Technical Awards：2022 JSAE Award The Outstanding Technical Paper Award - Surrogate Model Development for Prediction of Car Aerodynamics Using Machine LearningFig.4 Structure of proposed model for coeffi cient of aerodynamic drag （CD） estimationFig.5 3-dimensional distance function around car shapeNISSAN TECHNICAL REVIEW No.88 (2022)2.4 Distance function and hyper-parametersTable 2 Optimizer, loss function and hyper-parameters3. Dataset and validation resultsTable 1 Parameter of distance function3.1 DatasetHowever, in terms of convenience, it is desirable to avoid the use of different input data when estimating the fl ow fi eld and CD. Therefore, the input data for the CD estimation model are converted from the voxel into the distance function to unify the fl ow fi eld and CD estimation model input data into the distance function. The network structure in which the input data are unifi ed into a distance function is show in Fig. 4.First, the distance function to be input into the estimation model can be described as follows. The distance fi eld of the three-dimensional distance function used in this study is illustrated in Fig. 5. The colors indicate the distances from the car shape at each grid point. The distance function was created as follows. A bounding box was set around the car shape, and orthogonal equal-interval grid points were arranged in the bounding box. The shortest distance from the car shape was calculated for each grid point to create the relevant distance fi eld. The sizes of the bounding boxes, grid pitches, and numbers of grids are provided in Table 1. For the distance function used to predict CD, a smaller grid pitch is employed to ensure that even a slight shape change can be captured.The optimizers, loss functions, and hyper-parameters used in this study are listed in Table 2.The dataset is shown in Fig. 6. One case includes six pieces of information: the distance function, three components of the fl ow velocity vector, pressure, and CD value. Only the distance function is input into the estimation models, and the fl ow fi elds and CD value are the outputs of the models respectively. Training was performed such that these outputs matched the fl ow velocity, pressure, and CD value of the training case. For this study, 1,123 cases were prepared and divided in a ratio of 10:1 into training and testing datasets. The datasets included six types of cars: sedans, coupes, SUVs, hatchbacks, pickup trucks, and light cars. The proportions of car types included in the training and test datasets were approximately the same. The fl ow velocity vectors, pressures, and CD values used for training and test were calculated using commercial CFD software. The calculations were performed under straight running conditions at a car speed of 33.3 m/s and Reynolds number of 1.0×107. Because a grid unrelated to the distance function was used in the CFD calculations, the CFD calculation results were mapped to the grid for the distance function.8295
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