Machine Learning in Aerodynamic Shape Optimization

Control of flow separation: Paul K. Chang. Hemisphere, Washinhgton, 1976


 Advancements in computing power have recently made it possible to utilize machine learning and deep learning to push scientific computing forward in a range of disciplines, such as fluid mechanics, solid mechanics, materials science, etc. The incorporation of neural networks is particularly crucial in this hybridization process. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data is sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multi-physics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multi-physics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities are presented in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers.

Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics

Aiming at the problems of a long design period and imperfect surrogate modeling in the field of airfoil design optimization, a convolutional neural network framework for airfoil design and performance prediction (DPCNN) is established based on the deep learning method. The airfoil profile parameterization, physical field prediction, and performance prediction are achieved. The results show that the DPCNN framework can generate substantial perfect airfoil profiles with only three geometric parameters. It has significant advantages such as good robustness, great convergence, fast computation speed, and high prediction accuracy compared with the conventional machine learning method. When the train size is 0.1, the predicted results can be obtained within 5 ms. The prediction absolute errors of physical field of most sample points are lower than 0.002, and the relative errors of aerodynamic performance parameters are lower than 2.5%. Finally, the optimization attempt of operating parameters is completed by gradient descent method, which shows good stability and convergence. Overall, the DPCNN framework in this paper has outstanding advantages in time cost and prediction accuracy. 

Airfoil design and surrogate modeling for performance prediction based on deep learning method

Low-Reynolds-number high-lift airfoil design is critical to the performance of unmanned aerial vehicles (UAV). However, since laminar-to-turbulent transition dominates the aerodynamic performance of low-Reynolds-number airfoils and the transition position may exhibit an abrupt change even with a small geometric deformation, aerodynamic coefficient functions become discontinuous in this regime, which brings significant difficulties to the application of conventional aerodynamic design optimization methods. To efficiently perform low-Reynolds-number airfoil design, we present a tailored airfoil modal parameterization method, which reasonably defines the desired design space using deep-learning techniques. Coupled with surrogate-based optimization, the proposed method has shown to be effective and efficient in low-Reynolds-number high-lift airfoil design. It is found that it is necessary to consider laminar-to-turbulent transition and to perform multi-point optimization in practical low-Reynolds-number airfoil design. The maximal lift coefficient is an active constraint influencing the selection of the optimal cruise lift coefficient. The results show the complexity of low-Reynolds-number high-lift airfoil design and highlight the significance of the proposed method in the improvement of optimization efficiency. 

Low-Reynolds-number airfoil design optimization using deep-learning-based tailored airfoil modes

Surrogate-based aerodynamic shape optimization for delaying airfoil dynamic stall using Kriging regression and infill criteria

While dielectric-barrier-discharge (DBD) based plasma actuation systems have been successfully demonstrated to suppress massive flow separation over wind turbine blades to reduce the transient aerodynamic loadings acting on the turbine blades, it is still a non-trivial task to establish a best combination of various operating parameters for a DBD plasma actuation system to achieve the optimized flow control effectiveness. In the present study, a regression Kriging based metamodeling technique is developed to optimize the operating parameters of a DBD plasma actuation system for suppressing deep stall over the surface of a wind turbine blade section/airfoil model. The data points were experimentally obtained by embedding a nanosecond-pulsed DBD (NS-DBD) plasma actuator at the leading edge of the airfoil model. The applied voltage and frequency for the NS-DBD plasma actuation were used as the design variables to demonstrate the optimization procedure. The highest possible lift coefficient of the turbine airfoil model at deep stalled angles of attack (i.e., α = 22° and 24°) were selected as the objective function for the optimization. It was found that, while the metamodeling-based procedure could accurately predict the objective function within the bounds of the design variables with an uncertainty ~ 2%, a global accuracy level of ~ 97% was achieved within the whole design space.

https://link.springer.com/content/pdf/10.1007/s10409-020-00951-6.pdf

Metamodeling-based parametric optimization of DBD plasma actuation to suppress flow separation over a wind turbine airfoil model


 Conditional Invertible Neural Networks (cINNs) were used for generative inverse design of aerodynamic shapes for a given aerodynamic performance target. The methodology was used to generate two-dimensional (2-D) airfoil shapes for a target lift coefficient and three-dimensional (3-D) vehicle shapes for a low drag vehicle given an aerodynamic drag coefficient target. Training data for both cases was generated for the forward process i.e., aerodynamic performance as a function of design variables that define the airfoil or vehicle shape, using Design of Experiments (DOE) and Computational Fluid Dynamics (CFD) simulations. Due to the structure of the cINNs, the inverse process was learned implicitly i.e., samples from latent space were transformed back to the design variables. The designs generated by the trained cINN model were simulated under identical conditions to check if they met the desired aerodynamic performance target. The distribution of design variables conditioned on a performance target learned by the cINN model was compared to the distribution in the training data. Conditional invertible neural networks provide an easy-to-use tool to generate new designs that meet the desired aerodynamic performance, thereby, reducing the iteration time between aerodynamicists and stylists. In case of vehicle shape generation, since all generated vehicle shapes meet the aerodynamic performance target, the designer can select shapes that do not conflict with other design constraints such as the interior volume, comfort, styling, and various safety requirements.

Generative Inverse Design of Aerodynamic Shapes Using Conditional Invertible Neural Networks

The dynamic stall phenomenon produces adverse aerodynamic loading, which negatively affects the structural strength and life of aerodynamic systems. Aerodynamic shape optimization (ASO) provides a practical approach for delaying and mitigating dynamic stall characteristics without the addition of an auxiliary system. A typical ASO investigation requires multiple evaluations of accurate but time-consuming computational fluid dynamics (CFD) simulations. In the case of dynamic stall, unsteady CFD simulations are required for airfoil shape evaluation; combining it with high-dimensions of airfoil shape parameterization renders the ASO investigation computationally costly. In this study, metamodel-based optimization (MBO) is proposed using the multifidelity modeling (MFM) technique to efficiently conduct ASO investigation for computationally expensive dynamic stall cases. MFM methods combine data from accurate high-fidelity (HF) simulations and fast low-fidelity (LF) simulations to provide accurate and fast predictions. In particular, Cokriging regression is used for approximating the objective and constraint functions. The airfoil shape is parameterized using six PARSEC parameters. The objective and constraint functions are evaluated for a sinusoidally oscillating airfoil with the unsteady Reynolds-averaged Navier-Stokes equations at a Reynolds number of 135,000, Mach number of 0.1, and reduced frequency of 0.05. The initial metamodel is generated using 220 LF and 20 HF samples. The metamodel is then sequentially refined using the expected improvement infill criteria and validated with the normalized root mean square error. The refined metamodel is utilized for finding the optimal design. The optimal airfoil shape shows higher thickness, larger leading-edge radius, and an aft camber compared to baseline (NACA 0012). The optimal shape delays the dynamic stall occurrence by 3 degrees and reduces the peak aerodynamic coefficients. The performance of the MFM method is also compared with the single-fidelity metamodeling method using HF samples. Both the approaches produced similar optimal shapes; however, the optimal shape from MFM achieved a minimum objective function value while more closely satisfying the constraint at a computational cost saving of around 41%.

Aerodynamic Shape Optimization for Delaying Dynamic Stall of Airfoils Using Cokriging Regression

Multifidelity modeling similarity conditions for airfoil dynamic stall prediction with manifold mapping

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