A Multifidelity Multiobjective Optimization Framework for High-Lift Airfoils

Abstract

High-lift devices design is a challenging task as it involves highly complex flow features while being critical for the overall performance of the aircraft. When part of an optimization loop, the computational cost of the Computational Fluid Dynamics becomes increasingly problematic. Methods to reduce the optimization time has been of major interest over the last 50 years. This paper presents a multiobjective multifidelity optimization framework that takes advantage of two approximation levels of the flow equations: a rapid method that provides quick estimates but of relatively low accuracy and a reference method that provides accurate estimations at the cost of a longer run-time. The method uses a suboptimization, under a trust-region scheme, performed on the low-fidelity model corrected by a surrogate model that is fed by the high-fidelity tool. The size of the trust region is changed according to the accuracy of the corrected model. The multiobjective optimizer is used to set the positions of the flap and slat of a two-dimensional geometry with lift and drag as objectives with an empirical-based method and a Reynolds Averaged Navier-Stokes equations solver. The multifidelity method shows potential for discovering the complete Pareto front, yet it remains less optimal than the Pareto front from the high-fidelity-only optimization.

Design and Optimization of a Multi-Element Hydrofoil for a Horizontal-Axis Hydrokinetic Turbine

“…The measurements of the gap and overlap were provided in terms of a percentage of the chord length of the main element (gap = % C 1 , overlap = % C 1 ). The third parameter of the definition of the gap-overlap is the "deflection angle" (δ), which is defined as the angle between the main element and the flap chord; δ a positive value when the rotation flap is mobilized in a clockwise direction [29][30][31][32][33][34]42]. In addition to the mentioned variables, the flap chord length (C 2 ) was considered as a variable, which was given as a percentage of the main element chord (C 2 = % C 1 ), like the gap and the overlap.…”

“…Additionally, there are statistics or approximation mathematical methods [28]. Surrogate models can be used to predict the design objective(s) and optimize the operating conditions throughout the use of an optimizer to find the optimum design and, finally, to utilize the high fidelity approach to verify the proposed objective(s) [29][30][31][32].…”

“…Concerning the optimization schemes, they have been highlighted to range from Tabu search [29,31,32] to genetic algorithm (GA) [34,36], which are the most often used. In addition, Benini and coworkers [36] obtained satisfactory results when using Matlab ® R2019a software (R2019a, MathWorks Inc, Natick, MA, USA) [37], which offers a general vision of a multi-objective genetic algorithm (MOGA) that is available in the global optimization toolbox in Matlab (gamultiobj function of Genetic Algorithm and Direct Search ToolboxTM), which in turn uses a controlled, elitist genetic algorithm that is a variant of NSGA-II [38,39] to create a set of points on the Pareto front.…”

A parallel multi-fidelity optimization approach in induction hardening

“…Moreover, the use of Gaussian Process-based surrogates (Koziel and Leifsson, 2016) permit to predict gut potential offspring that will be evaluated. So far, multi-fidelity optimization has been mostly used in computational fluid dynamics (Bartz-Beielstein et al , 2018; Perdikaris et al , 2017; Demange et al , 2016). Nevertheless, it is well suited to every kind of expensive, i.e.…”