Source-linked AI summary
Application of Convolutional Neural Network to Predict Airfoil Lift Coefficient
Yao Zhang, Woong-Je Sung, Dimitri Mavris
TL;DR
The paper examines whether CNNs can support aerodynamic meta-modeling across varying airfoil geometries and flow conditions. It develops CNN architectures and artificial-image preprocessing, compares them with an MLP baseline, and reports comparable learning capability with competitive prediction accuracy and minimal geometric-representation constraints.
Problem
Aerodynamic meta-modeling must handle varied geometries and flow conditions, while conventional MLPs are not designed to exploit intrinsic spatial correlations.
Method
The study trains an MLP baseline and two CNN architectures using coordinate-based or 49 × 49 artificial-image inputs that combine airfoil geometry with flow conditions.
Results
CNN architectures show reasonable learning and prediction for unseen airfoil shapes, with AeroCNN-II producing comparable training trajectories and predictions clustered near actual lift coefficients.
Takeaways & Limitations
Combining geometric and non-geometric boundary conditions into an image-like array provides a useful perspective for applying image-recognition deep learning to aerodynamic meta-modeling.
Abstract
from arXiv · showhide
The adaptability of the convolutional neural network (CNN) technique for aerodynamic meta-modeling tasks is probed in this work. The primary objective is to develop suitable CNN architecture for variable flow conditions and object geometry, in addition to identifying a sufficient data preparation process. Multiple CNN structures were trained to learn the lift coefficients of the airfoils with a variety of shapes in multiple flow Mach numbers, Reynolds numbers, and diverse angles of attack. This is conducted to illustrate the concept of the technique. A multi-layered perceptron (MLP) is also used for the training sets. The MLP results are compared with that of the CNN results. The newly proposed meta-modeling concept has been found to be comparable with the MLP in learning capability; and more importantly, our CNN model exhibits a competitive prediction accuracy with minimal constraints in a geometric representation.
I. Nomenclature
The nomenclature defines symbols, abbreviations, activation functions, and dataset labels used throughout the paper.
- α and AoA denote angle of attack, while ρ and ¯ρ denote raw and processed pixel density.
- Cl denotes sectional lift coefficient, and CFD denotes computational fluid dynamics.
- CNN, MLP, FC, MSE, and ReLU identify network types, layer structure, error metric, and activation function.
- M∞ denotes freestream Mach number, NACA denotes National Advisory Committee for Aeronautics, and tanh denotes tangent sigmoid function.
- trn and vld label the training and validation datasets, respectively.
II. Introduction
Advances in computational power, data science, and machine learning are reshaping aerodynamic analysis and motivating data-driven meta-modeling. This approach seeks to balance modeling effort with design-space scope while addressing the growing volume of simulation and testing data.
- Data science and machine learning have expanded possibilities for understanding aerodynamics and fluid mechanics and for predictive and control capabilities.
- Aerodynamic meta-modeling aims to balance modeling efforts with the scope of the design space, a task presented as difficult.
- Data-driven surrogate models are gaining popularity because design, analysis, and optimization processes generate large volumes of physical-testing and simulation data.
- Researchers are proposing multiple machine-learning algorithms and applying deep-learning techniques to aerodynamics problems.
A. Convolutional Neural Network Architecture
The paper adapts CNN ideas from image recognition to aerodynamic meta-modeling by representing airfoil geometry and flow conditions in image-like inputs. Three architectures are tested, including an MLP baseline and two CNN variants with different data structures and convolution schemes.
- A. Convolutional Neural Network Architecture: Aerodynamic CNN meta-modeling modifies LeNet-5 to incorporate object geometry, flow conditions, and continuous regression outputs.
- A. Convolutional Neural Network Architecture: Unlike conventional aerodynamic meta-modeling, the proposed approach represents object geometry as an image-like pixel array.
- A. Convolutional Neural Network Architecture: The study tests a conventional two-hidden-layer MLP baseline alongside AeroCNN-I and AeroCNN-II CNN architectures.
