Vibrational resonance by using a real-time scale transformation method

Abstract

Vibrational resonance (VR) shows great advantages in signal enhancement. Nonlinear frequency modulated (NLFM) signals widely exist in various fields，so it is of great significance to enhance a NLFM signal. However, for the complex NLFM signal, where its instantaneous frequency of the signal varies nonlinearly, the traditional VR method is no longer applicable. To solve this problem, a rescaled VR method by a real-time scale transformation method is proposed. Its basic principle is to use the real-time scale coefficient and auxiliary signal parameters to match a NLFM signal in a nonlinear system. The corresponding numerical simulation is carried out to process three kinds of typical NLFM signals. The results manifest the excellent performance of the proposed method for the signal enhancement of NLFM signals. The method can process NLFM signals with an arbitrary frequency variation. Consequently, it has certain theoretical and practical values in some fields.

Discover an accurate approximation of dynamical system without prior information and customized design

“…Over the past century, scholars have been trying to explore dynamic constraints and balance from data, which aims to achieve accurate prediction [1,2], including the motions of celestial bodies, the moving of mechanics, and the change in the weather. Constructing the dynamical systems is crucial to reveal the nature of the system [1,3,4].…”

“…The system is interpretable and includes primary characteristics [4]. Predictions of various characteristics approximately achieve under a variety of conditions [2,[6][7][8][9]. However, designing targeted methods for different problems takes time and effort and is extremely difficult in many cases [10].…”