基于颤振样本识别和颤振度分析的颤振边界预测方法

陈鸣峰; 周丽

doi:10.13224/j.cnki.jasp.20220311

基于颤振样本识别和颤振度分析的颤振边界预测方法

doi: 10.13224/j.cnki.jasp.20220311

陈鸣峰,
周丽^*, ,

南京航空航天大学航空航天结构力学及控制全国重点实验室，南京 210016

基金项目: 国家自然科学基金（52075243）；江苏省高校优势学科建设工程资助项目

详细信息

作者简介:
陈鸣峰（1998-），男，硕士生，主要从事飞机颤振边界预测研究。E-mail：cmf425@nuaa.edu.cn

通讯作者:
周丽（1963-），女，教授、博士生导师，博士，主要从事结构健康监测研究。E-mail：lzhou@nuaa.edu.cn

中图分类号: V216.2⁺4
计量
- 文章访问数: 130
- HTML浏览量: 42
- PDF量: 39
- 被引次数: 0
出版历程
- 收稿日期: 2022-05-06
- 网络出版日期: 2024-08-01

Flutter boundary prediction method based on flutter-sample identification and flutter-degree analysis

CHEN Mingfeng,
ZHOU Li^{*
, ,}

State Key Laboratory of Mechanics and Control for Aerospace Structures，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China

摘要

摘要:
提出一种基于机器学习的颤振边界预测方法，能够在风速到达亚临界状态前进行颤振速度的预测。从风洞响应信号中提取颤振信号特征，根据飞行状态的不同建立分类模型；接着分别在不同颤振样本下建立回归模型，用于颤振度分析。进行预测时，根据待测数据的分类表现，将颤振度分析的结果进行加权计算，得到当前风速对应的颤振度，再计算出颤振风速。在进行机器学习的算法选择时，使用朴素贝叶斯算法、支持向量机法、K近邻算法等机器学习算法进行分类模型的构建，用线性回归、支持向量机法、高斯过程回归等进行回归模型的构建。结果显示：K近邻算法在分类算法中表现最优，而高斯过程回归算法在回归算法中表现最优。通过试验数据的交叉验证，该方法可以通过颤振样本识别和颤振度分析，在离颤振边界较远时，较为准确地预测出颤振临界速度。
- 颤振边界预测 /
- 机器学习 /
- 特征提取 /
- 颤振样本识别 /
- 颤振度分析
Abstract:
A flutter boundary prediction method based on machine learning was proposed, which can predict the flutter speed before the wind speed reaches the subcritical state. The flutter signal features were firstly extracted from the wind tunnel response signals, and the classification model was established according to different flight states. Then, regression models were established under different flutter-samples for flutter-degree analysis. To predict the flutter boundary, the results of flutter-degree analysis were weighted to obtain the flutter degree corresponding to the current wind speed according to the classification performance of the response data, and then the flutter wind speed was calculated. In the selection of machine learning algorithms, machine learning algorithms such as Naive Bayes, Support Sector Machine and k-Nearest Neighbor were performed to construct the classification model, while Linear Regression, Support Vector Machine and Gaussian Process Regression were performed to construct the regression model, which was used for flutter-sample identification and flutter-degree analysis respectively. The results showed that the k-Nearest Neighbor algorithm performed best in the classification algorithm, while the Gaussian Process Regression algorithm performed best in the regression algorithm. Through cross validation of test data, this method can accurately predict the flutter speed when it was far from the flutter boundary.
- flutter boundary prediction /
- machine learning /
- feature extraction /
- flutter-sample identification /
- flutter-degree analysis

HTML

图 1 基于颤振样本识别和颤振度分析的颤振临界速度预测流程图

Figure 1. Flow chart of flutter boundary prediction based on flutter-sample identification and flutter-degree analysis

下载: 全尺寸图片幻灯片

图 2 某型飞机机翼的低速风洞试验

Figure 2. Low speed wind tunnel test of an aircraft wing

下载: 全尺寸图片幻灯片

图 3 阶梯状风速和“平滑化”后风速

Figure 3. Stepped wind speed and “smoothed” wind speed

下载: 全尺寸图片幻灯片

图 4 多余数据剔除后风速对比图

Figure 4. Comparison diagram of wind speed after elimination of redundant data

下载: 全尺寸图片幻灯片

图 5 频谱幅值及其倒数与风速关系图

Figure 5. Relationship between spectrum amplitude or its reciprocal and wind speed

下载: 全尺寸图片幻灯片

图 6 颤振度与风速的关系图

Figure 6. Relationship between flutter-degree and wind speed

下载: 全尺寸图片幻灯片

表 1 各分类算法对于颤振样本识别情况的统计结果

Table 1. Statistical results of classification algorithm for flutter-sample identification

各类算法	评价指标
各类算法	准确度/%	AUC
分类决策树	66.5	0.913
朴素贝叶斯	38.0	0.739
支持向量机法	72.0	0.975
K近邻算法	80.1	0.961

下载: 导出CSV

表 2 各回归算法对于颤振度分析预测情况的统计结果

Table 2. Statistical results of prediction of each regression algorithm for flutter-degree analysis

各回归算法	评价指标
各回归算法	RMSE	MAE	R-squared
线性回归	0.0596	0.0379	0.93
回归决策树	0.0386	0.0253	0.97
支持向量机	0.0502	0.0298	0.95
高斯过程回归	0.0303	0.0202	0.98

下载: 导出CSV

表 3 第5组试验数据分类结果统计

Table 3. Statistics of classification results of the fifth group of test data

颤振样本	相似度/%	颤振样本	相似度/%
1	11.39	11	3.96
2	0	12	6.44
3	0	13	20.79
4	0.49	14	0
6	6.93	15	0
7	38.61	16	0
8	4.46	17	3.96
9	0.99	18	0
10	1.98	19	0

下载: 导出CSV

表 4 各最低相似阈值下的颤振预测误差统计

Table 4. Statistics of flutter prediction error under each lowest similarity threshold

颤振度	颤振预测误差/%
颤振度	b=3	b=5	b=7	b=9	b=12	b=15
0.4	−8.60	−8.60	−7.94	−9.23	−9.23	−9.23
0.6	−1.73	−2.02	−0.83	−0.83	−3.84	−3.84
0.8	−4.12	−4.97	−5.56	−7.39	−8.34	−8.34
0.9	0.39	0.17	−0.87	−1.10	−1.25	−1.33

下载: 导出CSV

表 5 最小有效预测风速统计情况

Table 5. Statistics of minimum effective predicted wind speed

数据组别	最小有效预测风速/（m/s）	颤振临界速度/（m/s）
1	17.7	33.3
2	27.0	38.6
3	29.2	38.6
4	28.3	38.7
5	15.6	39
6	20.0	36.4
7	17.7	35.9
8	11.7	35.8
9	25.2	35.9
10	18.1	37.6
11	13.2	35.2
12	11.1	35
13	12.1	35.1
14	26.6	36.8
15	23.8	36.4
16	26.2	37.4
17	14.9	36.5
18	22.4	37.2
19	24.3	29.7

下载: 导出CSV

表 6 颤振预测误差统计情况

Table 6. Statistics of flutter prediction error

组别	颤振预测误差/%
组别	D=0.4	D=0.5	D=0.6	D=0.7	D=0.8	D=0.9
1			−5.37	−8.20	−5.88	−6.81
2				−4.87	−7.77	−0.44
3					−9.15	−10.94
4					−5.51	−12.53
5	−7.94	3.71	−0.83	−0.02	−5.56	−0.87
6			−4.05	4.70	−0.48	−7.52
7		−5.21	−6.60	−4.61	−5.32	−6.69
8	−7.99	−5.64	−6.91	−6.40	1.99	−5.98
9					−4.44	−5.64
10			−6.35	−7.22	−9.36	−18.02
11	−7.56	−8.24	−5.03	−6.41	−10.46	−8.26
12	−10.78	4.62	−5.95	−0.35	−4.5	−10.61
13	−8.12	−4.37	−5.4	−5.82	−7.14	−11.56
14					−8.94	−9.80
15				−6.95	−5.96	−3.36
16					−11.20	−4.07
17		−3.76	−6.35	−2.57	−6.09	−12.3
18					−10.59	−12.45
19						−3.88
注：空白位置表示该颤振度对应的速度小于最小有效预测风速。

下载: 导出CSV

参考文献(25)

[1]	李扬,周丽. 颤振边界预测的系统稳定性分析方法[J]. 航空动力学报,2018,33(4): 980-988. LI Yang,ZHOU Li. Flutter boundary prediction research depending on system stability analysis methods[J]. Journal of Aerospace Power,2018,33(4): 980-988. (in Chinese LI Yang, ZHOU Li. Flutter boundary prediction research depending on system stability analysis methods[J]. Journal of Aerospace Power, 2018, 33(4): 980-988. (in Chinese)
[2]	LIND R. Flight-test evaluation of flutter prediction methods[J]. Journal of Aircraft,2003,40(5): 964-970. doi: 10.2514/2.6881
[3]	肖军,周新海,谷传纲,等. 二维叶栅气固耦合颤振分析[J]. 航空动力学报,2006,21(1): 106-111. XIAO Jun,ZHOU Xinhai,GU Chuangang,et al. Flutter analysis of 2-D cascades under gas-solid coupled conditions[J]. Journal of Aerospace Power,2006,21(1): 106-111. (in Chinese doi: 10.3969/j.issn.1000-8055.2006.01.020 XIAO Jun, ZHOU Xinhai, GU Chuangang, et al. Flutter analysis of 2-D cascades under gas-solid coupled conditions[J]. Journal of Aerospace Power, 2006, 21(1): 106-111. (in Chinese) doi: 10.3969/j.issn.1000-8055.2006.01.020
[4]	张伟伟,钟华寿,肖华,等. 颤振飞行试验的边界预测方法回顾与展望[J]. 航空学报,2015,36(5): 1367-1384. ZHANG Weiwei,ZHONG Huashou,XIAO Hua,et al. Review and prospect of flutter boundary prediction methods for flight flutter testing[J]. Acta Aeronautica et Astronautica Sinica,2015,36(5): 1367-1384. (in Chinese ZHANG Weiwei, ZHONG Huashou, XIAO Hua, et al. Review and prospect of flutter boundary prediction methods for flight flutter testing[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(5): 1367-1384. (in Chinese)
[5]	IOVNOVICH M,NAHOM T,PRESMAN M,et al. Assessment of advanced flutter flight-test techniques and flutter boundary prediction methods[J]. Journal of Aircraft,2018,55(5): 1877-1889. doi: 10.2514/1.C034716
[6]	ZIMMERMAN N H,WEISSENBURGER J T. Prediction of flutter onset speed based on flight testing at subcritical speeds[J]. Journal of Aircraft,1964,1(4): 190-202. doi: 10.2514/3.43581
[7]	李扬,周丽,杨秉才. 基于自然激励技术的颤振边界预测[J]. 航空动力学报,2016,31(11): 2744-2749. LI Yang,ZHOU Li,YANG Bingcai. Flutter boundary prediction based on natural excitation technique[J]. Journal of Aerospace Power,2016,31(11): 2744-2749. (in Chinese LI Yang, ZHOU Li, YANG Bingcai. Flutter boundary prediction based on natural excitation technique[J]. Journal of Aerospace Power, 2016, 31(11): 2744-2749. (in Chinese)
[8]	仲继泽,徐自力. 基于动网格降阶算法的机翼颤振边界预测[J]. 振动与冲击,2017,36(4): 185-191. ZHONG Jize,XU Zili. Wing flutter prediction using a reduced dynamic mesh method[J]. Journal of Vibration and Shock,2017,36(4): 185-191. (in Chinese ZHONG Jize, XU Zili. Wing flutter prediction using a reduced dynamic mesh method[J]. Journal of Vibration and Shock, 2017, 36(4): 185-191. (in Chinese)
