叶片非整阶振动的叶尖定时压缩感知重构

王增增; 刘蒙永; 马宏伟; 李泽涛; 张明

doi:10.13224/j.cnki.jasp.20250066

叶片非整阶振动的叶尖定时压缩感知重构

doi: 10.13224/j.cnki.jasp.20250066

王增增^1,,
刘蒙永²,
马宏伟^{1, 2,*, ,},
李泽涛²,
张明²

1.
北京航空航天大学航空发动机研究院，北京 102206
2.
北京航空航天大学能源与动力工程学院，北京 102206

基金项目: 国家自然科学基金（51776011）；国家科技重大专项（2017-Ⅴ-0016-0068）；重点实验室基金（6142702020203）

详细信息

作者简介:
王增增（1991-），男，博士生，主要从事叶轮机械气体动力学及流固耦合振动研究

通讯作者:
马宏伟（1968-），男，教授、博士生导师，博士，研究领域为叶轮机内流测试技术。E-mail：mahw@buaa.edu.cn

中图分类号: V231.3
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- 被引次数: 0
出版历程
- 收稿日期: 2025-02-11
- 网络出版日期: 2025-11-06

Tip timing compress sensing reconstruction of blade non-synchronous vibration

1.
Research Institute of Aero-Engine，Beihang University，Beijing 102206，China
2.
School of Energy and Power Engineering，Beihang University，Beijing 102206，China

摘要

摘要:
分别基于条件数优化传感器排布压缩感知算法、随机传感器排布结合振动方程字典压缩感知重构算法，对2.5倍转频的叶片非整阶振动信号进行了压缩感知重构误差分析对比，发现条件数优化传感器排布算法在幅值精度上低于基于随机传感器排布结合振动方程字典的算法，在相同传感器数量条件下，随机传感器排布的生成方式所得重构精度的稳定性远低于条件数优化传感器排布算法。为提高压缩感知对非整阶信号的幅值重构精度，获得更加稳定的重构误差水平，以恢复矩阵条件数1为最适度目标，通过遗传变异优化传感器排布，结合振动方程构造字典，获得振动方程的系数，重构非整阶振动信号，相较于以上两种算法，幅值重构精度得以提高，重构误差分布的稳定性提高。通过压气机非整阶实验数据对三种算法进行了重构精度及稳定性验证，结果表明：10支传感器数量条件下，传感器排布优化的压缩感知振动方程重构的方法重构误差最大值为0.021，小条件数遗传优化重构误差最大值为0.025，随机传感器排布振动方程重构误差最大值为0.06。传感器数量降至4时，基于传感器排布优化的振动方程重构算法重构非整阶振动实验数据的误差最大值为0.05，表明此算法具有较高的重构稳定性和精度。
- 叶尖定时 /
- 非整阶振动 /
- 压缩感知 /
- 矩阵条件数 /
- 遗传优化
Abstract:
The compressed sensing reconstruction error analysis and comparison of 2.5 times rotating frequency blade non-synchronous vibration signals were conducted based on the condition number optimized sensor arrangement compressed sensing algorithm and the random sensor arrangement combined with the vibration equation dictionary compressed sensing reconstruction algorithm. It was found that the condition number optimized sensor arrangement algorithm was lower in amplitude accuracy than the algorithm based on the random sensor arrangement combined with the vibration equation dictionary. Under the same number of sensors, the stability of the reconstruction accuracy obtained by the generation method of the random sensor arrangement was far lower than the condition number optimized sensor arrangement algorithm. In order to improve the amplitude reconstruction accuracy of compressed sensing for non-synchronous vibration signals and obtain a more stable reconstruction error level, the condition number 1 of the recovery matrix was taken as the optimal objective. By optimizing the sensor layout through genetic variant and combining it with the vibration equation to construct a dictionary, the coefficients of the vibration equation were obtained to reconstruct non-synchronous vibration signals. Compared with the above two algorithms, the amplitude reconstruction accuracy was improved and the stability of the reconstruction error distribution was enhanced. The reconstruction accuracy and stability of three algorithms were verified through non-synchronous vibration experimental data of the compressor. The results showed that under the condition of 10 sensors, the maximum reconstruction error of the compression sensing vibration equation reconstruction method with optimized sensor arrangement was 0.021, the maximum reconstruction error of genetic optimization with small condition number was 0.025, and the maximum reconstruction error of the vibration equation with random sensor arrangement was 0.06. When the number of sensors decreased to 4, the maximum error of the vibration equation reconstruction algorithm based on sensor layout optimization for reconstructing non-synchronous vibration experimental data was 0.05, indicating that this algorithm had high reconstruction stability and accuracy.
- blade tip timing /
- non-synchronous vibration /
- compressed sensing /
- matrix condition number /
- genetic optimization

