基于短时傅里叶变换的Duffing振子微弱信号检测
收稿日期: 2014-10-17
修回日期: 2015-01-07
网络出版日期: 2015-01-13
基金资助
陕西省自然科学基础研究计划项目 (2014JM8344)
Weak signal detection with Duffing oscillator based on short time Fourier transform
Received date: 2014-10-17
Revised date: 2015-01-07
Online published: 2015-01-13
Supported by
Project supported by the Natural Science Foundation of Shaanxi Province (2014JM8344)
研究了Duffing振子信号检测过程中混沌、间歇混沌和大周期状态的时频特征,提出了一种基于检测统计量的任意频率信号检测方法。通过对系统不同状态下的输出序列进行短时傅里叶变换(STFT)发现,等幅线和三维时频分布能够体现出不同状态的显著差异,且可以完全区分出每一种状态。从构造统计量的易实现性出发,用三维时频分布中的幅时曲线作为衡量不同状态的依据,并将不同频率对应的幅时曲线的均值最大量作为检测统计量,该统计量的计算可以借助快速傅里叶变换(FFT)操作提高时效性。在此基础上,引入频率控制单元,给出了任意频率信号的检测方法步骤,方法的关键是将检测统计量最大值处所在的频率作为待测信号频率范围的一个端点,另一个端点为毗邻的两个检测统计量值较大者所在频率点。实验给出了不同状态的检测统计量范围,进而以此范围为判据,实现了振子对任意频率信号的检测,说明了方法的可行性,为Duffing振子信号检测问题的研究提供了一种新的思路。
牛德智 , 陈长兴 , 陈婷 , 任晓岳 , 王卓 , 程蒙江川 , 蒋金 . 基于短时傅里叶变换的Duffing振子微弱信号检测[J]. 航空学报, 2015 , 36(10) : 3418 -3429 . DOI: 10.7527/S1000-6893.2015.0012
Time frequency characteristic of three statuses such as chaos, intermittent chaos and great period appearing in signal detection process with Duffing oscillator is studied and a frequency signal detection method based on new detection statistics is proposed. By analyzing on system output sequence in different statuses with short time Fourier transform (STFT), it is found that contour line of amplitude and three-dimensional time frequency distribution could represent differences of three statuses and recognize the three statuses utterly. Considering being easily operated on the detection statistics, amplitude-time characteristic in three-dimensional time frequency distribution is made as a foundation to weigh different statuses. Further, maximum of average value of number in amplitude-time characteristic corresponding to each frequency is set to final detection statistic, whose computation could be realized by fast Fourier transform (FFT) so that there will be high time effectiveness. On the basis of it, frequency control unit is brought in Duffing oscillator and scheme of any frequency signal detection is given. The key point of the scheme is to find the maximum among all detection statistics and makes its matching frequency as one port of unknown signal frequency range. Then the other port is the matching frequency of secondary maximum among other two detection statistics adjacent to the maximum. After experiment, the range of detection statistics of each status is given. Thus, according to the range, any frequency signal detection by Duffing oscillator is realized, which shows feasibility of the method and provides one new thought for studying signal detection problem with Duffing oscillator.
[1] Wang Y S, Jiang W Z, Zhao J J, et al. A new method of weak signal detection using Duffing oscillator and its simulation research[J]. Acta Physica Simica, 2008, 57(4): 2053-2059 (in Chinese). 王永生, 姜文志, 赵建军, 等. 一种Duffing弱信号检测新方法及仿真研究[J]. 物理学报, 2008, 57(4): 2053-2059.
[2] Xu Y C,Yang C L. New method of weak signal frequency detection using high-level Chaotic oscillator[J]. Journal of Harbin Institute of Technology, 2010, 42(3): 446-450 (in Chinese). 徐艳春, 杨春玲. 高阶混沌振子的微弱信号频率检测新方法[J]. 哈尔滨工业大学学报, 2010, 42(3): 446-450.
[3] Birx D L. Chaotic oscillator and CMFFNS for signal detection in noise environments[C]//IEEE International Joint Conference on Neural Network. Piscataway, NJ: IEEE Press, 1992, 2: 881-888.
[4] Anil K, Satish K, Lai Y C, et al. Inducing chaos in electronic circuits by resonant perturbations[J]. IEEE Transactions on Circuits and Systems, 2007, 54(5): 1109-1119.
[5] Hesan V, Gharehpetian G B, Mehdi K.Application of duffing oscillators for passive islanding detection of inverter-based distributed generation units[J]. IEEE Transactions on Power Delivery, 2012, 27(4): 1973-1983.
[6] Zhang X Y, Guo H X, Wang B H, et al. A new method for detecting line spectrum of ship-radiated noise using Duffing oscillator[J]. Chinese Science Bulletin, 2007, 52(14): 1906-1912.
[7] Fu Y Q, Wu D M, Zhang L, et al. A circular zone partition method for identifying Duffing oscillator state transition and its application to BPSK signal demodulation[J]. Science China Information Sciences, 2011, 54(2): 1274-1282.
[8] Jiang W L, Wu S Q, Zhang J C. Two methods of weak signal detection of duffing oscillator and their difference[J]. Journal of Yanshan University, 2002, 26(2): 114-118 (in Chinese). 姜万录, 吴胜强, 张建成. Duffing振子的两种检测微弱信号的方法及区别[J]. 燕山大学学报, 2002, 26(2): 114-118.
