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为解决传统方法在判断离心压气机动态失稳过程中因信号强非线性导致误判错判, 针对其动态时序属非线性信号, 基于分形理论提出自适应变分模态分解(adaptive variational mode decomposition with fractal, AFVMD)方法以同时实现降噪与非线性特征提取, 采用相空间重构法还原系统动力学结构. 以某离心压气机失稳过程中叶轮动态压力数据为对象, 验证所提出算法的优越性, 分析其吸引子状态. 结果表明: 在处理具有非线性特征的含噪信号时, AFVMD比小波降噪具有更好的降噪效果与特征提取能力; 相空间将失速发展过程可视化, 最小流量状态所对应的相空间呈现“毛球状”; 随失速的发展, 相空间将逐渐发散; 经小波与AFVMD方法预处理的信号所对应相形对失速过程更加敏感; 通过经AFVMD处理的信号进行重构可更早捕获失速征兆, 其更小的最大Lyapunov指数表明该方法提升了流动混沌系统的可预测性, 为压气机失稳分析、预测提供新思路与方法.
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关键词:
- 混沌 /
- Lyapunov指数 /
- 变分模态分解 /
- 分形
A novel signal processing method named adaptive variational mode decomposition with the fractal (AFVMD), which is based on variational mode decomposition and fractal theory, is proposed in this paper for solving a problem that it is easy to misjudge the working conditions of the centrifugal compressor. The measured signal of a compressor is unstable, so a traditional method is used to analyze the nonlinear phenomenon of the stall flutter. Owing to the fact that the robustness of VMD method is strong and its combination with the fractal dimension can accurately describe self-similarity and fractal characteristics of a measured signal, the proposed AFVMD method can not only achieve noise reduction, but also extract nonlinear feature from a complex signal. Taking the dynamic pressure data of the impeller during the instability of a centrifugal compressor as an object to verify the effectiveness and superiority of the proposed AFVMD method, the results are obtained as follows. Firstly, compared with the wavelet noise reduction method, the proposed AFVMD method has both noise reduction and feature extraction functions, and the compressor pressure pulsation spectrum has more significant stall characteristics. Secondly, none of the traditional nonlinear analysis methods can reflect the stall process, so the chaotic phase space attractor is used to visualize the flow field changes. Due to the reasonable choice of the delay time and the embedding dimension, the physical information originally mixed in the signal is separated, so that the attractor phase diagram method has a better process of judging the flow stall than the frequency spectrum method. The results show that the proposed AFVMD method can judge the compressor about to enter into the deep surge earlier. Thirdly, In order to quantify the superiority of the proposed method, if the process of surging and the occurrence of deep wheezing can be predicted in advance, the largest Lyapunov exponent is used as an evaluation index. The above results show that the largest Lyapunov exponent of the proposed AFVMD is smallest for illustrating that the signal has more accurate flow field nonlinear information, which improves the predictability of the signal.-
Keywords:
- chaotic /
- Lyapunov exponent /
- variational mode decomposition /
- fractal
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图 5 流场降噪效果对比 (a) 最小流量工况1; (b) 最小流量工况2; (c) 浅喘工况1; (d) 浅喘工况2
Fig. 5. De-noise effectiveness comparisons of the flow field information: (a) The minimum flow condition 1; (b) the minimum flow condition 2; (c) the shallow breath condition 1; (d) the shallow breath condition 2.
图 6 不同工况相空间 (a) 原始序列; (b) 小波降噪处理序列; (c) AFVMD处理序列
Fig. 6. Reconstructed phase space of different conditions: (a) The original signals; (b) the signals proceed by the wavelet; (c) the signals processed by the AFVMD.
表 1 算法效果对比
Table 1. Comparison of denoising effectiveness.
采用方法 信噪比/dB 分形维数 未处理 — 1.74 Sym4小波 –3.87 1.49 AFVMD –49.3 1.42 
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表 2 最佳延迟时间及嵌入维数
Table 2. Optimal parameters including delay time and embedded dimension.
