基于符号回归的轴流压气机特性数据建模

刘锬韬; 高丽敏; 冯旭栋; 王现林; 刘志春

doi:10.13224/j.cnki.jasp.20260167

基于符号回归的轴流压气机特性数据建模

doi: 10.13224/j.cnki.jasp.20260167

1.
珠海格力电器股份有限公司博士后科研工作站，珠海 100084
2.
西北工业大学动力与能源学院，西安 710072
3.
四川燃气涡轮研究院高空模拟技术重点实验室，四川绵阳 621000
4.
华中科技大学能源与动力工程学院，武汉 430074

基金项目: 国家自然科学基金（92152301）；国家科技重大专项（J2019-Ⅱ-0016-0037）

详细信息

作者简介:
刘锬韬（1989-），男，博士，主要从事叶轮机械气动热力学研究。E-mail：liutantao@mail.nwpu.edu.cn

中图分类号: V231.1；TK472
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- 文章访问数: 23
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- 被引次数: 0
出版历程
- 收稿日期: 2026-05-16
- 网络出版日期: 2026-10-13

Modeling of axial compressor characteristic data based on symbolic regression

1.
Postdoctoral workstation，Gree Electric Appliances，Incorporated of Zhuhai，Zhuhai 100084，China
2.
School of Power and Energy，Northwestern Polytechnical University，Xi’an 710072，China
3.
Science and Technology on Altitude Simulation Laboratory，Sichuan Gas Turbine Establishment，Mianyang 621000，China
4.
School of Energy and Power Engineering，Huazhong University of Science and Technology，Wuhan 430074，China

摘要

摘要:
为完整准确地描述不同压比轴流压气机的全转速范围的特性数据规律，在以前研究的基础上，利用符号回归机器学习方法对各种压比压气机峰值效率点参数之间的规律进行了进一步地探索，并提出了使用符号回归对多数据源多参数复杂模型的建模方法。使用PySR符号回归库，通过数据逐条拟合，多轮筛选验证，从47份压气机特性数据中，总结出了压气机峰值效率点参数之间的具有一定普适性的规律：总压比-转速、流量-转速之间具有双曲正切函数规律，而效率-转速具有分段二次及指数关系；利用构造的峰值效率点关系式及以前研究中提出的特性线近喘振区和近堵塞区的关联式构造了压气机特性非线性模型，可以对大部分压气机几乎全转速范围特性进行预测，且具有较高预测精度。
- 轴流压气机 /
- 特性建模 /
- 符号回归 /
- 机器学习 /
- 峰值效率点
Abstract:
To comprehensively and accurately characterize the performance characteristics of axial compressors with a variety of pressure ratios across the full rotational speed range, based on previous research, this study further investigated the parametric relationships at the peak efficiency points of compressors with all pressure-ratio using a symbolic regression which is a machine learning approach. A modeling framework leveraging symbolic regression for complex, multi-source, and multi-parameter systems is proposed. Using the PySR symbolic regression library, data points are fitted individually and subjected to multi-round screening and validation. From the characteristic data of 47 compressors, general correlations on the peak efficiency points are derived: both the total pressure ratio–rotational speed and mass flow rate–rotational speed relationships conform to a hyperbolic tangent function, whereas the efficiency–rotational speed relationship exhibits a piecewise quadratic and exponential behavior. By integrating these derived correlations on peak efficiency points with previously established equations for the near-surge and near-choke regions of the characteristic curves, a nonlinear compressor performance model was developed. The proposed model demonstrates the capability to predict the performance characteristics of a broad range of compressors over nearly the entire speed range with high fidelity.
- axial compressor /
- characteristic modeling /
- symbolic regression /
- machine learning /
- peak efficiency point

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图 1 表达式变异与杂交

Figure 1. Expression mutation and hybridization

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图 2 特征总压比分布直方图

Figure 2. Histogram of characteristic total pressure ratio

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图 3 特征总压比效率分布图

Figure 3. Scatter of characteristic total pressure ratio with efficiency

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图 4 峰值效率点流量与转速关系（线条颜色对应压气机的特征总压比）

Figure 4. Relationship between mass flow of peak efficiency points and speed （colors of lines represent characteristic total pressure ratio）

