shown that the force-based approach performs better than the Proper Orthogonal Decomposition method, especially at low sample counts, both with and without adaptive scaling. The sample points, from which the surrogate model is built, are determined using an optimised Latin Hypercube sampling plan. The Latin Hypercube sampling plan is extended to include both continuous and categorical values, which further improve the surrogate's predictive capability when categorical design parameters, such as on/off parameters, are included in the design space. The performance of the force-based surrogate model is compared with four other gradient-free optimisation techniques: Random Sample, Differential Evolution, Nelder–Mead and Bayesian Optimisation. The surrogate model performed as good as, or better than these algorithms, for 17 out of the 18 investigated benchmark problems.

Radial Basis Function interpolation


Surrogate model

Evolutionary algorithm

Latin Hypercube Sampling

Bayesian optimisation

Global optimisation

Proper Orthogonal Decomposition


Black box optimisation




Magnus Urquhart

Chalmers, Mekanik och maritima vetenskaper, Fordonsteknik och autonoma system

Emil Ljungskog

Chalmers, Mekanik och maritima vetenskaper, Fordonsteknik och autonoma system

Simone Sebben

Chalmers, Mekanik och maritima vetenskaper, Fordonsteknik och autonoma system

Applied Soft Computing Journal

1568-4946 (ISSN)

Vol. 88 106050


Rymd- och flygteknik


Sannolikhetsteori och statistik



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