延迟时间(嵌入维数) 工况 原序列 小波 AFVMD 最小流量1 11 (2) 20 (3) 24 (3) 最小流量2 4 (2) 20 (3) 23 (3) 浅喘1 4 (2) 19 (3) 33 (3) 浅喘2 4 (2) 20 (3) 30 (3) 浅喘3 13 (2) 22 (3) 36 (3) 浅喘4 4 (2) 22 (3) 36 (3) 深喘1 8 (2) 23 (3) 32 (2) 深喘2 5 (2) 26 (3) 38 (2) 深喘3 2 (2) 23 (3) 37 (2) 深喘4 17 (2) 28 (3) 32 (2)
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[1] Day I J 2016 J. Turbomach. 138 1
Google Scholar
[2] 刘俊杰, 苏三买, 孙占恒 2017 航空动力学报 32 2284
Google Scholar
Liu J J, Su S S, Sun Z H 2017 Chin. J. Areonaut. 32 2284
Google Scholar
[3] 刘小华, 周燕佩, 孙大坤, 马云飞, 孙晓峰 2014 航空学报 35 2980
Google Scholar
Liu X H, Zhou Y P, Sun D K, Ma Y F, Sun X F 2014 Chin. J. Areonaut. 35 2980
Google Scholar
[4] Eck M, Geist S, Peitsch D 2017 Appl. Sci. 7 285
Google Scholar
[5] Xu R Z, Sun D K, Dong X, Li F Y, Sun X F, Li J 2019 J. Therm. Sci. 28 864
[6] 陈振, 徐鉴 2013 振动与冲击 32 108
Google Scholar
Chen Z, Xu J 2013 J. Vib. Shock 32 108
Google Scholar
[7] 郭贵喜, 王振华, 王洪祥, 高辉国, 薛秀生 2013 航空发动机 39 63
Google Scholar
Guo G X, Wang Z H, Wang H X, Gao H G, Xue X S 2013 Aeroengine 39 63
Google Scholar
[8] Chervyakov N, Lyakhov P, Kaplun D, Butusov D, Nagornov N 2018 Electron. 7 135
Google Scholar
[9] Qiu X, Ren Y, Suganthan P N, Amaratunga A J G 2017 Appl. Soft Comput. 54 248
Google Scholar
[10] Sweeney K T, Mcloone S F, Ward T E 2013 IEEE Trans. Biomed. Eng. 60 99
Google Scholar
[11] Guo Y, Naik G R, Nguyen H 2013 35 th Annual International Conference of the IEEE Engineering in Medicine and Biology Society Osaka, Japan, July 3−7, 2013 p6812
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Google Scholar
[13] 张文超, 谭思超, 高璞珍 2013 物理学报 62 060502
Google Scholar
Zhang W C, Tan S C, Gao P Z 2013 Acta Phys. Sin. 62 060502
Google Scholar
[14] 武友利, 吕建伟, 董福安, 李世飞 2005 空军工程大学学报 6 15
Google Scholar
Wu Y L, Lv J W, Dong F A, Li S F 2005 J. Air Force Eng. Univ. 6 15
Google Scholar
[15] 刘志刚, 杨荣菲, 向宏辉 2014 测控技术 33 54
Google Scholar
Liu Z G, Yang R F, Xiang H H 2014 Meas. Control Technol. 33 54
Google Scholar
[16] Mossayebi F D, Qammar H K 2019 SN Appl. Sci. 1 5
Google Scholar
[17] Xue X, Wang T 2019 Appl. Therm. Eng. 153 106
Google Scholar
[18] 胥永刚, 何正嘉 2003 振动与冲击 22 26
Google Scholar
Xu Y G, He Z J 2003 J. Vib. Shock 22 26
Google Scholar
[19] Dragomiretskiy K, Zosso D 2014 IEEE Trans. Signal Process. 62 532
Google Scholar
[20] 刘洋, 曹云东, 侯春光 2015 中国电机工程学报 35 4088
Google Scholar
Liu Y, Cao Y D, Hou C G 2015 Proc. CSEE 35 4088
Google Scholar
[21] 郝研 2012 博士学位论文 (天津: 天津大学)
Hao Y 2012 Ph. D. Dissertation (Tianjin: Tianjin University) (in Chinese)
[22] 张月征, 纪洪广, 向鹏, 彭华, 宋朝阳 2016 岩石力学与工程学报 35 3222
Google Scholar
Zhang Y Z, Ji H G, Xiang P, Peng H, Song Z Y 2016 Chin. J. Rock Mech. Eng. 35 3222
Google Scholar
[23] Sarkar N, Chaudhuri B B 1994 IEEE Trans. Sys. 24 115
Google Scholar
[24] Packard N H, Crutchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
Google Scholar
[25] Auerbach D, Cvitanovic P, Eckmann J P, Gunaratne G, Procaccia I 1987 Phys. Rev. Lett. 58 2387
Google Scholar
[26] Viola P, Wells W M 1995 Proceedings of IEEE International Conference on Computer Vision North Dakota, America, June 20−23, 1995 p102
[27] Falzarano M, Shaw S W, Troesh A W 1992 Int. J. Bifurcation Chaos Appl. Sci. Eng. 2 101
Google Scholar
[28] Falconer K J 2014 Biometrics 46 499
Google Scholar
[29] Mandelbrot B B 1967 Sci. 156 636
Google Scholar
[30] 唐鹏 2017 博士学位论文 (深圳: 深圳大学)
Tang P 2017 Ph. D. Dissertation (Shenzhen: Shenzhen University) (in Chinese)
[31] Manfred M 1997 Comput. Chem. Eng. 21 1149
Google Scholar
[32] 刘海涛, 郑四发, 连小珉, 但佳壁 2014 声学学报 39 353
Google Scholar
Liu H T, Zheng S F, Lian X M, Dan J B 2014 Acta Acust. 39 353
Google Scholar
[33] 杨永锋, 任兴民, 秦卫阳, 吴亚峰, 支希哲 2008 物理学报 57 6139
Google Scholar
Yang Y F, Ren X M, Qin W Y, Wu Y F, Zhi X Z 2008 Acta Phys. Sin. 57 6139
Google Scholar
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