A B-Spline-Based Generative Adversarial Network Model for Fast Interactive Airfoil Aerodynamic Optimization

Airfoil aerodynamic optimization is of great importance in aircraft design; however, it relies on high-fidelity physics-based models that are computationally expensive to evaluate. In this work, we provide a methodology to reduce the computational cost for airfoil aerodynamic optimization. Firstly, we develop a B-spline based generative adversarial networks (BSplineGAN) parameterization method to automatically infer design space with sufficient shape variability. Secondly, we construct multi-layer neural network (MNN) surrogates for fast predictions on aerodynamic drag, lift, and pitching moment coefficients. The BSplineGAN has a relative error lower than 1% when fitting to UIUC database. Verification of MNN surrogates shows the root means square errors (RMSE) of all aerodynamic coefficients are within the range of 20%–40% standard deviation of testing points. Both normalized RMSE and relative errors are controlled within 1%. The proposed methodology is then demonstrated on an airfoil aerodynamic optimization. We also verified the baseline and optimized designs using a high-fidelity computational fluid dynamic solver. The proposed framework has the potential to enable web-based fast interactive airfoil aerodynamic optimization

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

A multifidelity multiobjective optimization framework for high-lift airfoils

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 sub-optimization, 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 ap 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

Approximated models for aerodynamic coefficients estimation in a multidisciplinary design environment

In this paper variable fidelity analyses are investigated. Moreover different kind of approximations to be used in a wide multidisciplinary design environment for aircraft design are built. In order to obtain the surrogate models used in the main design process, a proper framework is built by different design of experiments techniques for process and variables management. Approximated models for the estimation of aerodynamic coefficients are evaluated on design spaces of different dimensions and considering different set of variables (i.e. geometric parameters and flight conditions). They are mainly based on the hybrid combination of Vortex Lattice Method (VLM) models representing the basic low fidelity analysis) and 3D finite volume Computational Fluid Dynamics models (representing the basic high fidelity analysis). Different strategies for the evaluation of the surrogate model are considered and an original methodology for the model construction is here presented

CFDNet: a deep learning-based accelerator for fluid simulations

CFD is widely used in physical system design and optimization, where it is used to predict engineering quantities of interest, such as the lift on a plane wing or the drag on a motor vehicle. However, many systems of interest are prohibitively expensive for design optimization, due to the expense of evaluating CFD simulations. To render the computation tractable, reduced-order or surrogate models are used to accelerate simulations while respecting the convergence constraints provided by the higher-fidelity solution. This paper introduces CFDNet -- a physical simulation and deep learning coupled framework, for accelerating the convergence of Reynolds Averaged Navier-Stokes simulations. CFDNet is designed to predict the primary physical properties of the fluid including velocity, pressure, and eddy viscosity using a single convolutional neural network at its core. We evaluate CFDNet on a variety of use-cases, both extrapolative and interpolative, where test geometries are observed/not-observed during training. Our results show that CFDNet meets the convergence constraints of the domain-specific physics solver while outperforming it by 1.9 - 7.4x on both steady laminar and turbulent flows. Moreover, we demonstrate the generalization capacity of CFDNet by testing its prediction on new geometries unseen during training. In this case, the approach meets the CFD convergence criterion while still providing significant speedups over traditional domain-only models.Comment: It has been accepted and almost published in the International Conference in Supercomputing (ICS) 202

Progressive construction of a parametric reduced-order model for PDE-constrained optimization

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by a given Reduced-Order Model (ROM) is defined with the goal of converging to the solution of a given PDE-constrained optimization problem. For each reduced optimization problem, the constraining ROM is trained from sampling the High-Dimensional Model (HDM) at the solution of some of the previous problems in the sequence. The reduced optimization problems are equipped with a nonlinear trust-region based on a residual error indicator to keep the optimization trajectory in a region of the parameter space where the ROM is accurate. A technique for incorporating sensitivities into a Reduced-Order Basis (ROB) is also presented, along with a methodology for computing sensitivities of the reduced-order model that minimizes the distance to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced optimization framework is applied to subsonic aerodynamic shape optimization and shown to reduce the number of queries to the HDM by a factor of 4-5, compared to the optimization problem solved using only the HDM, with errors in the optimal solution far less than 0.1%

Airfoil Design under Uncertainty using Non-Intrusive Polynomial Chaos Theory and Utility Functions

Fast and accurate airfoil design under uncertainty using non-intrusive polynomial chaos (NIPC) expansions and utility functions is proposed. The NIPC expansions provide a means to efficiently and accurately compute statistical information for a given set of input variables with associated probability distribution. Utility functions provide a way to rigorously formulate the design problem. In this work, these two methods are integrated for the design of airfoil shapes under uncertainty. The proposed approach is illustrated on a numerical example of lift-constrained airfoil drag minimization in transonic viscous flow using the Mach number as an uncertain variable. The results show that compared with the standard problem formulation the proposed approach yields more robust designs. In other words, the designs obtained by the proposed approach are less sensitive to variations in the uncertain variables than those obtained with the standard problem formulation