[9] Zhai D Q, Liu C X, Liu Y, et al. Determ ination of the parameters of unknown signals based on intermittent chaos[J]. Acta Physica Sinica, 2010, 59(2): 816-825 (in Chinese). 翟笃庆, 刘崇新, 刘尧, 等. 利用阵发混沌现象测定未知信号参数[J]. 物理学报, 2010, 59(2): 816-825.
[10] Wang G Y, Chen D J, Lin J Y, et al. The application of chaotic oscillators to weak signal detection[J]. IEEE Transactions on Industrial Electronics, 1999, 46(2): 440-444.
[11] Xu Y C. Study of weak photo-electric signal detection based on chaotic oscillator[D]. Harbin: Harbin Institute of Technology, 2010 (in Chinese). 徐艳春. 基于混沌振子的微弱光电信号检测技术研究[D]. 哈尔滨: 哈尔滨工业大学, 2010.
[12] Cong C, Li X K, Song Y. A method of detecting line spectrum of ship-radiated noise using a new intermittent chaotic oscillator[J]. Acta Physica Sinica, 2014, 63(6): 064301-1-12 (in Chinese). 丛超, 李秀坤, 宋扬. 一种基于新型间歇混沌振子的舰船线谱检测方法[J]. 物理学报, 2014, 63(6) : 064301-1-12
[13] Lai Z H, Leng Y G, Sun J Q, et al.Weak characteristic signal detection based on scale transformation of buffing oscillator[J]. Acta Physica Sinica, 2012, 61(5): 050503-1-9 (in Chinese). 赖志慧, 冷永刚, 孙建桥, 等. 基于Duffing振子的变尺度微弱特征信号检测方法研究[J]. 物理学报, 2012, 61(5): 050503-1-9.
[14] Xu X M, Dai P, Yang B C, et al. Weak photoacoustic signal detection in photoacoustic cell[J]. Acta Physica Sinica, 2013, 62(20): 204303-1-9 (in Chinese). 许雪梅, 戴鹏, 杨兵初, 等. 光声池中微弱光声信号检测[J]. 物理学报, 2013, 62(20): 204303-1-9.
[15] Li Y, Xu K, Yang B J, et al. Analysis of the geometric characteristic quantity of the periodic solutions of the chaotic oscillator system and the quantitative detection of weak periodic signal[J]. Acta Physica Sinica, 2008, 57(6): 3353-3358 (in Chinese). 李月, 徐凯, 杨宝俊, 等. 混沌振子系统周期解几何特征量分析与微弱周期信号的定量检测[J]. 物理学报, 2008, 57(6): 3353-3358.
[16] Liu H B, Wu D W, Dai C J, et al. A new weak sinusoidal signal detection method based on duffing oscillators[J]. Acta Electronica Sinica, 2013, 41(1): 8-12 (in Chinese). 刘海波, 吴德伟, 戴传金, 等. 基于Duffing振子的弱正弦信号检测方法研究[J]. 电子学报, 2013, 41(1): 8-12.
[17] Wei H D, Gan L, Li L P. Weak signal detection by buffing oscillator based on hamiltonian[J]. Journal of University of Electronic Science and Technology of China, 2012, 41(2): 203-207 (in Chinese). 魏恒东, 甘露, 李立萍. 基于哈密顿量的Duffing振子微弱信号检测[J]. 电子科技大学学报, 2012, 41(2): 203-207.
[18] Yang H Y, Ye H, Wang G Z, et al. Study on Lyapunov exponent and Floquet exponent of Duffing oscillator[J]. Chinese Journal of Scientific Instrument, 2008, 29(5): 927-932 (in Chinese). 杨红英, 叶昊, 王桂增, 等. Duffing振子的Lyapunov指数与Floquet 指数研究[J]. 仪器仪表学报, 2008, 29(5): 927-932.
[19] Jin T, Zhang H. Statistical approach to weak signal detection and estimation using Duffing chaotic oscillators[J]. Science China: Information Science, 2011, 41(10): 1184-1199 (in Chinese). 金天, 张骅. 基于统计方法的混沌Duffing振子弱信号检测与估计[J]. 中国科学: 信息科学, 2011, 41(10): 1184-1199.
[20] Rui G S, Zhang Y, Miao J, et al. A weak signal detection method by duffing system with the gain[J]. Acta Electronica Sinica, 2012, 40(6): 1269-1273 (in Chinese). 芮国胜, 张洋, 苗俊, 等. 联合增益递推的Duffing系统弱信号检测算法[J]. 电子学报, 2012, 40(6): 1269-1273.
[21] Lu X J, Zheng Z Q, Guo H W. Online aircraft parameter identification using recursive fourier transform[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(2): 532-540 (in Chinese). 鲁兴举, 郑志强, 郭鸿武. 基于递推傅里叶变换的飞行器参数在线辨识方法[J]. 航空学报, 2014, 35(2): 532-540.
[22] Bian H L, Chen G J. Anti-aliasing nonstationary signals detecion algorithm based on interpolation in the frequency domain using the short time Fourier transform[J]. Journal of Systems Engineering and Electronics, 2008, 19(3): 419-426.
/
| 〈 |
|
〉 |
CJA