Phase Dependent and Independent Frequency Identification of Weak Signals Based on Duffing Oscillator via Particle Swarm Optimization

In detecting weak signals based on the Duffing oscillator, it is usually assumed that the frequency is known, which is not always the case. This paper studies the problem of detecting the frequency of the to-be-detected weak signal based on the Duffing oscillator. For this purpose, the variance of the Duffing oscillator’s output is exploited, which has the property of multi-extremum single-maximum (MESM) distribution with the frequency of the periodic signal. The impact of signal’s phase on the MESM distribution is discussed. When the signal’s phase is known, the frequency of the signal can be directly identified as that with the maximal variance, which leads to a nonlinear optimization problem that can be solved by a particle swarm optimization (PSO) algorithm. When the phase is unknown, the π/2-phase-shift method is to be exploited integrated with a PSO algorithm. It is shown that the frequency can be precisely and efficiently identified by this method, whose effectiveness is verified by simulation results in Matlab.