The work presented here provides the guidelines and results for designing and implementing a highly sensitive modified Van der Pol – Duffing oscillator with a trigonometric damping function (VTD). This VTD can exhibit periodic and quasi-chaotic behavior necessary for application in weak signal detection. Here, we present two proposals: (1) A method based on a quasi-chaotic intermittent array (ANLIOA), whose all VTD parameters are calculated and fine-tuned toward a critical state between chaotic and periodic state through a Lyapunov exponent procedure, and (2) A method based on a single oscillator in an adaptive stopping oscillation system (ANLSOS), where VTD is established within an oscillatory regime. Both systems can detect non-stationary signals while reconstructing the time-frequency spectrogram in high resolution within severe noise conditions. The systems were adapted for the detection of a synthesized Doppler signal corresponding to the blood flow velocity profile from an artery. Comparative results using typical oscillators such as Duffing or Van der Pol demonstrate the superiority of the VTD oscillator in detection when used for both methods, whose mean absolute percentage error reached around 6% for a signal-to-noise ratio (SNR) of −10 dB. Furthermore, compared to other time-frequency methods, ANLIOA and ANLSOS promise high precision in detecting Doppler signals with low rates of frequency changes while minimizing energy emission and avoiding possible bio-thermal effects.

中文翻译：

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基于非Liènard振荡器的自适应多普勒生物信号检测器和时频表示

这里介绍的工作为设计和实现具有三角阻尼函数 (VTD) 的高度灵敏的改进型范德波尔-杜芬振荡器提供了指南和结果。该 VTD 可以表现出弱信号检测应用所需的周期性和准混沌行为。在这里，我们提出了两个建议：（1）基于准混沌间歇阵列（ANLIOA）的方法，其所有 VTD 参数都通过 Lyapunov 指数过程计算并微调到混沌状态和周期状态之间的临界状态，以及(2) 一种基于自适应停止振荡系统 (ANLSOS) 中的单个振荡器的方法，其中 VTD 是在振荡范围内建立的。两种系统都可以检测非平稳信号，同时在严重噪声条件下以高分辨率重建时频频谱图。该系统适用于检测与动脉血流速度分布相对应的合成多普勒信号。使用 Duffing 或 Van der Pol 等典型振荡器的比较结果表明，两种方法均使用 VTD 振荡器在检测方面的优越性，在信噪比 (SNR) 为 -10 的情况下，其平均绝对百分比误差达到 6% 左右D b。此外，与其他时频方法相比，ANLIOA 和 ANLSOS 能够以低频率变化率检测多普勒信号，同时最大限度地减少能量排放并避免可能的生物热效应。