# Fully Convolutional Neural Network Prediction Method for Aerostatic Performance of Bluff Bodies Based on Consistent Shape Description

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## Abstract

**:**

## 1. Introduction

## 2. Input Design

#### 2.1. Wall Distance Field

#### 2.2. Space Coordinate Field

## 3. Output Design

## 4. Neural Network Framework Design

## 5. Test Design

#### 5.1. Computational Case Design

#### 5.2. Data Preparation

## 6. Model Performance Evaluation and Optimization

#### 6.1. Optimization of the Number of Hidden Layers

#### 6.2. Hidden Layer Size Optimization

## 7. Pressure Field Prediction Effect

## 8. Wall Pressure Prediction Results

## 9. Drag Coefficient Prediction

#### 9.1. Compared to Using Shape as Input

#### 9.2. Compared to Using the Drag Coefficient as Output

## 10. Conclusions

- (1)
- The overall average relative error of the drag coefficient is 9.42%.
- (2)
- The shape is described by the combination of the wall distance field and the space coordinate field. This improves the prediction accuracy by 13.25% compared to when the shape is directly used as the model input.
- (3)
- A step-by-step strategy in which the pressure field is used as the model output is proposed. The model prediction accuracy is improved by 10.22% when using the pressure field as the model input compared to directly predicting the drag coefficient.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 10.**Comparison of pressure field prediction effects of four typical shapes. The first column is the predicted value. (

**a**) The ellipse with AR = 0.71. (

_{1}**b**) The hexagon with AR = 0.56 R = 0.3. (

_{1}**c**) The rectangle with AR = 0.71. (

_{1}**d**) The diamond with AR = 0.71. The second column is the true value. (

_{1}**a**) The ellipse with AR = 0.71. (

_{2}**b**) The hexagon with AR = 0.56 R = 0.3. (

_{2}**c**) The rectangle with AR = 0.71. (

_{2}**d**) The diamond with AR = 0.71.

_{2}**Figure 11.**Comparison of the prediction effects of the wall pressure field of the four shapes. (

**a**) The ellipse with AR = 0.71. (

**b**) The ellipse with AR = 4. (

**c**) The hexagon with AR = 0.56 R = 0.3. (

**d**) The hexagon with AR = 7 R = 0.1. (

**e**) The rectangle with AR = 0.71. (

**f**) The rectangle with AR = 4. (

**g**) The diamond with AR = 0.71. (

**h**) The diamond with AR = 4.

Basic shape | ||||

Distance R from upper corner to X = 0 | [0.1, 0.2, 0.3, 0.4] | — | — | — |

B | 1 | |||

AR = B/H | [0.5, 0.56, 0.625, 0.71, 0.83, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] | |||

Quantity | 60 | 15 | 15 | 15 |

Model Settings | UNet_2-2 | UNet_3-2 | UNet_4-2 | UNet_5-2 | UNet_6-2 |
---|---|---|---|---|---|

MAE | 0.2313 | 0.2038 | 0.1942 | 0.2190 | 0.1593 |

Parameter quantity | 1.016 × 10^{6} | 4.262 × 10^{6} | 1.724 × 10^{7} | 6.915 × 10^{7} | 2.768 × 10^{8} |

Model Settings | UNet_2-3 | UNet_3-3 | UNet_4-3 | UNet_5-3 | UNet_6-3 |
---|---|---|---|---|---|

MAE | 0.1801 | 0.1175 | 0.1696 | 0.1456 | 0.1234 |

Parameter quantity | 1.533 × 10^{6} | 6.401 × 10^{6} | 2.587 × 10^{7} | 1.037 × 10^{8} | 4.152 × 10^{8} |

Model Settings | UNet_3-3-16 | UNet_3-3-32 | UNet_3-3-64 | UNet_3-3-128 |
---|---|---|---|---|

MAE | 0.1531 | 0.0942 | 0.1175 | 0.1700 |

Parameter quantity | 4.010 × 10^{5} | 1.601 × 10^{6} | 6.401 × 10^{6} | 2.559 × 10^{7} |

Shape | R = 0.1 Hexagon | R = 0.2 Hexagon | R = 0.3 Hexagon | R = 0.4 Hexagon | Circle | Rectangle | Diamond |
---|---|---|---|---|---|---|---|

Average relative error (%) | 7.690 | 22.20 | 45.33 | 26.72 | 17.26 | 21.37 | 18.13 |

Shape | R = 0.1 Hexagon | R = 0.2 Hexagon | R = 0.3 Hexagon | R = 0.4 Hexagon | Circle | Rectangle | Diamond |
---|---|---|---|---|---|---|---|

Average relative error (%) | 3.450 | 7.740 | 12.14 | 5.010 | 9.110 | 13.08 | 15.42 |

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**MDPI and ACS Style**

Li, K.; Li, H.; Li, S.; Chen, Z.
Fully Convolutional Neural Network Prediction Method for Aerostatic Performance of Bluff Bodies Based on Consistent Shape Description. *Appl. Sci.* **2022**, *12*, 3147.
https://doi.org/10.3390/app12063147

**AMA Style**

Li K, Li H, Li S, Chen Z.
Fully Convolutional Neural Network Prediction Method for Aerostatic Performance of Bluff Bodies Based on Consistent Shape Description. *Applied Sciences*. 2022; 12(6):3147.
https://doi.org/10.3390/app12063147

**Chicago/Turabian Style**

Li, Ke, Hai Li, Shaopeng Li, and Zengshun Chen.
2022. "Fully Convolutional Neural Network Prediction Method for Aerostatic Performance of Bluff Bodies Based on Consistent Shape Description" *Applied Sciences* 12, no. 6: 3147.
https://doi.org/10.3390/app12063147