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本文引用格式:赵志杰,田瑞兰,杨泽峰,王秋宝,杜以昌.改进类Lorenz系统在微弱谐波信号识别中的应用[J].动力学与控制学报,2019,17(6):575~583;   Zhao Zhijie,Tian Ruilan,Yang Zefeng,Wang Qiubao,Du Yichang.Application of improved Lorenz like system in recognition of weak harmonic signal[J].Journal of Dynamics and Control,2019,17(6):575-583.
改进类Lorenz系统在微弱谐波信号识别中的应用    点此下载全文
赵志杰  田瑞兰  杨泽峰  王秋宝  杜以昌
石家庄铁道大学 非线性动力学研究所, 石家庄 050043;石家庄铁道大学 数理系, 石家庄 050043,石家庄铁道大学 非线性动力学研究所, 石家庄 050043,石家庄铁道大学 非线性动力学研究所, 石家庄 050043,石家庄铁道大学 非线性动力学研究所, 石家庄 050043;石家庄铁道大学 数理系, 石家庄 050043,石家庄铁道大学 数理系, 石家庄 050043
基金项目:国家自然科学基金资助项目(11872253,11602151),河北省杰出青年科学基金项目(A2017210177),河北省杰出青年科学基金培育项目(A2015210097),基础研究团队专项支持项目(311008)资助的课题
DOI:10.6052/1672-6553-2019-017
摘要:
      基于类Lorenz系统构建了改进类Lorenz系统.借助概率论、数理统计原理,揭示了不同功率噪声对该系统阈值可信度的影响;利用加入微弱谐波信号前、后系统吸引子个数变化的阈值差值,识别出待测谐波信号的幅值.利用系统的分岔图,研究加入高斯白噪声前后系统吸引子的个数随参数变化的情况.在强噪声作用下,通过大数定律,从加入微弱谐波信号前、后系统分岔图中统计系统阈值,以统计数据中的众数作为所构建系统的阈值.利用阈值的差值识别出了与内置周期驱动力同频微弱谐波信号的幅值,且检测效果的可信度和正确率为89.5%,检测最低信噪比为-33dB.数值仿真对比结果表明改进类Lorenz系统比Duffing系统、受控类Lorenz系统具有阈值可信度高、检测门限低、信噪比低的优势,更适合在强噪声背景下识别信号参数.进一步地,在Simulink仿真结果的基础上,通过Multisim软件搭建改进类Lorenz系统的模拟电路图,验证本文的理论研究结果在工程实际化中有一定的可行性.
关键词:改进类Lorenz系统,吸引子,分岔图,阈值可信度,检测系统模拟电路
Application of improved Lorenz like system in recognition of weak harmonic signal    Download Fulltext
Zhao Zhijie  Tian Ruilan  Yang Zefeng  Wang Qiubao  Du Yichang
Fund Project:
Abstract:
      An improved Lorenz-like system was constructed for weak harmonic signal recognition in strong noise. Applying the law of large numbers, the thresholds were calculated from the bifurcation diagrams, and the mode of statistical data was taken as the critical value. The influence of the noise on the thresholds was also revealed. The amplitude of the weak harmonic signal was identified by the threshold difference of the change in the number of attractors detected before and after adding the weak harmonic signal to the system. The results showed that the reliability and accuracy was 89.5% and the minimum signal-to-noise ratio(SNR) was -33dB. Compared to the Duffing system and the controlled Lorenz-like system, the improved Lorenz-like system had the advantages of higher threshold reliability, lower SNR and lower detection threshold, which was more suitable for identifying signal parameters in strong noise. Additionally, the theoretical results were validated by the analog circuit of the improved Lorenz-like system created by Multisim software.
Keywords:improved Lorenz-like system,attractor,bifurcation diagram,threshold reliability,analog circuit
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