基于符号回归与待定系数优化的气膜冷却经验关联式构造方法

严晓; 马灿; 苏欣荣; 袁新

doi:10.19805/j.cnki.jcspe.2026.240812

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基于符号回归与待定系数优化的气膜冷却经验关联式构造方法

动力设备与系统 | 更新时间：2026-10-10

- 基于符号回归与待定系数优化的气膜冷却经验关联式构造方法
- A Method for Constructing Empirical Correlation Equations for Film Cooling Based on Symbolic Regression and Undetermined Coefficient Optimisation
- 动力工程学报 2026年46卷第4期页码：30-38
- 作者机构：
  
  1. 清华大学热科学与动力工程教育部重点实验室,北京,100084
  2. 中国船舶重工集团公司第七一九研究所船舶热能动力全国重点实验室,湖北,武汉,430205
- 作者简介：
  
  严晓(2002—),男,云南楚雄人,硕士研究生,研究方向为透平冷却机理研究。苏欣荣(通信作者),男,副研究员,博士,E-mail:suxr@mail.tsinghua.edu.cn。
- 基金信息：
  
  国家自然科学基金面上项目(52276031);国家科技重大专项资助项目(J2019-II-0008-0028,J2019-III-0007-0050)
- DOI：10.19805/j.cnki.jcspe.2026.240812
  中图分类号： TK474.8
- 纸质出版：2026
- 稿件说明：
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严晓, 马灿, 苏欣荣, 袁新. 基于符号回归与待定系数优化的气膜冷却经验关联式构造方法[J]. 动力工程学报, 2026, 46(4): 30-38.
严晓, 马灿, 苏欣荣, 袁新. 基于符号回归与待定系数优化的气膜冷却经验关联式构造方法[J]. 动力工程学报, 2026, 46(4): 30-38. DOI： 10.19805/j.cnki.jcspe.2026.240812.

DOI： 10.19805/j.cnki.jcspe.2026.240812

摘要

针对透平设计中经验关联式构造依赖学者经验

半经验半拟合方法不确定性大

且传统多项式拟合泛化性差、物理意义不足的问题

提出一种基于符号回归与待定系数优化的气膜冷却经验关联式构造方法。以气膜冷却横向平均有效度和表面有效传热系数为研究对象

针对工业设计场景

改进符号回归方法

通过选取关键特征量

添加待定系数并结合最小二乘法优化

构造适用于不同孔型、湍流度等工况的关联式。结果表明:根据改进后的方法所构造的关联式拟合效果优异

Abstract

To address the problems in turbine design where the construction of empirical correlations relies heavily on expert experience

the semi-empirical and semi-fitting method exhibits significant uncertainties

and traditional polynomial fitting suffers from poor generalization and insufficient physical interpretability

a method for constructing film cooling empirical correlations based on symbolic regression and optimization of undetermined coefficients was proposed. Taking the laterally averaged effectiveness and surface effective heat transfer coefficient of film cooling as the research objects

the symbolic regression method was improved for industrial design scenarios. By selecting key feature variables

incorporating undetermined coefficients

and optimizing with the least square method

correlations applicable to various working conditions such as different hole types and turbulence intensities were constructed. Results show that the correlations established by the improved method demonstrate excellent fitting performance

with a maximum correlation coefficient of 0.997 2 and a maximum relative error of 8.47% for the surface heat transfer coefficient. The correlations comply with the physical laws of film cooling and can effectively extrapolate to predict parameter values under other working conditions.

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Keywords

references

BILLARD L, DIDAY E. Regression analysis for interval-valued data[M]//KIERS H A L, RASSON J P, GROENEN P J F, et al. Data analysis, classification, and related methods. Berlin: Springer, 2000: 369-374.

左劼. 基因表达式编程核心技术研究[D]. 成都: 四川大学, 2004.

LOPES H S, WEINERT W R. EGIPSYS: an enhanced gene expression programming approach for symbolic regression problems[J]. International Journal of Applied Mathematics and Computer Science, 2004, 14(3): 375-384.

MAKKE N, CHAWLA S. Interpretable scientific discovery with symbolic regression: a review[J]. Artificial Intelligence Review, 2024, 57(1): 1-38.

何柏河. 数据特征机制下的符号回归研究[D]. 北京: 中国石油大学, 2023.

鲁强, 张洋. 基于蒙特卡洛树搜索的符号回归算法[J]. 计算机工程与设计, 2020, 41(8): 2158-2164.LU Qiang, ZHANG Yang. Solving symbol regression based on Monte Carlo tree search[J]. Computer Engineering and Design, 2020, 41(8): 2158-2164.

MARTIUS G, LAMPERT C H. Extrapolation and learning equations[C]//5th International Conference on Learning Representations. Toulon,France: OpenReview.net, 2017.

SCHMELZER M, DWIGHT R P, CINNELLA P. Discovery of algebraic reynolds-stress models using sparse symbolic regression[J]. Flow, Turbulence and Combustion, 2020, 104(2): 579-603.

MA W, ZHANG J, FENG K,et al.Dimensional homogeneity constrained gene expression programming for discovering governing equations[J].Journal of Fluid Mechanics, 2024, 985:38.

HE Zizhou, WU Chenyu, ZHANG Yufei. A field inversion and symbolic regression enhanced Spalart-Allmaras model for airfoil stall prediction[J]. Physics of Fluids,2024, 36(6): 065111.

刘鹏敏, 崔晓峰, 林翅翔, 等. 进气条件对扇形孔气膜冷却特性的影响[J]. 动力工程学报, 2023, 43(3): 319-325.LIU Pengmin, CUI Xiaofeng, LIN Chixiang, et al. Effect of inlet condition on film cooling performance of a fan-shaped hole[J]. Journal of Chinese Society of Power Engineering, 2023, 43(3): 319-325.

唐学智, 李录平, 黄章俊, 等. 孔间距对燃气轮机动叶气膜冷却效果的影响[J]. 动力工程学报, 2018, 38(2): 105-113, 131.TANG Xuezhi, LI Luping, HUANG Zhangjun, et al. Influence of hole spacing on the film cooling effectiveness of a gas turbine moving blade[J]. Journal of Chinese Society of Power Engineering, 2018, 38(2): 105-113, 131.

COLBAN W F, THOLE K A, BOGARD D. A film-cooling correlation for shaped holes on a flat-plate surface[J]. Journal of Turbomachinery, 2011, 133(1): 011002.

林翅翔, 崔晓峰, 戴韧. 预测扇形孔气膜冷却效率的一种新关联式及应用[J]. 动力工程学报, 2023, 43(11): 1440-1447.LIN Chixiang, CUI Xiaofeng, DAI Ren. A new correlation for predicting film cooling effectiveness of fan-shaped holes and its application[J]. Journal of Chinese Society of Power Engineering, 2023, 43(11): 1440-1447.

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