Gradient-Based Aerodynamic Robust Optimization Using the Adjoint Method and Gaussian Processes

Sabater, Christian; Görtz, Stefan

doi:10.1007/978-3-030-57422-2_14

Cited by 7 publications

(2 citation statements)

References 18 publications

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“…The basic equations of fluid dynamics in the control volume are based on Navier stokes equations that are comprised of equation for conservation of mass and momentum are given as, [13] 1. Continuity equation…”

Section: Numerical Domain and Gridmentioning

confidence: 99%

Numerical Study on Low Speed Electric Car for Public Transportation to Predict Its Aerodynamic Performance and Stability

Mamo

Gopal

Yoseph

et al. 2023

ETJ

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Energy efficiency and dynamic stability of Battery Electric Vehicle (BEV) is highly influenced by size of powertrain, aerodynamic characteristics and driving conditions. The main idea of this work was to study aerodynamic performance of BEV sized based on Ethiopian driving profile and BAJAJ QUTE chassis platform. Numerical analysis was conducted to reveal various surface features and side wind velocities influence using coefficients of aerodynamic forces and moments, vector and contour plots of CFD (Computational Fluid Dynamics). From the analysis, it was found that average aerodynamic coefficients and moments with side wind are much higher than simulated values of original car with corresponding values of CD (3.11), CL (0.45), YM (-240.52Nm) and RM (-363.84Nm). The power requirement to overcome aerodynamic road load with 10m/sec side wind has increased (13.36kW) by 3.3 times as compared to no wind effect power of (4.05kW). The car moving through a straight level road found to be stable at any side-wind below 15m/sec, but it could reach to unstable condition in curved road. For car moving in any road under side-wind greater than 15m/s, there is a chance of turnover and breakaway of a lane.

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Section: Numerical Domain and Gridmentioning

confidence: 99%

Numerical Study on Low Speed Electric Car for Public Transportation to Predict Its Aerodynamic Performance and Stability

Mamo

Gopal

Yoseph

et al. 2023

ETJ

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show abstract

“…Adjoint equations Solving the adjoint equations is an efficient method for obtaining the exact derivative information [9][10][11]. Both the continuous adjoint [4] and the discrete adjoint [12] have been used to obtain the sensitivities of the RANS equations and train a deep neural networks using gradient-based optimization.…”

Section: Differentiation Of Physical Modelsmentioning

confidence: 99%

Ensemble Gradient for Learning Turbulence Models from Indirect Observations

Ströfer¹

2021

CICP

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Training data-driven turbulence models with high fidelity Reynolds stress can be impractical and recently such models have been trained with velocity and pressure measurements. For gradient-based optimization, such as training deep learning models, this requires evaluating the sensitivities of the RANS equations. This paper explores the use of an ensemble approximation of the sensitivities of the RANS equations in training data-driven turbulence models with indirect observations. A deep neural network representing the turbulence model is trained using the network's gradients obtained by backpropagation and the ensemble approximation of the RANS sensitivities. Different ensemble approximations are explored and a method based on explicit projection onto the sample space is presented. As validation, the gradient approximations from the different methods are compared to that from the continuous adjoint equations. The ensemble approximation is then used to learn different turbulence models from velocity observations. In all cases, the learned model predicts improved velocities. However, it was observed that once the sensitivity of the velocity to the underlying model becomes small, the approximate nature of the ensemble gradient hinders further optimization of the underlying model. The benefits and limitations of the ensemble gradient approximation are discussed, in particular as compared to the adjoint equations.

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Optimization Under Uncertainty of Shock Control Bumps for Transonic Wings

Sabater

2021

Advances in Uncertainty Quantification and Optimization Under Uncertainty With Aerospace Applications

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Gradient-Based Aerodynamic Robust Optimization Using the Adjoint Method and Gaussian Processes

Cited by 7 publications

References 18 publications

Numerical Study on Low Speed Electric Car for Public Transportation to Predict Its Aerodynamic Performance and Stability

Numerical Study on Low Speed Electric Car for Public Transportation to Predict Its Aerodynamic Performance and Stability

Ensemble Gradient for Learning Turbulence Models from Indirect Observations

Optimization Under Uncertainty of Shock Control Bumps for Transonic Wings

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