采用K-SVD字典训练稀疏基的压缩感知叶尖间隙数据重构方法

吴军; 冯成斌; 宋丰成; 袁少博; 于之靖

doi:10.13433/j.cnki.1003-8728.20220068

采用K-SVD字典训练稀疏基的压缩感知叶尖间隙数据重构方法

doi: 10.13433/j.cnki.1003-8728.20220068

吴军^{1, 2,},
冯成斌¹,
宋丰成¹,
袁少博³,
于之靖³

1.
中国民航大学航空工程学院, 天津 300300
2.
天津大学精密测试技术及仪器国家重点实验室, 天津 300072
3.
中国民航大学电子信息与自动化学院, 天津 300300

基金项目:

国家自然科学基金项目 52005500

中央高校基本科研业务费高水平成果培育专项 3122023PY06

详细信息

作者简介:
吴军(1986-), 副教授, 博士研究生, 研究方向为视觉测量技术, 发动机故障诊断与监测, j_wu@cauc.edu.cn

中图分类号: TH822
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- PDF下载量: 25
- 被引次数: 0
出版历程
- 收稿日期: 2021-07-30
- 刊出日期: 2023-07-25

A Sparse Basis Compressed Sensing Tip Clearance Data Reconstruction Method was Trained with K-SVD Dictionary

1.
Aeronautical Engineering College, Civil Aviation University of China, Tianjin 300300, China
2.
State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China
3.
Electronic Information and Automation College, Civil Aviation University of China, Tianjin 300300, China

摘要

摘要: 航空发动机叶尖间隙是监控其运行状态的有效参数，现有间隙测量方法很难满足超高转速下间隙距离的奈奎斯特采样率，因此无法有效提取精确的叶尖间隙值。本文基于压缩感知原理，针对间隙距离数据特征提出一种采用K-SVD(K-singular value decomposition)字典训练稀疏基的数据重构方法，该方法首先构建出K-SVD字典稀疏基对数据进行稀疏化表示，然后使用m序列高斯随机矩阵对数据进行压缩观测，最后基于压缩欠采样观测值使用正交匹配追踪算法对数据进行重构，进而精确提取叶尖间隙值。实验结果表明，在欠采样条件下间隙距离数据可精确恢复重构，与高采样率下的间隙数据相比，重构误差不超过0.02 mm。
- 叶尖间隙 /
- 欠采样 /
- 压缩感知 /
- K-SVD字典稀疏基 /
- 正交匹配追踪算法
Abstract: The measurement of blade tip clearance is an effective parameter to monitor the running state of aeroengine. The existing clearance measurement methods are difficult to meet the Nyquist sampling rate of clearance distance under ultra-high rotating speed, so the accurate tip clearance value cannot be effectively extracted. In terms of the principle of compressed sensing, a data reconstruction method by using K-SVD(K-singular value decomposition) dictionary to train the sparse base according to the gap distance data features is proposed. In this method, the sparse base of K-SVD dictionary is firstly constructed to perform the sparse representation of the data. Then, the m-sequence Gaussian random matrix was used to compress the data. Finally, the orthogonal matching pursuit algorithm was used to reconstruct the data based on the compressed observations, and then the tip clearance values were accurately extracted. The experimental results show that the gap distance data can be accurately reconstructed under the condition of under-sampling, and the reconstruction error is below 0.02 mm comparing with the gap data under the condition of high sampling rate.
- tip clearance /
- under sampling /
- compressed sensing /
- K-SVD dictionary sparse base /
- orthogonal matching pursuit algorithm

HTML全文

图 1 基于K-SVD字典训练稀疏基的压缩感知叶尖间隙数据重构方法流程图

Figure 1. Flowchart of the compressed sensing reconstruction method for evaluating blade tip clearance data based on K-SVD dictionary training with sparse bases

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图 2 K-SVD字典稀疏基训练流程图

Figure 2. Flowchart of the K-SVD dictionary training process for sparse bases

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图 3 叶尖间隙数据重构总体流程图

Figure 3. Overall flowchart of blade tip clearance data reconstruction

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图 4 使用K-SVD字典稀疏基的压缩感知OMP算法的叶尖间隙数据重构结果

Figure 4. Reconstruction results for blade tip clearance data using the compressed sensing OMP algorithm with K-SVD dictionary sparse bases

