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Pulse signal detection is widely used in nuclear explosion electromagnetic pulse detection, lightning signal detection, power system partial discharge detection, electrostatic discharge detection, and other fields. The signal strength becomes weak with the increase of the detection distance and may be submerged in strong Gaussian noise for remote detection. Therefore, the detection and recovery of the weak signals, especially the weak pulse signals, have important applications in signal processing area. Some methods have been reported to detect and estimate weak pulse signals in strong background noise. Coupled Duffing oscillators are usually used in processing periodic signals, though it is still in an exploration stage for aperiodic transient signals. There remain some problems to be solved, for example, the system performance depends on some initial values, results are valid only for the period-doubling bifurcation state, the waveform time domain information cannot be accurately estimated, etc. In this paper, we explain the reasons why there exist these inherent defects in the current weakly coupled Duffing oscillators. In order to solve the above-mentioned problems, a new signal detection and recovery model is constructed, which is characterized by coupling the restoring force and damping force of the two oscillators simultaneously. A large coupling coefficient is applied to the two Duffing oscillators, and a generalized " in-well out-of-synchronization”phenomenon arises between the oscillators which conduces to detecting and recovering the weak pulse signals, and also overcoming the defects mentioned above. Using the metrics of signal-to-noise ratio improvement (SNRI) and waveform similarity, the effects of amplitude and period of periodic driving force, coupling coefficient, step size and damping coefficient on signal detection and waveform recovery are studied. Finally, experiments are performed to detect and recover the following three kinds of pulses: square wave pulses, double exponential pulses, and Gaussian derivative pulses. The input SNR thresholds of these three waveforms are –15, –12, and –16 dB, respectively, under the detection probabilities and waveform similarity all being greater than 0.9 simultaneously. The maximum error of the pulse amplitude and pulse width are both less than 5% of their corresponding true values. In summary, the strongly coupled Duffing system has advantages of being able to operate in any phase-space state and being no longer limited by the initial values. Especially, the time domain waveform of weak pulse signals can be well recovered in the low SNR case, and the error and the minimum mean square error are both very low.
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Keywords:
- weak pulse signal/
- strongly coupled Duffing oscillators/
- signal detection/
- parameter estimation
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] -
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 
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脉冲类型 波形时域特征 Duffing振子参数 方波 上升时间0.1 ms $\omega = 50$ rad/s 半高宽1 s 计算步长0.1 ms 双指数脉冲 上升时间3 ${\text{μs}}$ $\omega = 5 \times {10^5}$ rad/s 半高宽25 ${\text{μs}}$ 计算步长10 ns 高斯导数脉冲 上升时间1.5 ${\text{μs}}$ $\omega = 4 \times {10^6}$ rad/s 峰峰宽1.45 ${\text{μs}}$ 计算步长1 ns DownLoad:
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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 DownLoad:
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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 DownLoad:
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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 DownLoad:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
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