Acta Physica Sinica, Volume. 68, Issue 8, 080501-1(2019)
Figures & Tables(16)
Fig. 1. Detection of weak pulse signal using the strongly coupled Duffing oscillators: (a) Input signal; (b) output signal; (c) phase space of oscillator 1 and (d) oscillator 2; (e) time domain diagram of variable and (f) 强耦合Duffing振子检测微弱脉冲信号 (a)输入信号; (b)输出信号; (c)振子1相图; (d)振子2相图; (e)变量 时域图; (f)变量 时域图
Fig. 2. Bifurcation diagram of Duffing oscillator with parameter
Fig. 3. SNRI and
Fig. 4. SNRI and
Fig. 5. SNRI and
Fig. 7. SNRI and
Fig. 8. Detection of square wave signal with SNR of –15 dB: (a) Input signal; (b) output signal检测信噪比–15 dB的方波信号 (a)输入信号; (b)输出信号
Fig. 9. Detection of double exponential pulse with SNR of –12 dB: (a)Input signal; (b) output signal检测信噪比–12 dB的双指数脉冲 (a)输入信号; (b)输出信号
Fig. 10. Detection of Gaussian derivative pulse with SNR –16 dB: (a) Input signal; (b) output signal检测信噪比–16 dB的高斯导数脉冲 (a)输入信号; (b)输出信号
Fig. 11. Contrast experimental results: input signal (a); output signal of weakly coupled Duffing oscillators (b) and strongly coupled Duffing oscillators (c)对比实验结果 (a)输入信号; (b)弱耦合Duffing振子输出信号; (c)强耦合Duffing振子输出信号
Table 1. Values range and default values of parameters in strongly coupled Duffing oscillators
View tableView in ArticleTable 1. Values range and default values of parameters in strongly coupled Duffing oscillators
参数 取值区间 默认值 F [0, 2] 0.2 $\omega $ ${\rm rad}\cdot {{\rm s}^{-1}} $ [1 × 105, 5 × 107] 5 × 106 k [10–1, 103] 10 $\xi$ [10–2, 102] 0.7 计算步长/ns [20, 1] 1
Table 2.
Waveform characteristics and partial oscillator parameters
波形特征及部分振子参数
View tableView in ArticleTable 2.
Waveform characteristics and partial oscillator parameters
波形特征及部分振子参数
脉冲类型 波形时域特征 Duffing振子参数 方波 上升时间0.1 ms $\omega = 50$ 半高宽1 s 计算步长0.1 ms 双指数脉冲 上升时间3 ${\text{μs}}$ $\omega = 5 \times {10^5}$ 半高宽25 ${\text{μs}}$ 计算步长10 ns 高斯导数脉冲 上升时间1.5 ${\text{μs}}$ $\omega = 4 \times {10^6}$ 峰峰宽1.45 ${\text{μs}}$ 计算步长1 ns
Table 3.
Detection results of strongly coupled Duffing oscillators
强耦合Duffing振子检测结果
View tableView in ArticleTable 3.
Detection results of strongly coupled Duffing oscillators
强耦合Duffing振子检测结果
脉冲类型 输入信噪比/dB –20 –19 –18 –17 –16 –15 –14 –13 –12 –11 –10 方波 检测概率/% 14.0 21.5 41.5 60.5 78.0 91.5 99.0 100 100 100 100 波形相似度 r 0.88 0.90 0.92 0.93 0.94 0.95 0.96 0.97 0.97 0.98 0.98 双指数脉冲 检测概率/% 0.5 4.5 5.5 10.0 23.5 51.0 67.5 87.5 95.5 100 100 波形相似度 r 0.67 0.71 0.74 0.78 0.81 0.84 0.86 0.88 0.90 0.91 0.92 高斯导数脉冲 检测概率/% 37.5 55.0 73.0 86.5 94.0 99.5 100 100 100 100 100 波形相似度 r 0.85 0.87 0.88 0.89 0.90 0.91 0.92 0.92 0.93 0.93 0.93
Table 4.
Estimation results of pulse signals amplitude
脉冲信号幅值估计结果
View tableView in ArticleTable 4.
Estimation results of pulse signals amplitude
脉冲信号幅值估计结果
脉冲类型 输入信噪比/dB –16 –15 –14 –13 –12 –11 –10 方波 真实值 — 0.1125 0.1262 0.1416 0.1589 0.1783 0.2000 估计值 — 0.1114 0.1304 0.1375 0.1641 0.1761 0.1943 误差/% — –0.98 3.34 –2.90 3.29 –1.24 –2.85 MSE/10–4 — 1.26 1.43 0.75 2.04 1.23 2.49 双指数脉冲 真实值 — — — — 0.1589 0.1783 0.2000 估计值 — — — — 0.1586 0.1773 0.2032 误差/% — — — — –0.16 –0.55 1.62 MSE/10–4 — — — — 2.79 6.43 5.03 高斯导数脉冲 真实值 0.1002 0.1125 0.1262 0.1416 0.1589 0.1783 0.2000 估计值 0.1039 0.1180 0.1297 0.1423 0.1595 0.1807 0.1960 误差/% 3.74 4.93 2.78 0.52 0.41 1.35 –2.02 MSE/10–4 0.29 0.89 0.79 1.60 0.82 1.46 0.71
Table 5.
Estimation results of pulse signals width
脉冲信号宽度估计结果
View tableView in ArticleTable 5.
Estimation results of pulse signals width
脉冲信号宽度估计结果
脉冲类型 输入信噪比/dB –16 –15 –14 –13 –12 –11 –10 方波 真实值/s — 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 估计值/s — 1.0011 0.9988 0.9941 0.9984 0.9972 0.9986 误差/% — 0.11 –0.12 –0.59 –0.16 –0.28 –0.14 MSE/10–4 — 1.40 1.11 0.57 0.13 0.56 0.45 双指数脉冲 真实值/ ${\text{μ}}{\rm s}$ — — — — 25 25 25 估计值/ ${\text{μ}}{\rm s}$ — — — — 25.22 24.79 24.68 误差/% — — — — 0.89 –0.84 –1.27 MSE — — — — 15.8 3.8 7.7 高斯导数脉冲 真实值/ ${\text{μ}}{\rm s}$ 1.45 1.45 1.45 1.45 1.45 1.45 1.45 估计值/ ${\text{μ}}{\rm s}$ 1.38 1.52 1.52 1.47 1.48 1.52 1.46 误差/% –5.02 4.99 4.61 1.43 2.37 4.49 0.34 MSE 0.011 0.023 0.017 0.032 0.024 0.003 0.012
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Bao-Feng Cao, Peng Li, Xiao-Qiang Li, Xue-Qin Zhang, Wang-Shi Ning, Rui Liang, Xin Li, Miao Hu, Yi Zheng.
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Received: Oct. 16, 2018
Accepted: --
Published Online: Oct. 29, 2019
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