HTML

图 1 BTT测量叶片振动原理

Figure 1. Principle of BTT measure blade vibration

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图 2 压缩感知与BTT结合重构流程

Figure 2. Process of compressed sensing reconstruct BTT signal

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图 3 遗传变异优化传感器排布流程

Figure 3. Genetic variant optimization of sensors layouts

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图 4 18支BTT传感器压缩感知小条件数重构时域

Figure 4. Reconstruction of time region with 18 BTT sensors based on condition number optimized compressed sensing

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图 5 18支BTT传感器压缩感知最小条件数重构频域

Figure 5. Reconstruction of frequency region with 18 BTT sensors based on minimum condition number optimized compressed sensing

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图 6 幅值重构误差随传感器数量变化图

Figure 6. Reconstruction error varying with sensor number

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图 7 基于18支BTT传感器，随机传感器排布振动方程的压缩感知重构时域

Figure 7. Reconstruction of time region with 18 BTT sensors based on random sensor layout and vibration equation compressed sensing

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图 8 基于振动方程的压缩感知重构频域

Figure 8. Reconstruction of frequency region based on random sensor layout and vibration equation compressed sensing

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图 9 基于振动方程压缩感知的重构误差分布

Figure 9. Reconstruction error of with vibration equation compressed sensing

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图 10 遗传优化弧度分布的传感器排布（8支传感器前10次优化）

Figure 10. Genetic optimized sensor layouts on arc distribution（the first 10 times optimizations of 8 sensors）

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图 11 遗传优化传感器排布和压缩感知振动方程重构时域

Figure 11. Reconstruction of time region based on genetic optimized sensor layouts and vibration equation compressed sensing

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图 12 遗传优化传感器排布振动方程压缩感知重构信号频域

Figure 12. Frequency region based on genetic optimized sensor layouts and vibration equation compressed sensing

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图 13 优化传感器排布振动方程压缩感知重构误差

Figure 13. Reconstruct error based on optimized sensor layouts and vibration equation compressed sensing

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图 14 压气机实验叶片应变时程曲线

Figure 14. Compressor experimental blade strain time curve

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图 15 压气机叶片振动欠采样信号与频谱

Figure 15. Compressor blade vibration under-sampled signal and its spectrum

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图 16 随机传感器排布方式与小条件数压缩感知方法重构信号

Figure 16. Random sensor arrangement and condition number compression sensing method reconstruct the signal

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图 17 随机传感器排布方式与振动方程压缩感知方法重构信号

Figure 17. Rrandom sensor layout and vibration equation compression sensing method reconstruct the signal

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图 18 遗传优化传感器排布小条件数与振动方程重构信号与原始信号的时程曲线

Figure 18. Time curves of reconstruct and original signal based on genetic optimized sensor’s position and condition number vibration equation method

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图 19 不同压缩感知方法的重构误差分布

Figure 19. Reconstruction error based on different compression sensing methods

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图 20 传感器数量对重构误差的影响

Figure 20. Influence of sensor number to reconstruct error

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图 21 6支传感器小条件数优化振动方程重构效果

Figure 21. Condition number optimized vibration equation reconstruction with 6 sensors

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图 22 8支传感器小条件数优化振动方程重构效果

Figure 22. Condition number optimized vibration equation reconstruction with 8 sensors

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图 23 10支传感器小条件数优化振动方程重构效果

Figure 23. Condition number optimized vibration equation reconstruction with 10 sensors

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参考文献(31)