[9]	邓海均,熊波,罗新福,等. 连续式跨声速风洞短轴探管设计与试验[J]. 航空动力学报,2022,37(6): 1171-1180. DENG Haijun,XIONG Bo,LUO Xinfu,et al. Design and test of short centerline probe in continuous transonic wind tunnel[J]. Journal of Aerospace Power,2022,37(6): 1171-1180. (in Chinese DENG Haijun, XIONG Bo, LUO Xinfu, et al. Design and test of short centerline probe in continuous transonic wind tunnel[J]. Journal of Aerospace Power, 2022, 37(6): 1171-1180. (in Chinese)
[10]	郑宇宁. 多源不确定性条件下气动弹性系统颤振可靠性分析方法[J]. 振动与冲击,2021,40(3): 54-62. ZHENG Yuning. Flutter reliability analysis method of aeroelastic system under multi-source uncertainty[J]. Journal of Vibration and Shock,2021,40(3): 54-62. (in Chinese ZHENG Yuning. Flutter reliability analysis method of aeroelastic system under multi-source uncertainty[J]. Journal of Vibration and Shock, 2021, 40(3): 54-62. (in Chinese)
[11]	MCNAMARA J J,FRIEDMANN P P. Flutter-boundary identification for time-domain computational aeroelasticity[J]. AIAA Journal,2007,45(7): 1546-1555. doi: 10.2514/1.26706
[12]	夏存江,詹于游. 基于改进的SENet航空发动机振动预测[J]. 航空动力学报,2022,37(12): 2807-2817. XIA Cunjiang,ZHAN Yuyou. Vibration prediction of aeroengines based on enhanced SENet model[J]. Journal of Aerospace Power,2022,37(12): 2807-2817. (in Chinese XIA Cunjiang, ZHAN Yuyou. Vibration prediction of aeroengines based on enhanced SENet model[J]. Journal of Aerospace Power, 2022, 37(12): 2807-2817. (in Chinese)
[13]	LIAKOS K G,BUSATO P,MOSHOU D,et al. Machine learning in agriculture: a review[J]. Sensors,2018,18(8): 2674. doi: 10.3390/s18082674
[14]	JORDAN M I,MITCHELL T M. Machine learning: trends,perspectives,and prospects[J]. Science,2015,349(6245): 255-260. doi: 10.1126/science.aaa8415
[15]	何清,李宁,罗文娟,等. 大数据下的机器学习算法综述[J]. 模式识别与人工智能,2014,27(4): 327-336. HE Qing,LI Ning,LUO Wenjuan,et al. A survey of machine learning algorithms for big data[J]. Pattern Recognition and Artificial Intelligence,2014,27(4): 327-336. (in Chinese doi: 10.3969/j.issn.1003-6059.2014.04.007 HE Qing, LI Ning, LUO Wenjuan, et al. A survey of machine learning algorithms for big data[J]. Pattern Recognition and Artificial Intelligence, 2014, 27(4): 327-336. (in Chinese) doi: 10.3969/j.issn.1003-6059.2014.04.007
[16]	KADEN M,LANGE M,NEBEL D,et al. Aspects in classification learning-review of recent developments in learning vector quantization[J]. Foundations of Computing and Decision Sciences,2014,39(2): 79-105. doi: 10.2478/fcds-2014-0006
[17]	邱德红,陈传波. 融合无监督和监督学习策略生成的多分类决策树[J]. 小型微型计算机系统,2004,25(4): 555-559. QIU Dehong,CHEN Chuanbo. Construction of multi-classification decision tree combining unsupervised and supervised learning strategy[J]. Journal of Chinese Computer Systems,2004,25(4): 555-559. (in Chinese doi: 10.3969/j.issn.1000-1220.2004.04.018 QIU Dehong, CHEN Chuanbo. Construction of multi-classification decision tree combining unsupervised and supervised learning strategy[J]. Journal of Chinese Computer Systems, 2004, 25(4): 555-559. (in Chinese) doi: 10.3969/j.issn.1000-1220.2004.04.018
