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Airfoil optimization can be achieved in numerous ways, the conventional one being wind tunnel experimentation and CFD simulation. To reduce the necessary computation power and to increase the effectiveness in arriving at global optimum solutions, the need for alternatives is essential. Hence, several deep learning frameworks were used and collated.

The above figure represents a process known as meta-modeling or surrogate modeling (*refer to this link to know more about surrogate models*). To build a robust method of determining the aerodynamic coefficients and to establish a functional relation between the geometric parameters of the airfoil and the aerodynamic coefficients, two different deep learning framework was used, namely, convolutional neural network (CNN) and multi-layer perceptron (MLP). Both these architectures use gradient descent algorithm to optimize the weights and biases, the primary difference between these two is in the type of inputs that are being fed to the encoder. In CNN the inputs are images of the airfoil and in MLP the inputs are raw data in matrix form. An illustration below shows a deep neural network architecture for airfoil optimization. The inputs to this are the geometric features such as chord length, leading-edge radius, and relative thickness. This is mapped to the outputs of the neural network, i.e., the aerodynamic coefficients.

The CNN architecture is based on the LeNet-5 architecture. The key parameters also known as hyperparameters that are considered in developing this framework are filter or kernel, stride, and padding. The filters are utilized for edge detection and this too uses backpropagation and gradient descent algorithm to determine the filter inputs. Stride is the number of pixel shifts over the input matrix. Padding refers to the number of pixels added to an image when it is being processed by the kernel of a CNN. The input matrix is defined by airfoil geometry, consequently, the hyperparameters are quantified based on the application and the accuracy demanded. This is followed by a valid convolution or the same convolution, it’s called a valid convolution if it does not contain padding, and it’s called the same convolution if it contains padding. The pooling operation is usually executed, to reduce the dimensionality of the learning process, by averaging or taking the maximum value. Lastly, the fully connected layers encompass the overall pixels in an array format. The figure below shows a modified version of the LeNet-5 architecture.

The metamodeling process provided accurate models for airfoil optimization. The results show that the predicted and actual values from the study coincide and the mean-squared error (MSE) reduced significantly with training epochs but the performance of CNN architecture was slightly better than MLP. Therefore the use of metamodeling shows promising results in processing aerodynamic coefficients of airfoils.

Refer the paper below for information.Y. Zhang, W. J. Sung, and D. N. Mavris, “Application of convolutional neural network to predict airfoil lift coefficient,” in

2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2018, p. 1903.

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