[1]	马宏伟, 蒋浩康. 压气机转子通道内尖区三维平均流场[J]. 航空动力学报, 1997, 12(2): 167-171. MA Hongwei, JIANG Haokang. Three-dimensional flow field inside a compressor rotor tip region[J]. Journal of Aerospace Power, 1997, 12(2): 167-171. MA Hongwei, JIANG Haokang. Three-dimensional flow field inside a compressor rotor tip region[J]. Journal of Aerospace Power, 1997, 12(2): 167-171.
[2]	马宏伟, 蒋浩康. 压气机不同状态下转子出口三维紊流流场[J]. 航空动力学报, 1997, 12(3): 268-272. MA Hongwei, JIANG Haokang. 3D turbulent flow at compressor rotor exitunder different flow conditions[J]. Journal of Aerospace Power, 1997, 12(3): 268-272. MA Hongwei, JIANG Haokang. 3D turbulent flow at compressor rotor exitunder different flow conditions[J]. Journal of Aerospace Power, 1997, 12(3): 268-272.
[3]	MA Hongwei, WEI Wei, OTTAVY X. Experimental investigation of flow field in a laboratory-scale compressor[J]. Chinese Journal of Aeronautics, 2017, 30(1): 31-46. doi: 10.1016/j.cja.2016.09.016
[4]	BLEVINS R D. 流体诱发振动[M]. 吴恕三, 译. 北京: 机械工业出版社, 1983. BLEVINS R D. Flow-induced vibration[M]. WU Sanshu, translate. Beijing: China Machine Press, 1983. (in Chinese BLEVINS R D. Flow-induced vibration[M]. WU Sanshu, translate. Beijing: China Machine Press, 1983. (in Chinese)
[5]	BAUMGARTNER M, KAMEIER F A H J. Non-engine order blade vibration in a high pressure compressor[R]. Melbourne, Australia: 12th International Symposium on Airbreathing Engines, 1995.
[6]	HOLZINGER F, WARTZEK F. Self-excited blade vibration experimentally investigated in transonic compressors: rotating instabilities and flutter[J]. Journal of Turbomachinery, 2016, 138: 041006. doi: 10.1115/1.4032163
[7]	IM H S, ZHA Gecheng. Effects of rotor tip clearance on tip clearance flow potentially leading to NSV in an axial compressor[R]. ASME Paper GT2012-68148s, 2012.
[8]	ESPINAL D, IM H S, ZHA Gecheng. Full-annulus simulation of nonsynchronous blade vibration excitation of an axial compressor[J]. Journal of Turbomachinery, 2018, 140(3): 031008. doi: 10.1115/1.4038337
[9]	GAN Jiaye, IM H S, ESPINAL D, et al. Investigation of a compressor rotor non-synchronous vibration with and without fluid-structure interaction[R]. ASME Paper GT2014-26478, 2014.
[10]	王增增, 马宏伟. 航空发动机轴流压气机非整阶振动实验研究进展[J]. 航空动力学报, 2022, 37(11): 2416-2429. WANG Zengzeng, MA Hongwei. Overview of experimental research on non-synchronous vibration in aero-engine axial compressor[J]. Journal of Aerospace Power, 2022, 37(11): 2416-2429. (in Chinese WANG Zengzeng, MA Hongwei. Overview of experimental research on non-synchronous vibration in aero-engine axial compressor[J]. Journal of Aerospace Power, 2022, 37(11): 2416-2429. (in Chinese)
[11]	FAN C, RUSSHARD P, WANG A, et al. Analysis of blade tip timing data from fan blades with synchronous and non-synchronous vibration[J]. Journal of Physics: Conference Series, 2018, 1149: 012014. doi: 10.1088/1742-6596/1149/1/012014
[12]	CARASSALE L, COLETTI F, GUIDA R. Multi-channel spectral analysis of non-synchronous vibrations of bladed disks measured by blade tip timing[R]. ASME Paper GT2020-15512, 2020.
[13]	张玉贵, 段发阶, 方志强, 等. 旋转叶片异步振动的频率识别技术[J]. 振动与冲击, 2007, 26(12): 106-108, 174-175. ZHANG Yugui, DUAN Fajie, FANG Zhiqiang, et al. Frequency identification technique for asynchronous vibration of rotating blades[J]. Journal of Vibration and Shock, 2007, 26(12): 106-108, 174-175. (in Chinese ZHANG Yugui, DUAN Fajie, FANG Zhiqiang, et al. Frequency identification technique for asynchronous vibration of rotating blades[J]. Journal of Vibration and Shock, 2007, 26(12): 106-108, 174-175. (in Chinese)