[18]	徐平峰,王树达,尚来旭,等. 基于自助法的高斯贝叶斯网结构学习[J]. 长春工业大学学报,2020,41(4): 313-321. XU Pingfeng,WANG Shuda,SHANG Laixu,et al. Structural learning of Gaussian Bayesian networks by bootstrap[J]. Journal of Changchun University of Technology,2020,41(4): 313-321. (in Chinese XU Pingfeng, WANG Shuda, SHANG Laixu, et al. Structural learning of Gaussian Bayesian networks by bootstrap[J]. Journal of Changchun University of Technology, 2020, 41(4): 313-321. (in Chinese)
[19]	祁亨年. 支持向量机及其应用研究综述[J]. 计算机工程,2004,30(10): 6-9. QI Hengnian. Support vector machines and application research overview[J]. Computer Engineering,2004,30(10): 6-9. (in Chinese doi: 10.3969/j.issn.1000-3428.2004.10.003 QI Hengnian. Support vector machines and application research overview[J]. Computer Engineering, 2004, 30(10): 6-9. (in Chinese) doi: 10.3969/j.issn.1000-3428.2004.10.003
[20]	黄铭,孙林夫,任春华,等. 改进KNN的时间序列分析方法[J]. 计算机科学,2021,48(6): 71-78. HUANG Ming,SUN Linfu,REN Chunhua,et al. Improved KNN time series analysis method[J]. Computer Science,2021,48(6): 71-78. (in Chinese doi: 10.11896/jsjkx.200500044 HUANG Ming, SUN Linfu, REN Chunhua, et al. Improved KNN time series analysis method[J]. Computer Science, 2021, 48(6): 71-78. (in Chinese) doi: 10.11896/jsjkx.200500044
[21]	HUANG Guangbin,ZHOU Hongming,DING Xiaojian,et al. Extreme learning machine for regression and multiclass classification[J]. IEEE Transactions on Systems,Man,and Cybernetics,Part B (Cybernetics),2012,42(2): 513-529. doi: 10.1109/TSMCB.2011.2168604
[22]	王惠文,孟洁. 多元线性回归的预测建模方法[J]. 北京航空航天大学学报,2007,33(4): 500-504. WANG Huiwen,MENG Jie. Predictive modeling on multivariate linear regression[J]. Journal of Beijing University of Aeronautics and Astronautics,2007,33(4): 500-504. (in Chinese doi: 10.3969/j.issn.1001-5965.2007.04.028 WANG Huiwen, MENG Jie. Predictive modeling on multivariate linear regression[J]. Journal of Beijing University of Aeronautics and Astronautics, 2007, 33(4): 500-504. (in Chinese) doi: 10.3969/j.issn.1001-5965.2007.04.028
[23]	KIM H J,FAY M P,YU Binbing,et al. Comparability of segmented line regression models[J]. Biometrics,2004,60(4): 1005-1014. doi: 10.1111/j.0006-341X.2004.00256.x
[24]	何志昆,刘光斌,赵曦晶,等. 高斯过程回归方法综述[J]. 控制与决策,2013,28(8): 1121-1129,1137. HE Zhikun,LIU Guangbin,ZHAO Xijing,et al. Overview of Gaussian process regression[J]. Control and Decision,2013,28(8): 1121-1129,1137. (in Chinese HE Zhikun, LIU Guangbin, ZHAO Xijing, et al. Overview of Gaussian process regression[J]. Control and Decision, 2013, 28(8): 1121-1129, 1137. (in Chinese)
[25]	SCHULZ E,SPEEKENBRINK M,KRAUSE A. A tutorial on Gaussian process regression: modelling,exploring,and exploiting functions[J]. Journal of Mathematical Psychology,2018,85: 1-16. doi: 10.1016/j.jmp.2018.03.001