College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, People's Republic of China.
Institute of Complexity Science, Qingdao University, Qingdao 266071, People's Republic of China.
Philos Trans A Math Phys Eng Sci. 2021 Mar 8;379(2192):20200235. doi: 10.1098/rsta.2020.0235. Epub 2021 Jan 18.
Vibrational resonance (VR) intentionally applies high-frequency periodic vibrations to a nonlinear system, in order to obtain enhanced efficiency for a number of information processing tasks. Note that VR is analogous to stochastic resonance where enhanced processing is sought via purposeful addition of a random noise instead of deterministic high-frequency vibrations. Comparatively, due to its ease of implementation, VR provides a valuable approach for nonlinear signal processing, through detailed modalities that are still under investigation. In this paper, VR is investigated in arrays of nonlinear processing devices, where a range of high-frequency sinusoidal vibrations of the same amplitude at different frequencies are injected and shown capable of enhancing the efficiency for estimating unknown signal parameters or for detecting weak signals in noise. In addition, it is observed that high-frequency vibrations with differing frequencies can be considered, at the sampling times, as independent random variables. This property allows us here to develop a probabilistic analysis-much like in stochastic resonance-and to obtain a theoretical basis for the VR effect and its optimization for signal processing. These results provide additional insight for controlling the capabilities of VR for nonlinear signal processing. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
振动共振（VR）有意向非线性系统施加高频周期性振动，以提高许多信息处理任务的效率。请注意，VR 类似于随机共振，通过有目的地添加随机噪声而不是确定性高频振动来寻求增强的处理。相比之下，由于其易于实现，VR 通过仍在研究中的详细模式为非线性信号处理提供了一种有价值的方法。在本文中，VR 在非线性处理设备的阵列中进行了研究，其中注入了一系列幅度相同但频率不同的高频正弦振动，并证明能够提高估计未知信号参数或检测噪声中弱信号的效率。此外，观察到不同频率的高频振动在采样时间可以被视为独立的随机变量。该属性允许我们在这里进行概率分析——类似于随机共振——并为 VR 效应及其优化提供信号处理的理论基础。这些结果为控制 VR 进行非线性信号处理的能力提供了更多的见解。本文是主题为“驱动非线性系统中的振动和随机共振（第 1 部分）”的一部分。