[14]	CANDES E J, WAKIN M B. An introduction to compressive sampling[J]. IEEE Signal Processing Magazine, 2008, 25(2): 21-30. doi: 10.1109/MSP.2007.914731
[15]	郭俊锋, 石斌, 魏兴春, 等. 基于K-SVD字典学习算法的稀疏表示振动信号压缩测量重构方法[J]. 机械工程学报, 2018, 54(7): 97-106. GUO Junfeng, SHI Bin, WEI Xingchun, et al. A method of reconstruction of compressed measuring for mechanical vibration signals based on K-SVD dictionary-training algorithm sparse representation[J]. Journal of Mechanical Engineering, 2018, 54(7): 97-106. (in Chinese doi: 10.3901/JME.2018.07.097 GUO Junfeng, SHI Bin, WEI Xingchun, et al. A method of reconstruction of compressed measuring for mechanical vibration signals based on K-SVD dictionary-training algorithm sparse representation[J]. Journal of Mechanical Engineering, 2018, 54(7): 97-106. (in Chinese) doi: 10.3901/JME.2018.07.097
[16]	温江涛, 孙洁娣, 于洋, 等. 基于小波包字典优化的旋转机械振动信号压缩感知重构方法[J]. 振动与冲击, 2018, 37(22): 164-172. WEN Jiangtao, SUN Jiedi, YU Yang, et al. Compressed Sensing reconstruction forrotating machinery vibration signals based on the wavelet packet dictionary optimization[J]. Journal of Vibration and Shock, 2018, 37(22): 164-172. (in Chinese WEN Jiangtao, SUN Jiedi, YU Yang, et al. Compressed Sensing reconstruction forrotating machinery vibration signals based on the wavelet packet dictionary optimization[J]. Journal of Vibration and Shock, 2018, 37(22): 164-172. (in Chinese)
[17]	PAN Minghao, YANG Yongmin, GUAN Fengjiao, et al. Sparse representation based frequency detection and uncertainty reduction in blade tip timing measurement for multi-mode blade vibration monitoring[J]. Sensors, 2017, 17(8): 1745.
[18]	SPADA R P, NICOLETTI R. Applying compressed sensing to blade tip timing data: a parametric analysis[C]//Proceedings of the 10th International Conference on Rotor Dynamics-IFToMM. Cham: Springer, 2019: 121-134.
[19]	DIAMOND D H, STEPHAN HEYNS P. A novel method for the design of proximity sensor configuration for rotor blade tip timing[J]. Journal of Vibration and Acoustics, 2018, 140(6): 061003. doi: 10.1115/1.4039931
[20]	张效溥, 田杰, 孙宗翰, 等. 基于任意传感器排布的叶尖定时信号压缩感知辨识方法[J]. 航空动力学报, 2020, 35(1): 41-51. ZHANG Xiaopu, TIAN Jie, SUN Zonghan, et al. Compressive sensing identification method of blade tip timing signals based on arbitrary sensor arrangement[J]. Journal of Aerospace Power, 2020, 35(1): 41-51. (in Chinese ZHANG Xiaopu, TIAN Jie, SUN Zonghan, et al. Compressive sensing identification method of blade tip timing signals based on arbitrary sensor arrangement[J]. Journal of Aerospace Power, 2020, 35(1): 41-51. (in Chinese)
[21]	张智伟, 柴鹏飞, 孙宗翰, 等. 高可靠小条件数压缩感知叶尖定时信号辨识[J]. 航空动力学报, 2021, 36(3): 509-519. ZHANG Zhiwei, CHAI Pengfei, SUN Zonghan, et al. High reliability identification method of blade tip timing signals based on compressed sensing under small condition number[J]. Journal of Aerospace Power, 2021, 36(3): 509-519. (in Chinese ZHANG Zhiwei, CHAI Pengfei, SUN Zonghan, et al. High reliability identification method of blade tip timing signals based on compressed sensing under small condition number[J]. Journal of Aerospace Power, 2021, 36(3): 509-519. (in Chinese)
