基于Hilbert的单边带调制随机共振的微弱信号检测
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摘要
为了克服经典随机共振中的小参数检测条件的限制,介绍了基于Hilbert变换的单边带频率调制技术,并与二阶随机共振系统相结合,提出了运用调制随机共振的方法实现工程中大信号检测的应用。针对小采样频率和大采样频率进行了分开讨论,并对基频信号的选取做了相关研究。研究结果发现,小采样频率下,Hilbert单边带频率调制技术结合二阶系统有很好的检测效果。大采样频率下,可以结合变尺度处理进行优化。数值仿真分析表明,基频信号取在频率轴分辨率的10～60倍时,会有一个较高的并且较稳定的输出信噪比。并将变尺度Hilbert单边带频率调制技术运用于实际的轴承内外圈故障信号检测中,能明显、准确的检测出单频故障大信号。
In order to overcome the limitations of small parameter detection conditions in classical stochastic resonance, this paper mainly introduces the single sideband modulation technology based on Hilbert transform combined with a second-order stochastic resonance system, and the application of modulation stochastic resonance to realize large signal detection in engineering is proposed. At the same time, the paper discusses the cases of small sampling frequency and large sampling frequency, and makes relevant research on the selection of fundamental frequency signals. It demonstrates that the Hilbert single sideband frequency modulation has a good detection effect under the condition of small sampling frequency combined with the second-order system, but under the condition of large sampling frequencies, it can be promoted combined with scale transformation. Numerical simulation analysis shows that the baseband signal has a higher and more stable output signal-to-noise ratio when it takes about 10～60 times the frequency axis resolution. The effect of this technique combined with second-order systems is significantly better than first-order systems. Finally, the scale transformation with Hilbert single sideband frequency modulation technology is applied to the bearing inner and outer ring fault signal detection, and it is found that the large frequency fault signal can be detected obviously and accurately.
In order to overcome the limitations of small parameter detection conditions in classical stochastic resonance, this paper mainly introduces the single sideband modulation technology based on Hilbert transform combined with a second-order stochastic resonance system, and the application of modulation stochastic resonance to realize large signal detection in engineering is proposed. At the same time, the paper discusses the cases of small sampling frequency and large sampling frequency, and makes relevant research on the selection of fundamental frequency signals. It demonstrates that the Hilbert single sideband frequency modulation has a good detection effect under the condition of small sampling frequency combined with the second-order system, but under the condition of large sampling frequencies, it can be promoted combined with scale transformation. Numerical simulation analysis shows that the baseband signal has a higher and more stable output signal-to-noise ratio when it takes about 10～60 times the frequency axis resolution. The effect of this technique combined with second-order systems is significantly better than first-order systems. Finally, the scale transformation with Hilbert single sideband frequency modulation technology is applied to the bearing inner and outer ring fault signal detection, and it is found that the large frequency fault signal can be detected obviously and accurately.
引文
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[11] 林敏, 黄咏梅. 调制随机共振及其在微弱信号检测中的应用[J]. 传感器与微系统, 2006, 25(2): 81-82.LIN M, HUANG Y M. Modulated stochastic resonance and its application in weak signal detection[J]. Transducer and Microsystem Technologies, 2006, 25(2):81-82.
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[13] 贺利芳, 曹莉, 张天骐. Levy噪声中EMD降噪的随机共振研究[J]. 电子测量与仪器学报, 2017, 31(1): 21-28.HE L F, CAO L, ZHANG T Q. Stochastic resonance study of EMD noise reduction in Levy noise[J]. Journal of Electronic Measurement and Instrumentation, 2017, 31(1): 21-28.
[14] 贺利芳, 崔莹莹, 张天骐, 等. 基于幂函数型双稳随机共振的故障信号检测方法[J]. 仪器仪表学报, 2016, 37(7): 1457-1467.HE L F, CUI Y Y, ZHANG T Q, et al. Fault signal detection method based on power function type bistable stochastic resonance[J]. Chinese Journal of Scientific Instrument, 2016, 37(7): 1457-1467.
[15] LI J, ZHANG Y, XIE P. A new adaptive cascaded stochastic resonance method for impact features extraction in gear fault diagnosis[J]. Measurement, 2016(91): 499-508.
[2] 焦尚彬, 杨蓉, 张青, 等. α稳定噪声驱动的非对称双稳随机共振现象[J]. 物理学报, 2015, 64(2): 49-57.JIAO SH B, YANG R, ZHANG Q, et al. Asymmetric bistable stochastic resonance driven by α-stabilized noise[J]. Acta Physica Sinica, 2015, 64(2): 49-57.
