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At present, commonly used methods of weak signal detection such as the wavelet threshold denoising method, digital filtering method, the Fourier frequency domain transformation etc. can achieve the lowest detection of signal-to-noise ratio (SNR) of -10 dB, and the bidirectional ring coupled Duffing oscillator can reach the lowest detected SNR of -20 dB. But the discharge pulse signal with a lower SNR often appears in on-site testing, so the existing detection methods are difficult to meet the practical requirements of weak signal detection. In order to effectively solve the problem, a new method for weak pulse signal detection is proposed based on an extended-Duffing oscillator. The main idea of this method is to make the Duffing oscillator model transform to an extended-Duffing oscillator model by using the general time scale transformation. This approach can effectively expand the frequency detection range for weak signal detection. In addition, because the critical amplitude of the Duffing system depends on various parameters, such as system parameters, initial values, driving signal frequency, and calculation step of Runge - Kutta method etc.. However, the Melnikov method is an approximate analytical method, which does not take into account the factors such as initial values and calculation step, therefore, the Melnikov method is not suitable for numerical simulations, and lack of practicality. For this, the critical amplitude of chaos with high accuracy is determined only through the simulation experiment. Experimental results show that the critical amplitude is equal to 0.825010 when the incentive angular frequency of the extended-Duffing oscillator equals 10000 rad/s, and the extended-Duffing oscillator changes from the critical chaotic state to the large scale cycle state for small changes (10-6) of the driving amplitude. The simulation results show that the extended-Duffing oscillator not only has a good noise immunity performance, but also can effectively detect weak partial discharge pulse signal so that the signal-to-noise ratio can be lower than -40 dB. This method further expands the detection range and application fields of weak signals.
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Keywords:
- extended Duffing oscillator /
- weak signal detection /
- partial discharge pulse signal /
- strong background noise
[1] Li Y, Yang B J, Du L Z, Yuan Y 2003 Chin. Phys. 12 0714
[2] Xiang X Q, Shi B C 2010 Chaos 20 013104
[3] Lai Z H, Leng Y G, Sun J Q, Fan S B 2012 Acta Phys. Sin. 61 050503 (in Chinese) [赖志慧, 冷永刚, 孙建桥, 范胜波 2012 61 050503]
[4] Birx D I 1992 IEEE Int. Joint Conf. Neural Networks 22 881
[5] Ji C P, Guo W P, Ji H H 2013 Control of Noise and Vibration 33 040207 (in Chinese) [冀常鹏, 郭伟平, 姬红红 2013 噪声与振动控制 33 040207]
[6] Zhao W L, Huang Z Q, Zhao J X 2011 J. Circuits and Systems 16 06120 (in Chinese) [赵文礼, 黄振强, 赵景晓 2011 电路与系统学报 16 06120]
[7] Zhao W L, Fan J, Wu M, Wang W Q 2014 Control Theory & Application 31 020250 (in Chinese) [赵文礼, 范剑, 吴敏, 王万强 2014 控制理论与应用 31 020250]
[8] Yuan Y, Li Y, Mandic D P, Yang B J 2009 Chin. Phys.B 18 958
[9] Wu Y F, Zhang S P, Sun J W, Rolfe P 2011 Acta Phys. Sin. 60 020511 (in Chinese) [吴勇峰, 张世平, 孙金玮, Peter Rolfe 2011 60 020511]
[10] Wu Y F, Huang S P, Jin G B 2013 Acta Phys. Sin. 62 130505 (in Chinese) [吴勇峰, 黄绍平, 金国彬 2013 62 130505]
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[1] Li Y, Yang B J, Du L Z, Yuan Y 2003 Chin. Phys. 12 0714
[2] Xiang X Q, Shi B C 2010 Chaos 20 013104
[3] Lai Z H, Leng Y G, Sun J Q, Fan S B 2012 Acta Phys. Sin. 61 050503 (in Chinese) [赖志慧, 冷永刚, 孙建桥, 范胜波 2012 61 050503]
[4] Birx D I 1992 IEEE Int. Joint Conf. Neural Networks 22 881
[5] Ji C P, Guo W P, Ji H H 2013 Control of Noise and Vibration 33 040207 (in Chinese) [冀常鹏, 郭伟平, 姬红红 2013 噪声与振动控制 33 040207]
[6] Zhao W L, Huang Z Q, Zhao J X 2011 J. Circuits and Systems 16 06120 (in Chinese) [赵文礼, 黄振强, 赵景晓 2011 电路与系统学报 16 06120]
[7] Zhao W L, Fan J, Wu M, Wang W Q 2014 Control Theory & Application 31 020250 (in Chinese) [赵文礼, 范剑, 吴敏, 王万强 2014 控制理论与应用 31 020250]
[8] Yuan Y, Li Y, Mandic D P, Yang B J 2009 Chin. Phys.B 18 958
[9] Wu Y F, Zhang S P, Sun J W, Rolfe P 2011 Acta Phys. Sin. 60 020511 (in Chinese) [吴勇峰, 张世平, 孙金玮, Peter Rolfe 2011 60 020511]
[10] Wu Y F, Huang S P, Jin G B 2013 Acta Phys. Sin. 62 130505 (in Chinese) [吴勇峰, 黄绍平, 金国彬 2013 62 130505]
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