[22]	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. XU Jinghui, QIAO Baijie, TENG Guangrong, et al. Parameter identification of blade tip timing signal using compressed sensing[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(5): 524229. (in Chinese XU Jinghui, QIAO Baijie, TENG Guangrong, et al. Parameter identification of blade tip timing signal using compressed sensing[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(5): 524229. (in Chinese)
[23]	徐海龙, 杨拥民, 胡海峰, 等. 基于压缩感知的叶端定时欠采样多频叶片振动盲重构研究[J]. 机械工程学报, 2019, 55(13): 113-121. XU Hailong, YANG Yongmin, HU Haifeng, et al. Compressed sensing-based blind reconstruction of multi-frequency blade vibration from under-sampled BTT signals[J]. Journal of Mechanical Engineering, 2019, 55(13): 113-121. (in Chinese doi: 10.3901/JME.2019.13.113 XU Hailong, YANG Yongmin, HU Haifeng, et al. Compressed sensing-based blind reconstruction of multi-frequency blade vibration from under-sampled BTT signals[J]. Journal of Mechanical Engineering, 2019, 55(13): 113-121. (in Chinese) doi: 10.3901/JME.2019.13.113
[24]	吴淑明, 胡海峰, 赵志斌, 等. 增强稀疏分解及其在叶片振动参数识别中的应用[J]. 机械工程学报, 2019, 55(19): 19-27. WU Shuming, HU Haifeng, ZHAO Zhibin, et al. Enhancing sparse decomposition based vibration parameter identification[J]. Journal of Mechanical Engineering, 2019, 55(19): 19-27. (in chinese WU Shuming, HU Haifeng, ZHAO Zhibin, et al. Enhancing sparse decomposition based vibration parameter identification[J]. Journal of Mechanical Engineering, 2019, 55(19): 19-27. (in chinese)
[25]	ZHANG Z W, CHAI P F, CHEN Y, et al. Optimization of non-uniform sensor placement for blade tip timing based on equiangular tight frame theory[R]. ASME Paper GT2021-59104, 2021.
[26]	KNILL C, ROOS F, SCHWEIZER B, et al. Random multiplexing for an MIMO-OFDM radar with compressed sensing-based reconstruction[J]. IEEE Microwave and Wireless Components Letters, 2019, 29(4): 300-302. doi: 10.1109/LMWC.2019.2901405
[27]	VAN DER SLUIS A. Stability of solutions of linear algebraic systems[J]. Numerische Mathematik, 1970, 14(3): 246-251. doi: 10.1007/BF02163333
[28]	孙建邦, 李建兵, 王鼎, 等. 基于遗传模型改进蜂群算法的稀疏阵列优化[J]. 强激光与粒子束, 2021, 33(12): 123005. SUN Jianbang, LI Jianbing, WANG Ding, et al. Thinned array optimization based on genetic model improved artificial bee colony algorithm[J]. High Power Laser and Particle Beams, 2021, 33(12): 123005. (in Chinese SUN Jianbang, LI Jianbing, WANG Ding, et al. Thinned array optimization based on genetic model improved artificial bee colony algorithm[J]. High Power Laser and Particle Beams, 2021, 33(12): 123005. (in Chinese)
[29]	敖春燕, 乔百杰, 刘美茹, 等. 基于非接触式测量的旋转叶片动应变重构方法[J]. 航空动力学报, 2020, 35(3): 569-580. AO Chunyan, QIAO Baijie, LIU Meiru, et al. Dynamic strain reconstruction method of rotating blades based on no-contact measurement[J]. Journal of Aerospace Power, 2020, 35(3): 569-580. (in Chinese AO Chunyan, QIAO Baijie, LIU Meiru, et al. Dynamic strain reconstruction method of rotating blades based on no-contact measurement[J]. Journal of Aerospace Power, 2020, 35(3): 569-580. (in Chinese)
[30]	杨康, 王维民, 张娅, 等. 透平机械叶片动应变非接触测量研究[J]. 风机技术, 2021, 63(3): 82-87. YANG Kang, WANG Weimin, ZHANG Ya, et al. Study on non contact measurement of dynamic strain of turbine blades[J]. Chinese Journal of Turbomachinery, 2021, 63(3): 82-87. (in Chinese YANG Kang, WANG Weimin, ZHANG Ya, et al. Study on non contact measurement of dynamic strain of turbine blades[J]. Chinese Journal of Turbomachinery, 2021, 63(3): 82-87. (in Chinese)
[31]	ZHANG H, ZHANG M, DONG X, et al. Non-synchronous vibration and related tip clearance flow characteristic in a low-speed axial fan[R]. ASME Paper GT2024-129094, 2024