[3] 田祥友, 冷永刚, 范胜波. 一阶线性系统的调参随机共振研究[J]. 物理学报, 2013, 62(2): 103-110.TIAN X Y, LENG Y G, FAN S B. Study on the adjusted stochastic resonance of first-order linear systems[J]. Acta Physica Sinica, 2013, 62(2): 103-110.
[4] 冷永刚. 基于Kramers逃逸速率的调参随机共振机理[J]. 物理学报, 2009, 58(8): 5196-5200.LENG Y G. Parametric-tuned stochastic resonance mechanism based on Kramers escape rate [J]. Journal of Physics, 2009, 58 (8): 5196-5200.
[5] 范春凤, 龚克,陈新武,等. 频移变尺度自适应随机共振在大信号检测中的应用[J].信阳师范学院学报(自然科学版) 2010,23(3): 415-419.FAN CH F, GONG K,CHEN X W, et al. Application of frequency-shifted and re-scaling adaptive stochastic resonance in signal detection[J]. Journal of Xinyang Normal University (Natural Science Edition) 2010,23(3): 415-419.
[6] 赖志慧, 饶锡新,刘建胜,等. 基于Duffing振子的信号频谱重构随机共振研究[J].振动与冲击,2016,35(21): 9-16.LAI ZH H, RAO X X,LIU J X, et al. Signal spectrum reconstruction stochastic resonance method based on a duffing oscillator[J]. Journal of Vibration and Shock 2016,35(21): 415-419.
[7] 刘进军, 冷永刚,赖志慧,等. 基于频域信息交换的随机共振研究[J].物理学报,2016,65(22): 193-206.LIU J J, LENG Y G, LAI ZH H, et al. Stochastic resonance based on frequency domain information information exchange[J]. Acta Physica Sinica 2016,65(22): 193-206.
[8] 易甜, 张刚, 张天骐,等. 二阶随机共振系统的冲击信号检测[J]. 西安交通大学学报, 2018,52(6): 106-113.YI T, ZHANG G, ZHANG T Q, et al. Research on the impact signal detection based on second-order stochastic resonance[J]. Journal of Xi'an Jiaotong University, 2018,52(6): 106-113.
[9] 陆思良. 基于随机共振的微弱信号检测模型及应用研究[D]. 合肥:中国科学技术大学, 2015.LU S L. Models and applications of stochastic resonance-based weak signal detection[D].Hefei: University of Science and Technology of China, 2015.
[10] LU S L, HE Q B, KONG F R. Effects of underdamped step-varying second-order stochastic resonance for weak signal detection[J]. Digital Signal Processing, 2015(36): 93-103.
[11] 林敏, 黄咏梅. 调制随机共振及其在微弱信号检测中的应用[J]. 传感器与微系统, 2006, 25(2): 81-82.LIN M, HUANG Y M. Modulated stochastic resonance and its application in weak signal detection[J]. Transducer and Microsystem Technologies, 2006, 25(2):81-82.
[12] 李忠虎, 蔡志全. 基于调制随机共振的微弱信号频率检测方法[J]. 仪表技术与传感器, 2014(8): 104-106.LI ZH H, CAI ZH Q. Frequency of weak signal detection based on modulation stochastic resonance[J]. Instrument Technique and Sensor, 2014(8): 104-106.
[13] 贺利芳, 曹莉, 张天骐. Levy噪声中EMD降噪的随机共振研究[J]. 电子测量与仪器学报, 2017, 31(1): 21-28.HE L F, CAO L, ZHANG T Q. Stochastic resonance study of EMD noise reduction in Levy noise[J]. Journal of Electronic Measurement and Instrumentation, 2017, 31(1): 21-28.
[14] 贺利芳, 崔莹莹, 张天骐, 等. 基于幂函数型双稳随机共振的故障信号检测方法[J]. 仪器仪表学报, 2016, 37(7): 1457-1467.HE L F, CUI Y Y, ZHANG T Q, et al. Fault signal detection method based on power function type bistable stochastic resonance[J]. Chinese Journal of Scientific Instrument, 2016, 37(7): 1457-1467.
[15] LI J, ZHANG Y, XIE P. A new adaptive cascaded stochastic resonance method for impact features extraction in gear fault diagnosis[J]. Measurement, 2016(91): 499-508.