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图 5 叶尖间隙数据测量实验平台

Figure 5. Experimental platform for blade tip clearance data measurement

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图 6 叶尖间隙实验测量示意图

Figure 6. Schematic diagram of the blade tip clearance measurement experiment

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表 1 不同M值时重构平均误差表

Table 1. The average error table is reconstructed for different M values

欠采样观测数M	30	40	50	60	70	80
重构误差ε/mm	0.29	0.23	0.15	0.01	0.01	e^-12

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表 2 各方法提取叶尖间隙数据对比表

Table 2. Comparison of blade tip clearance data extraction methods

滑移台位置	叶尖间隙值	欠采样间隙值	欠采样间隙值误差	重构间隙值	重构间隙值误差
1	0.408 5	0.291 8	0.116 7	0.388 7	0.019 8
2	0.909 6	0.803 6	0.1060	0.890 0	0.019 6
3	1.412 3	1.301 9	0.110 4	1.392 0	0.020 3
4	1.899 6	1.803 7	0.095 9	1.879 7	0.019 9
5	2.396 5	2.299 6	0.096 9	2.376 5	0.020 0
6	2.897 2	2.837 3	0.059 9	2.877 1	0.020 1

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参考文献(27)

[1]	许敬晖, 乔百杰, 滕光蓉, 等. 基于压缩感知的叶端定时信号参数辨识方法[J]. 航空学报, 2021, 42(5): 524229. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202105013.htm XU J H, QIAO B J, TENG G R, et al. Parameter identification of blade tip timing signal using compressed sensing[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(5): 524229. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202105013.htm
[2]	罗佳奇, 陈泽帅, 曾先. 考虑几何设计参数不确定性影响的涡轮叶栅稳健性气动设计优化[J]. 航空学报, 2020, 41(10): 123826. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202010013.htm LUO J Q, CHEN Z S, ZENG X. Robust aerodynamic design optimization of turbine cascades considering uncertainty of geometric design parameters[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(10): 123826. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202010013.htm
[3]	ZHAO F T, JING X D, YANG M S, et al. Experimental study of rotor blades vibration and noise in multistage high pressure compressor and their relevance[J]. Chinese Journal of Aeronautics, 2020, 33(3): 870-878.
[4]	刘志博, 段发阶, 叶德超, 等. 叶尖定时信号趋势项自适应拟合[J]. 中国机械工程, 2021, 32(22): 2749-2756. doi: 10.3969/j.issn.1004-132X.2021.22.012 LIU Z B, DUAN F J, YE D C, et al. Adaptive fitting for blade tip timing Signal's trend terms[J]. China Mechanical Engineering, 2021, 32(22): 2749-2756. (in Chinese) doi: 10.3969/j.issn.1004-132X.2021.22.012
[5]	SUN H B, WANG J, CHEN K, et al. A tip clearance prediction model for multistage rotors and stators in aero-engines[J]. Chinese Journal of Aeronautics, 2021, 34(2): 343-357.
[6]	王博, 吴艳辉. 扩压叶栅叶尖非定常流动的涡动力学机理[J]. 航空学报, 2020, 41(11): 123881. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202011021.htm WANG B, WU Y H. Vortex-dynamics mechanism of tip-region unsteady flow in compressor cascade[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(11): 123881. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202011021.htm
[7]	胡延青, 申秀丽. 航空发动机叶尖径向间隙研究进展综述[J]. 航空发动机, 2014, 40(1): 60-67. https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ201401012.htm HU Y Q, SHEN X L. Overview on aeroengine radial tip clearance[J]. Aeroengine, 2014, 40(1): 60-67. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ201401012.htm
[8]	黄漫国, 刘德峰, 王燕山. 航空发动机叶尖间隙测量技术[C]//2014航空试验测试技术学术交流会论文集. 厦门: 中国航空学会, 2014: 589-601. HUANG M G, LIU D F, WANG Y S. Measurement technologies of blade tip clearance in the Aero-Engine[C]//Proceedings of Academic Exchange Conference on Aeronautical Test and Test Technology. Xiamen: Chinese Society of Aeronautics, 2014: 589-601. (in Chinese)
[9]	张济龙. 基于微波传感的叶尖间隙及叶尖定时测量方法研究[D]. 天津: 天津大学, 2017. ZHANG J L. Research on blade tip clearance and blade tip-timing measurement based on microwave sense[D]. Tianjin: Tianjin University, 2017. (in Chinese)
