基于PINN模型的导弹气动特性快速预测技术

蔺佳哲; 周岭; 武频; 袁雯琰; 周铸

doi:10.13700/j.bh.1001-5965.2021.0738

基于PINN模型的导弹气动特性快速预测技术

doi: 10.13700/j.bh.1001-5965.2021.0738

蔺佳哲¹,
周岭^1, ,,
武频²,
袁雯琰²,
周铸¹

1.
中国空气动力研究与发展中心计算空气动力研究所，绵阳 621000
2.
上海大学计算机工程与科学学院，上海 200444

详细信息

通讯作者:
E-mail：zlkk72@sina.com

中图分类号: V211.24；TJ760.11
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- 被引次数: 0
出版历程
- 收稿日期: 2021-12-06
- 录用日期: 2022-01-25
- 网络出版日期: 2022-02-23
- 整期出版日期: 2023-10-31

Rapid prediction technology of missile aerodynamic characteristics based on PINN model

1.
Computational Aerodynamic Research Institute，China Aerodynamics Research and Development Center，Mianyang 621000，China
2.
School of Computer Engineering and Science，Shanghai University，Shanghai 200444，China

More Information

Corresponding author: E-mail：zlkk72@sina.com

摘要

摘要:
随着内嵌物理机理神经网络（PINN）模型的兴起，PINN模型开始应用于许多学科领域。为了实现导弹气动特性的快速预测，借助工程算法，构建了导弹气动数据集，以此训练导弹气动特性预测模型，包含基于多任务学习的神经网络（MTLNN）模型及在MTLNN模型基础上内嵌物理知识的PINN模型。数值模拟通过选取测试集，对比了MTLNN模型和PINN模型的预测效果，结果表明：PINN模型的预测精度较高，且基本控制在1%以内。探究PINN模型的泛化能力，测试集选取导弹气动数据集包络范围之外的数据，PINN模型预测精度仍然高于MTLNN模型。由于PINN模型引入了气动特性参数之间的物理机理，模型对训练样本数量的依赖程度降低，可以进一步节约数据获取成本，为导弹优化设计提供有力工具。
- 内嵌物理机理神经网络 /
- 导弹 /
- 气动特性 /
- 快速预测 /
- 数据驱动
Abstract:
With the rise of the physical-informed neural network (PINN) model, the PINN model has been applied to many subjects. With the aid of the missile engineering algorithm, the missile aerodynamic data set is created in order to train the multi-task learning neural network (MTLNN) model and the physical-informed -PINN model, two models that can quickly predict missile aerodynamic characteristics. By selecting test sets, the numerical simulation compares the prediction results of the MTLNN model with the PINN model, and the result shows that the prediction accuracy of the PINN model is higher, and the prediction relative error is less than 1%. Finally, the generalization ability of PINN model is explored. The test set selects data outside the envelope range of the missile aerodynamic data set. In this case, the prediction accuracy of the PINN model is higher than that of the MTLNN model. The PINN model has a physical mechanism connecting the parameters that control aerodynamic properties, which makes the model less reliant on the volume of training samples. This can further reduce data collection costs and give a strong tool for missile optimization design.
- PIMTLNN /
- missile /
- aerodynamic characteristics /
- rapid prediction /
- data-driven

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图 1 导弹气动特性预测的流程

Figure 1. Flow chart of missile aerodynamic characteristics prediction

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图 2 基于多任务学习的神经网络结构框图

Figure 2. Block diagram of neural network structure based on multi-task learning

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图 3 PINN 模型结构框图

Figure 3. Structural block diagram of PINN model

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图 4 某型战术导弹二维截面

Figure 4. Two-dimensional section of a tactical missile

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图 5 C_A、C_N、C_mz、X_p的预测值与真实值RMSE随训练样本数的变化

Figure 5. RMSE of prediction results and real values of C_A, C_N, C_mz, X_p changing with number of training samples

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图 6 内插情况下 C_A、C_N、C_mz、X_p的预测结果

Figure 6. Prediction results of C_A, C_N, C_mz, X_p in case of interpolation

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图 7 内插情况下C_A、C_N、C_mz、X_p的预测结果与真实值的RMSE和MRE

Figure 7. RMSE and MRE of prediction results and real values of C_A, C_N, C_mz, X_p in case of interpolation

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图 8 外插情况下C_A、C_N、C_mz、X_p的预测结果

Figure 8. Prediction results of C_A、C_N, C_mz, X_p in case of extrapolation

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图 9 外插情况下C_A、C_N、C_mz、X_p的预测值与真实值的RMSE和MRE

Figure 9. RMSE and MRE of prediction results and real values of C_A, C_N, C_mz, X_p in case of extrapolation

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图 10 物理知识体量和训练数据数量二者的关系

Figure 10. Relationship between volume of physical knowledge and amount of training data

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图 11 C_N、C_mz、X_p的预测值与真实值RMSE、MRE随训练样本数的变化

Figure 11. RMSE and MRE of prediction results and real values of C_N, C_mz, X_pchanging with number of training samples

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表 1 基于多任务学习的网络参数

Table 1. Network parameters based on multi-task learning

编号	结构类型	神经元节点数	层数	激活函数
1	共享层/隐藏层	1024	1	relu
2	共享层/隐藏层	512	1	relu
3	共享层/隐藏层	256	3	relu
4	共享层/隐藏层	128	1	relu
5	任务层/隐藏层	64	1	relu
6	任务层/隐藏层	32	3	relu
7	任务层/隐藏层	16	5	relu
8	任务层/隐藏层	8	4	relu
9	任务层/输出层	1	1	linear

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表 2 不同状态的外插对比

Table 2. Extrapolation comparison of different states

测试集	气动特性参数	预测误差RMSE		误差减少/%	测试集	气动特性参数	预测误差RMSE		误差减少/%
测试集	气动特性参数	MTLNN模型	PINN模型	误差减少/%	测试集	气动特性参数	MTLNN模型	PINN模型	误差减少/%
第1组	C_A	0.003665	0.003758		第3组	C_A	0.003337	0.003812
	C_N	0.102228	0.093603	8.44		C_N	0.060644	0.027035	55.42
	C_mz	0.119224	0.076152	36.13		C_mz	0.047269	0.043482	8.01
	X_p	0.004239	0.002134	49.67		X_p	0.002280	0.003299
第2组	C_A	0.004096	0.002591	36.73	第4组	C_A	0.002605	0.002937
	C_N	0.045346	0.026937	40.60		C_N	0.046499	0.038052	18.17
	C_mz	0.047311	0.030314	35.93		C_mz	0.053012	0.043537	17.87
	X_p	0.001888	0.001613	14.56		X_p	0.001615	0.001481	8.28

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