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图 5 表达式筛选流程

Figure 5. Flowchart of expression sifting

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图 6 两表达式的预测偏差

Figure 6. Prediction errors of two expressions

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图 7 两表达式在四型压气机预测结果

Figure 7. Predictions of two expressions on four compressors

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图 8 压气机归一化峰值效率点总压比与转速关系（线条颜色对应压气机的特征点总压比）

Figure 8. Relationship between normalized total pressure of peak efficiency points ratio and speed （Colors of lines represent characteristic total pressure ratio）

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图 9 两表达式的预测偏差

Figure 9. Prediction errors of two expressions

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图 10 两种参数在四型压气机上预测结果

Figure 10. Predictions of two expressions on four compressors

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图 11 峰值效率点效率分布（线条颜色对应压气机的特征点总压比）

Figure 11. Distributions of peak efficiency （Colors of lines represent characteristic total pressure ratio）

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图 12 峰值效率点效率分段分布

Figure 12. Partial distributions of efficiency of peak efficiency points

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图 13 两型压气机峰值效率点效率预测曲线

Figure 13. Predictions of efficiency of peak efficiency points on two compressors

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图 14 压气机特性预测结果

Figure 14. Prediction results of compressors

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表 1 流量-转速的表达式

Table 1. Expressions of mass flow with speed

序号	参数数量	表达式	ε_mse×10⁴
1	3	$ y={c}_{2}+\tanh （{c}_{1}{x}^{{{c}_{3}}}） $	2.45
2	3	$ y={c}_{2}+\tanh （{x}^{{{c}_{3}}} （{c}_{1}+{x}^{3}）） $	2.61
3	3	$ y={c}_{2}+\tanh （{x}^{{{c}_{3}}} （{c}_{1}+{x}^{2}）） $	2.86
4	4	$ y={c}_{1}\tanh （{c}_{2}{x}^{{{c}_{4}}}） +{c}_{3} $	1.15
5	4	$ y={c}_{1}\tanh （{c}_{2}{x}^{{{c}_{4}}}+{c}_{3}） $	1.16
6	4	$ y=\tanh （x （{c}_{1}{x}^{{{c}_{4}}}+{c}_{2}）） +{c}_{3} $	1.61

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表 2 总压比-转速的表达式

Table 2. Expressions of total pressure ratio with speed

序号	参数数量	表达式	ε_mse×10⁴
1	4	$ y={b}_{1}\tanh （{b}_{2}{x}^{{{b}_{4}}}） +{b}_{3} $	1.21
2	4	$ \begin{gathered}y ={b}_{1}\exp （-{B}^{-1}） ,\\B ={b}_{2}\exp （\exp （{b}_{3}x）） +{b}_{4}\end{gathered} $	1.22
3	4	$ y={b}_{3}+ （{b}_{1}+1/x） \tanh （{b}_{2}{x}^{{{b}_{4}}}） $	1.83
4	3	$ y=\tanh （{b}_{1}{x}^{{{b}_{3}}}） +{b}_{2} $	3.52
5	3	$ y=\tanh （{b}_{2}{x}^{{{b}_{3}}}） /x+{b}_{1} $	4.44

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表 3 效率-转速的表达式

Table 3. Expressions of efficiency with speed

分段	表达式	ε_mse/10⁵
左	$ y=\exp （{c}_{1}{x}^{2} （{c}_{2}+x+{ （x-{{c}_{3}}） }^{-1}）） $	4.0
左	$ y=-{c}_{1}{x}^{2}{ （{{c}_{2}}x+1） }^{2}+1 $	5.3
左	$ y=-{c}_{1}{\mathrm{x}}^{2}\exp （{c}_{2}x） +1 $	5.4
左	$ y=1- （{x}^{2}+x）（{x}^{2}+3x）（{c}_{1}x+{c}_{2}） $	9.9
左	$ y=1+ （{x}^{3}+{x}^{2}）（-{c}_{1}x+{c}_{2}） $	1.0
右	$ y=1-{c}_{1}{x}^{{{c}_{2}}} $	7.0
右	$ y={c}_{1}{x}^{2} （-{c}_{2}x-{c}_{3}+\exp （\mathrm{x}）） +1 $	7.4
右	$ y=\exp （-{c}_{1}{x}^{{{c}_{2}}}） $	7.6
右	$ y=1-x （{c}_{1}{x}^{{{c}_{3}}}-{c}_{2}x） $	8.1
右	$ y=1-{a}_{1}{x}^{2} （{a}_{3}+x （2x-{a}_{2}）） $	8.1

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