针对现有混沌检测算法精度不高、状态响应滞后的问题,该文从混沌状态整体性、系统解频域特性等角度进行全面分析,提出一种基于摄动解主频功率比的弱信号检测方法,该算法不仅准确实现了临界状态的有效界定,提高了信号检测的可靠程度,而且揭示了系统各个状态之间的差别及物理含义。文中采用参数摄动法推导了Duffing-Van der pol振子的一阶摄动平衡解,证明了其为影响主频率分量的主要因素。在此基础上,采用经验模态分解方法对有效参量信息进行选择性重构,以最小均方误差约束准则下的比值系数重新定义了系统状态,得到系统主频功率比与策动力幅值之间的映射关系,并以此作为临界阈值确定的依据。实验结果表明,采用主频功率比准则的信号检测方法可靠性提高了约1个数量级,且算法的响应速度为传统分析方法的2倍以上。
Traditional chaotic detection methods have many problems, such as low criterion accuracy and delay state response. To cope with these problems, a weak signal detection method based on dominative frequency power ratio derived from system’s first-order perturbation solution is proposed in this paper. This algorithm is ascribable to the all-around analyses of chaotic state’s global property and system solution’s frequency-domain characteristics. It not only gives an effective and accurate critical threshold which could offer more reliable guarantee for signal detection, but also disclosures the differences between system states and the coherent physical meanings. The first-order perturbation equilibrium solution of Duffing-Van der pol oscillator is derived with parameter perturbation method, and it is proved that this solutionis is most significant to the dominative frequency. And then, the effective signal is selectively reconstructed through empirical mode decomposition, and system state is redefined with this ratio restrained under MMSE criterion. Finally the mapping relationship between power ratio of dominative frequencies and driving motivation amplitude is obtained and it is considered as determination criterion of critical threshold. Experimental results show that this algorithm could bring an promotion about one order of magnitude in system reliability, and the response speed is at least doubled compared with traditional methods.
孙文军,芮国胜,张洋,陈强. 基于系统一阶摄动解主频功率比的弱信号检测方法[J]. 电子与信息学报, 2016, 38(1): 160-167.
SUN Wenjun, RUI Guosheng, ZHANG Yang, CHEN Qiang. Weak Signal Detection Method Based on Dominative Frequency Power Ratio Derived from System’s First-order Perturbation Solution. JEIT, 2016, 38(1): 160-167.
DENG Donghu, ZHANG Qun, LUO Yin, et al.. The application of Duffing oscillators to micro-motion feature extraction of radar target under low SNR[J]. Journal of Electronics & Information Technology, 2014, 36(2): 453-458. doi: 10.3724/SP.J.1146.2013.00624.
[2]
JAISER A R, STEN K, and KYSLE P. A numerical solution of the nonlinear controlled Duffing oscillator by radial basis functions[J]. Computers and Mathematics with Applications, 2012(64): 2049-2065.
JIN Xiaoyan and ZHOU Xiyuan. A modulation classification algorithm for MPSK signals based on special Duffing oscillator[J]. Journal of Electronics & Information Technology, 2013, 35(8): 1882-1887. doi: 10.3724/SP.J.1146. 2012.01728.
[4]
MLOON F, TAYLE G, DILER B, et al. Pseudorandom number generator based on mixing of three chaotic maps[J]. Communications in Nonlinear Science and Numerical Simulation, 2014, 19(4): 1-8.
HAN Jianqun. A method of narrowing frequency range of intermittent sine signal detected by Duffing system[J]. Acta Electronica Sinica, 2013, 41(4): 733-738.
ZHANG Shuqing, ZHAI Xinpei, DONG Xuan, et al. Application of EMD and Duffing oscillator to fault line detection in un-effectively grounded system[J]. Proceedings of the CSEE, 2013, 33(10): 161-167.
[7]
MENG K L and STEVE S. Temporal and spectral responses of a softening Duffing oscillator undergoing route-to-chaos[J]. Communication Nonlinear Science Numerical Simulation, 2012(17): 5217-5228.
TANG Yuanzhang, LOU Jingjun, WENG Xuetao, et al. Spectrum property of period-doubling bifurcations of Duffing oscillator[J]. Journal of Vibration and Shock, 2014(2): 60-63.
[10]
JIMENEZ-TRIANA A, WALLACE K T, GUANRONG C, et al. Chaos control in Duffing system using impulsive parametric perturbations[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2010, 57(4): 305-309.
[11]
刘延彬, 陈予恕. 余维4的Duffing-Van der Pol方程全局分岔分析[J]. 振动与冲击, 2011(1): 69-72.
LIU Yanbin and CHEN Yunu. The global analyses on Duffing-Van der Pol equation of redundant dimension 4[J]. Journal of Vibration and Shock, 2011(1): 69-72.
YAO Tianliang, LIU Haifeng, XU Jianliang, et al. Noise-level estimation of noisy chaotic time series based on the invariant of the largest Lyapunov exponent[J]. Acta Physica Sinica, 2012, 61(6): 53-57.
RUI Guosheng, ZHANG Yang, MIAO Jun, et al. A weak signal detection method by Duffing System with the gain[J]. Acta Electronica Sinica, 2012, 40(6): 1269-1273.
YANG Hongying, YE Hao, WANG Guizeng, et al. Study on Lyapunov exponent and Floquet exponent of Duffing oscillator[J]. Chinese Journal of Scientific Instrument, 2008, 29(5): 927-932.
WEI Hengdong GAN Lu, and LI Liping. Weak signal detection by duffing oscillator based on hamiltonian[J]. Journal of University of Electronic Science and Technology of China, 2012, 41(2): 203-207.
[16]
DIMITRIOS E P, EFSTATHIOS E T, and MICHALIS P M. Exact analytic solutions for the damped Duffing nonlinear oscillator[J]. Chaos, Solitons and Fractals, 2006(334): 311-316.
[17]
IBRAHIM A M A and CHOUDHURY P K. On the Maxwell- Duffing approach to model photonic deflection sensor[J]. IEEE Photonics Journal, 2013, 5(4): 6800812.
LI Yue, XU Kai, YANG Baojun, 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.
HE Bin, YANG Canjun, and CHEN Ying. Study on enhancing delicacy Sensors using chaotic system[J]. Acta Electronica Sinica, 2003, 31(1): 68-70.
[20]
LI Keqiang, WANG Shangjiu, and ZHAO Yonggang. Multiple periodic solutions for asymptotically linear Duffing equations with resonance[J]. Journal of Mathematical Analysis and Applications, 2013, 397: 156-160.
WANG Wenbo and WANG Xiangli. Empirical mode decomposition pulsar signal denoising method based on predicting of noise mode cell[J]. Acta Physica Sinica, 2013, 13(7): 1-12.
[22]
ALEX E. Analytical solution of the damped Helmholtz- Duffing equation[J]. Applied Mathematics Letters, 2012(25): 2349-2353.
[23]
YANHUA H, XIANFENG C, SPENCER P S, et al. Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator[J]. IEEE Journal of Quantum Electronics, 2015, 51(3): 1-6.
[24]
YAZDI M K, AHMADIAN H, MIRZABEIGY A, et al. Dynamic analysis of vibrating systems with nonlinearities[J]. Communications in Theoretical Physics, 2012(2): 183-187.