基于物理嵌入神经网络的叶栅损失模型

冯云阳; 宋西镇; 袁巍; 鹿哈男

doi:10.13224/j.cnki.jasp.20220750

基于物理嵌入神经网络的叶栅损失模型

doi: 10.13224/j.cnki.jasp.20220750

冯云阳^{1, 2,},
宋西镇^{1, 2},
袁巍^{1, 2,*, ,},
鹿哈男^{1, 2}

1.
北京航空航天大学能源与动力工程学院，北京 102206
2.
北京航空航天大学航空发动机气动热力国家级重点实验室，北京 102206

详细信息

作者简介:
冯云阳（1995-），男，博士生，研究方向为压气机气动稳定性、人工智能辅助压气机设计

通讯作者:
袁巍（1974-），男，副教授、博士生导师，博士，研究方向为叶轮机气动力学、压气机稳定性、风力机、内流实验测试等。E-mail：07691@buaa.edu.cn

中图分类号: V231.3
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出版历程
- 收稿日期: 2022-09-30
- 网络出版日期: 2023-04-20

Physics-informed neural networks based cascade loss model

FENG Yunyang^{1, 2
,},
SONG Xizhen^{1, 2},
YUAN Wei^{1, 2,*
, ,},
LU Ha’nan^{1, 2}

1.
School of Energy and Power Engineering，Beihang University，Beijing 102206，China
2.
National Key Laboratory of Science and Technology on Aero-Engine Aero-thermodynamics， Beihang University，Beijing 102206，China

摘要

摘要:
为解决传统的叶栅损失经验模型在构建过程中对于强非线性函数关系总结能力不足，导致其适用局限性、可修正性不好等问题。在一般端到端人工神经网络的基础上，进一步发展了物理嵌入神经网络方法，通过将叶栅表面压力分布引入神经网络建立叶栅损失模型，对叶栅压力分布和性能进行预测。经验证，相对于经验模型，端到端神经网络模型总体损失预测误差降低22.3%，物理嵌入神经网络模型总体损失预测误差下降37.9%。
- 替代模型 /
- 损失预测 /
- 深度学习 /
- 神经网络 /
- 物理嵌入
Abstract:
It is difficult to modify and broaden the scope of application for empirical models because of its inadequate ability to fit strong nonlinear function relationship. In order to solve these problems, a physics-informed deep learning cascade loss model of embedding the pressure distribution of cascade into neural networks was proposed. The loss prediction error decreased by 22.3% compared with empirical model for end-to-end neural networks and 37.9% compared with physics-informed model.
- surrogate model /
- loss prediction /
- deep learning /
- neural networks /
- physics-informed

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图 1 传统压气机叶型设计流程

Figure 1. Design process of conventional compressor blade profile

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图 2 不同损失模型预测流程

Figure 2. Predicting process of different loss model

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图 3 物理嵌入模型架构

Figure 3. Structure of physics-informed model

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图 4 多层感知机

Figure 4. Multiple layer percenptron

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图 5 3层稠密连接网络

Figure 5. 3-layer dense block

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图 6 叶栅气流转角特性

Figure 6. Turning-angle characteristic of cascade

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图 7 S沿叶栅弦向分布（进口气流角为45°）

Figure 7. Chordwise distribution of S （45° inlet flow angle）

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图 8 不同攻角下模型预测误差

Figure 8. Normalized predicting error of models at different incidences

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图 9 不同来流马赫数下模型预测误差

Figure 9. Normalized predicting error of models at different inflow Mach numbers

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图 10 各模型样本损失预测及数值模拟结果对比

Figure 10. Loss predictions of different models and loss from CFD results

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图 11 叶栅壁面压力分布物理嵌入模型预测与数值模拟结果对比（每20个数据点显示1个点）

Figure 11. Comparison of cascade wall pressure distribution between physics-informed model prediction and CFD （1 scatter is displayed for every 20 points）

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表 1 部分叶栅几何参数取值范围

Table 1. Value ranges of geometry parameter of cascade

叶栅几何参数	取值范围
稠度$\delta$	（1, 3.3）
安装角$ \gamma $/（°）	（0, 55）
弯角$\varphi$/（°）	（0, 65）
最大相对厚度$ t/C $	（0.025, 0.15）
最大厚度位置$\bar{e}$	（0.25, 0.75）
最大挠度位置$\bar{f}$	（0.25, 0.75）

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表 2 各模型归一化误差

Table 2. Normalized errors of different models

模型名称	归一化误差
Lieblein模型	0.2496
Banjac模型	0.2014
无物理嵌入模型	0.1564
物理嵌入模型	0.1251

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表 3 特殊测试集上各模型预测误差

Table 3. Normalized predicting errors of different models on conventional sections

模型名称	归一化误差
Lieblein模型	0.184 0
Banjac模型	0.169 0
无物理嵌入模型	0.1628
物理嵌入模型	0.131 0

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表 4 样本几何参数及来流条件

Table 4. Geometry parameters and inlet conditions for samples

样本编号	几何参数				来流条件
样本编号	稠度	安装角/（°）	弯角/（°）	最大厚度	马赫数	攻角/（°）
1	1.930	38.04	25.02	0.048	0.862	0
2	1.460	53.85	10.00	0.038	0.553	3
3	1.750	34.32	27.90	0.045	0.928	6
4	2.500	0.50	56.32	0.073	0.447	−3
5	2.188	27.87	31.34	0.058	0.711	−6
6	2.090	36.08	37.35	0.054	0.660	3

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