- A. Convolutional Neural Network Architecture: AeroCNN-I processes a 2 × 50 coordinate array with local 2 × 5 kernels, while AeroCNN-II uses full 2D convolution on artificial images.
- A. Convolutional Neural Network Architecture: AeroCNN-II converts each entry into a 49 × 49 artificial image using 5 × 5 kernels, 25 filters, and 2 × 2 max pooling.
- A. Convolutional Neural Network Architecture: The artificial image combines airfoil shape and flow conditions by encoding external-space pixel values according to freestream Mach number and pixel density.
B. Data Preparation
The data-preparation process obtains airfoil coordinates, generates lift-coefficient data across varied conditions, and creates image-like representations for CNN input. Symmetry-based augmentation expands the dataset to about 80,000 entries.
- Accurate airfoil geometry is treated as critical, with coordinate data obtained from the UIUC Airfoil Data Site.
- The same geometry is nondimensionalized for different Mach numbers, producing distinct artificial-image encodings.
- The study focuses on sectional lift coefficient Cl and generates aerodynamic data through numerical simulations using XFOIL.
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C. Activation Functions
The study tests both tanh and ReLU as hidden-unit activation functions across varied network structures for lift-coefficient prediction.
- C. Activation Functions: Both tanh and ReLU units were tested as the main hidden-unit activations across varied network structures.The motivation includes tanh’s vanishing-gradient stagnation and ReLU’s reported benefits in image recognition.
IV. Results and Discussion
The results show that the CNN architectures can learn and predict airfoil lift coefficients, while differing from the MLP in learning speed and computational cost. AeroCNN-II also supports a unified artificial-image representation of airfoil geometry and flow conditions with reasonable generalization to unseen shapes.
- IV. Results and Discussion: MLP models with varied hidden-unit counts converged to similar training and validation MSE trajectories, defining an overall accuracy boundary.The datasets used an 85% training and 15% validation split.
- IV. Results and Discussion: AeroCNN-I curves dropped faster than MLP curves before reaching steady MSEs, indicating faster learning for the given number of epochs.The comparison used models with approximately the same number of adjustable parameters and a 30% training, 70% validation split.
- IV. Results and Discussion: 3,206 seconds versus 1,700 seconds: AeroCNN-I required more time than MLP for 500 epochs.The CNN required significantly more calculation steps and time per epoch for a similar number of adjustable parameters.
- IV. Results and Discussion: AeroCNN-II produced training and validation trajectories comparable to AeroCNN-I, supporting artificial images that combine airfoil geometry and flow conditions.AeroCNN-II applies full 2D convolution to the pre-processed artificial images.
- IV. Results and Discussion: With 95% training and 5% validation data at one Reynolds number, AeroCNN-II predictions clustered near the 45° line and showed reasonable generalization to unseen airfoils.Training samples fit better than validation samples, and lift-coefficient-versus-angle-of-attack plots showed reasonable performance for included and unseen airfoils.
- IV. Results and Discussion: As a proof of concept, the CNN architectures showed reasonable performance learning from examples and predicting lift coefficients for unseen airfoil shapes.This summarizes the reported training and prediction outcomes for the proposed architectures.
V. Conclusion
The study compares CNN-based and MLP approaches for predicting airfoil lift coefficients across varied geometries and flow conditions. Its artificial-image formulation combines geometric and non-geometric boundary conditions, while the reported figures show actual-versus-predicted lift curves.
- AeroCNN-II applies a single CNN framework to 2D aerodynamic problems with diverse flow conditions and sectional shapes.
- The CNN training represents airfoil shape, angle of attack, and freestream Mach number together in an image-like array.
- This geometric and non-geometric boundary-condition synthesis was successfully used to train a CNN for aerodynamic meta-modeling.
- The study presents results from AeroCNN-II training and compares predictions from CNN and conventional MLP techniques.
- The evaluation includes actual-versus-predicted Cl−α curves for an airfoil included in training and another not included in training.