Weak Signal Detection Method Based on Dominative Frequency PowerRatio Derived from Systems First-order Perturbation Solution
Funds:
The National Natural Science Foundation of China (41476089)
-
摘要: 針對現(xiàn)有混沌檢測算法精度不高、狀態(tài)響應(yīng)滯后的問題，該文從混沌狀態(tài)整體性、系統(tǒng)解頻域特性等角度進(jìn)行全面分析，提出一種基于攝動(dòng)解主頻功率比的弱信號檢測方法，該算法不僅準(zhǔn)確實(shí)現(xiàn)了臨界狀態(tài)的有效界定，提高了信號檢測的可靠程度，而且揭示了系統(tǒng)各個(gè)狀態(tài)之間的差別及物理含義。文中采用參數(shù)攝動(dòng)法推導(dǎo)了Duffing-Van der pol振子的一階攝動(dòng)平衡解，證明了其為影響主頻率分量的主要因素。在此基礎(chǔ)上，采用經(jīng)驗(yàn)?zāi)B(tài)分解方法對有效參量信息進(jìn)行選擇性重構(gòu)，以最小均方誤差約束準(zhǔn)則下的比值系數(shù)重新定義了系統(tǒng)狀態(tài)，得到系統(tǒng)主頻功率比與策動(dòng)力幅值之間的映射關(guān)系，并以此作為臨界閾值確定的依據(jù)。實(shí)驗(yàn)結(jié)果表明，采用主頻功率比準(zhǔn)則的信號檢測方法可靠性提高了約1個(gè)數(shù)量級，且算法的響應(yīng)速度為傳統(tǒng)分析方法的2倍以上。
-
關(guān)鍵詞:
- 信號處理 /
- 一階攝動(dòng)平衡 /
- 主頻功率比 /
- 臨界閾值 /
- 最小均方誤差
Abstract: 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 systems first-order perturbation solution is proposed in this paper. This algorithm is ascribable to the all-around analyses of chaotic states global property and system solutions 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. -
鄧冬虎, 張群, 羅迎, 等. Duffing 振子在低信噪比雷達(dá)目標(biāo)微動(dòng)特征提取中的應(yīng)用[J]. 電子與信息學(xué)報(bào), 2014, 36(2): 453-458. doi: 10.3724/SP.J.1146.2013.00624. 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. 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. 靳曉艷, 周希元. 一種基于特定Duffing振子的MPSK信號調(diào)制識別算法[J]. 電子與信息學(xué)報(bào), 2013, 35(8): 1882-1887. doi: 10.3724/SP.J.1146.2012.01728. 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. 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. 韓建群. 一種減小Duffing系統(tǒng)可檢測斷續(xù)正弦信號頻率范圍的方法[J]. 電子學(xué)報(bào), 2013, 41(4): 733-738. 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. 張淑清, 翟欣沛, 董璇, 等. EMD及Duffing振子在小電流系統(tǒng)故障選線方法中的應(yīng)用[J]. 中國電機(jī)工程學(xué)報(bào), 2013, 33(10): 161-167. 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. 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. 馮俊, 徐偉, 顧仁財(cái), 等. 有界噪聲與諧和激勵(lì)聯(lián)合作用下Duffing-Rayleigh振子的Melnikov混沌[J]. 物理學(xué)報(bào), 2011, 34(9): 170-177. FENG Jun, XU Wei, GU Rencai, et al. Melnikov chaos in Dufing-Rayleigh oscillator subjected to combined bounded noise and harmonic excitations[J]. Acta Physica Sinica, 2011, 34(9): 170-177. 唐元璋, 樓京俊, 翁雪濤, 等. Duffing 振子倍周期分岔譜特性[J]. 振動(dòng)與沖擊, 2014(2): 60-63. 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. 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. 劉延彬, 陳予恕. 余維4的Duffing-Van der Pol方程全局分岔分析[J]. 振動(dòng)與沖擊, 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. 姚天亮, 劉海峰, 許建良, 等. 基于最大Lyapunov指數(shù)不變性的混沌時(shí)間序列噪聲水平估計(jì)[J]. 物理學(xué)報(bào), 2012, 61(6): 53-57. 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. 芮國勝, 張洋, 苗俊, 等. 聯(lián)合增益遞推的Duffing系統(tǒng)弱信號檢測算法[J]. 電子學(xué)報(bào), 2012, 40(6): 1269-1273. 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. 楊紅英, 葉昊, 王桂增, 等. Duffing 振子的 Lyapunov 指數(shù)與 Floquet 指數(shù)研究[J]. 儀器儀表學(xué)報(bào), 2008, 29(5): 927-932. 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. 魏恒東, 甘露, 李立萍. 基于哈密頓量的Duffing振子微弱信號檢測[J]. 電子科技大學(xué)學(xué)報(bào), 2012, 41(2): 203-207. 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. 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. 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. 李月, 徐凱, 楊寶俊, 等. 混沌振子系統(tǒng)周期解幾何特征量分析與微弱周期信號的定量檢測[J]. 物理學(xué)報(bào), 2008, 57(6): 3353-3358. 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. 何斌, 楊燦軍, 陳鷹. 混沌周期解提高測量靈敏度算法及抗干擾分析[J]. 電子學(xué)報(bào), 2003, 31(1): 68-70. HE Bin, YANG Canjun, and CHEN Ying. Study on enhancing delicacy Sensors using chaotic system[J]. Acta Electronica Sinica, 2003, 31(1): 68-70. 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. 王文波, 汪祥莉. 噪聲模態(tài)單元預(yù)判的經(jīng)驗(yàn)?zāi)B(tài)分解脈沖星信號消噪[J]. 物理學(xué)報(bào), 2013, 13(7): 1-12. 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. ALEX E. Analytical solution of the damped Helmholtz Duffing equation[J]. Applied Mathematics Letters, 2012(25): 2349-2353. 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. 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. -
計(jì)量
- 文章訪問數(shù): 1197
- HTML全文瀏覽量: 125
- PDF下載量: 412
- 被引次數(shù): 0
下載:
