基于神经网络的线性稳定性分析方法

张二帅; 刘建新; 黄章峰

doi:10.7638/kqdlxxb-2024.0031

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基于神经网络的线性稳定性分析方法

研究论文 | 更新时间：2026-05-28

- 基于神经网络的线性稳定性分析方法
- Linear stability analysis based on neural network
- 空气动力学学报 2025年43卷第2期页码：60-74
- 作者机构：
  
  天津大学机械工程学院,天津,300072
- 作者简介：
  
  张二帅（1997—），男，河北邯郸人，硕士，研究方向：流动稳定性. E-mail：es_zhang@tju.edu.cn
  刘建新*，副教授，研究方向：流动稳定性和转捩. E-mail： shookware@tju.edu.cn
- 基金信息：
  
  国家自然科学基金重大项目（92052301）;国家自然科学基金面上项目（12172252）;国家自然科学基金（92271102）
- DOI：10.7638/kqdlxxb-2024.0031
  中图分类号： O357.4+1;V211
- 纸质出版：2025
- 稿件说明：
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张二帅, 刘建新, 黄章峰. 基于神经网络的线性稳定性分析方法[J]. 空气动力学学报, 2025, 43(2): 60−74.

ZHANG Ershuai, LIU Jianxin, HUANG Zhangfeng. Linear stability analysis based on neural network[J]. 2025, 43(2): 60-74.
张二帅, 刘建新, 黄章峰. 基于神经网络的线性稳定性分析方法[J]. 空气动力学学报, 2025, 43(2): 60−74. DOI： 10.7638/kqdlxxb-2024.0031

ZHANG Ershuai, LIU Jianxin, HUANG Zhangfeng. Linear stability analysis based on neural network[J]. 2025, 43(2): 60-74. DOI： 10.7638/kqdlxxb-2024.0031.

摘要

在实现e

方法时，需要搜索流场中的不稳定波，并大量求解当地边界层的稳定性问题，因此为高效求解当地边界层的不稳定波参数，提出了一种基于神经网络的线性稳定性分析方法（neural network-based linear stability analysis

NN-LSA）。采用卷积神经网络给出最不稳定波频率

、展向波数

、流向波数

和增长率

max

的初值对，再通过迭代法计算失稳扰动波的实际空间失稳波数和增长率。使用平板数据集训练神经网络模型，并利用平板和尖锥算例对NN-LSA方法的准确性和计算效率进行验证。结果表明：神经网络部分对不稳定波参数的预测结果与线性稳定性理论的计算结果吻合较好；LSA部分可根据神经网络提供的预测值，通过迭代法找到最不稳定波；NN-LSA方法的求解效率较高，求解时间比全局搜索方法约低20～50倍，大大减小了人为因素在计算过程中的影响。本文提出的NN-LSA方法可以实现自动分析边界层流动的线性稳定性，具有一定的应用潜力。

Abstract

The e

method

which has been widely used for predicting boundary-layer transition

necessitates a meticulous search for unstable modes by solving a large number of local boundary-layer stability problems

a process that can be very time-consuming. This paper proposes a novel neural network-based linear stability analysis (NN-LSA) method

that leverages convolutional neural networks to generate an initial guess of the frequency ($\omega $)

spanwise and streamwise wave nu

mbers ($ \beta$ and $\alpha_{\rm r} $)

and growth rate ($\sigma_{\rm max} $) of the most unstable mode. Subsequently

the actual values are iteratively calculated based on this initial guess. The neural network model is trained using a flat plate dataset and the accuracy and computational efficiency of NN-LSA are validated by both flat plate and sharp cone test cases. The results demonstrate that the unstable wave parameters of NN are good agreement with linear stability theory. The LSA component

based on the predicted values provided by NN

can iteratively caculate the most unstable waves. Moreover

the computational time of the NN-LSA method is approximately 20 to 50 times lower than global search method

significantly improving computational efficiency and reducing the influence of human factors in the calculation process. The proposed NN-LSA method enables automated analysis of the linear stability of boundary layer flows and shows promising potential for practical applications.

关键词

Keywords

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