Automated weak signal frequency estimation method based on Duffing oscillator and particle swarm optimization

Abstract

The frequency of a weak signal is used for fault diagnosis and target identification in various fields. By introducing particle swarm optimization (PSO) and spectral entropy (SE), an automated weak signal frequency estimation method based on the Duffing oscillator is proposed. The proposed method uses the differential structure to enhance the timing difference of the Duffing oscillator between the chaotic and large-scale periodic states, which is quantitatively distinguished by SE. Then, the frequency of the internal driving force is adaptively adjusted by the PSO to allow the SE to reach a minimum value where the driving frequency equals the weak signal frequency. A group of weak signals with different frequencies has been tested. The maximum relative frequency error is only 0.68%. Unlike other chaotic oscillator-based frequency estimation methods, the proposed method does not need to determine the phase state manually. A rough initial frequency search range is sufficient for automatic frequency measurement of the proposed method in this paper.

A new rolling bearing fault diagnoses method based on period-doubling bifurcation in the Hindmarsh–Rose model

“…The Jacobian matrix for a comprehensive mapping is presented in equation (19). The overall Jacobian matrix can be derived by multiplying the respective Jacobian matrices, as depicted in equation ( 20)…”

“…Han et al conducted composite fault diagnosis of wind turbine spindle bearings by integrating Teager energy operators with second-order random resonance [18]. Wang et al introduced a particle swarm optimization algorithm with spectral entropy to avoid the need for manual phase determination while utilizing Duffing oscillators for detecting weak signals [19]. Ai et al extended the classical stochastic resonance model to a two-well stochastic resonance model where the barrier height can be controlled directly by parameters.…”