[10]	WISEMAN M W, GUO T H. An investigation of life extending control techniques for gas turbine engines[C]//Proceedings of the 2001 American Control Conference. Arlington: IEEE, 2001: 3706-3707.
[11]	WU J, WEN B, ZHANG Q, et al. A novel blade tip clearance measurement method based on event capture technique[J]. Mechanical Systems and Signal Processing, 2020, 139: 106626.
[12]	李秋彦, 李刚, 魏洋天, 等. 先进战斗机气动弹性设计综述[J]. 航空学报, 2020, 41(6): 523430. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202006004.htm LI Q Y, LI G, WEI Y T, et al. Review of aeroelasticity design for advanced fighter[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(6): 523430. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202006004.htm
[13]	向宏辉, 葛宁, 高杰, 等. 周向非均匀叶尖间隙对轴流压气机性能的影响[J]. 航空学报, 2018, 39(2): 121491. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201802006.htm XIANG H H, GE N, GAO J, et al. Effect of circumferential non-uniform tip clearance on performance of axial compressor[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(2): 121491. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201802006.htm
[14]	CANDES E J, ROMBERG J, TAO T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.
[15]	DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.
[16]	钱秋亮, 董宝伟, 邵馨叶, 等. 改进近似函数的重构算法在滚动轴承故障信号中的应用研究[J]. 机械科学与技术, 2021, 40(11): 1747-1753. doi: 10.13433/j.cnki.1003-8728.20200280 QIAN Q L, DONG B W, SHAO X Y, et al. Application of reconstruction algorithm of improved approximate function in fault signal of rolling bearing[J]. Mechanical Science and Technology for Aerospace Engineering, 2021, 40(11): 1747-1753. (in Chinese) doi: 10.13433/j.cnki.1003-8728.20200280
[17]	AHARON M, ELAD M, BRUCKSTEIN A. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation[J]. IEEE Transactions on Signal Processing, 2006, 54(11): 4311-4322.
[18]	ELAD M, AHARON M. Image denoising via sparse and redundant representations over learned dictionaries[J]. IEEE Transactions on Image Processing, 2006, 15(12): 3736-3745.
[19]	王江萍, 段腾飞. 旋转机械振动信号频域随机压缩与故障诊断[J]. 机械科学与技术, 2018, 37(2): 293-299. doi: 10.13433/j.cnki.1003-8728.2018.0221 WANG J P, DUAN T F. Frequency domain random compression of vibration signal and fault detection for rotation machinery[J]. Mechanical Science and Technology for Aerospace Engineering, 2018, 37(2): 293-299. (in Chinese) doi: 10.13433/j.cnki.1003-8728.2018.0221
[20]	CANDẼS E J, ELDAR Y C, NEEDELL D, et al. Compressed sensing with coherent and redundant dictionaries[J]. Applied and Computational Harmonic Analysis, 2010, 31(1): 59-73.
[21]	BARANIUK R G. Compressive sensing[Lecture Notes][J]. IEEE Signal Processing Magazine, 2007, 24(4): 118-121.
[22]	周亚同, 王丽莉, 蒲青山. 压缩感知框架下基于K-奇异值分解字典学习的地震数据重建[J]. 石油地球物理勘探, 2014, 49(4): 652-660. https://www.cnki.com.cn/Article/CJFDTOTAL-SYDQ201404005.htm ZHOU Y T, WANG L L, PU Q S. Seismic data reconstruction based on K-SVD dictionary learning under compressive sensing framework[J]. Oil Geophysical Prospecting, 2014, 49(4): 652-660. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SYDQ201404005.htm
[23]	DONOHO D L, ELAD M, TEMLYAKOV V N. Stable recovery of sparse overcomplete representations in the presence of noise[J]. IEEE Transactions on Information Theory, 2006, 52(1): 6-18.
[24]	DONOHO D L, HUO X. Uncertainty principles and ideal atomic decomposition[J]. IEEE Transactions on Information Theory, 2001, 47(7): 2845-2862.
[25]	CHEN S S, DONOHO D L, SAUNDERS M A. Atomic decomposition by basis pursuit[J]. SIAM Review, 2001, 43(1): 129-159.
[26]	TROPP J A, GILBERT A C. Signal recovery from random measurements via orthogonal matching pursuit[J]. IEEE Transactions on Information Theory, 2007, 53(12): 4655-4666.
[27]	BLUMENSATH T, DAVIES M E. Iterative thresholding for sparse approximations[J]. Journal of Fourier Analysis and Applications, 2008, 14(5-6): 629-654.