Weak Signal Recognition Based On Holmes-Duffing Oscillator

Rotating machinery equipment failure will affect the performance of machinery and equipment,and even cause serious consequences.However,the early fault signal is very weak,so the detection of weak signal is very important.Due to the early weak signal is submerged in the huge noise,so the noise problem has become a major obstacle in weak signal detection.The weak signal detection is carried out by suppressing the noise.The noise is suppressed and the weak signal is lost.Weak signal detection based on nonlinear dynamics can be carried out without suppressing the weak signal,so it becomes an important method.This article is arranged as follows:Firstly,the detection principle of weak signal based on Duffing equation is described.Secondly,because of the sensitivity of the Duffing equation to the initial value,the choice of parameters has a great influence on the detection results.At present,the weak signal is detected by Duffing equation.In view of this situation,the influence of the parameters on the weak signal detection is analyzed,and a set of better detection parameters is determined.In addition,the detection of weak signal is mostly suitable for the signal with a certain frequency,the efficiency is low,and the influence of the initial phase of the signal to be detected is ignored.In view of this situation,this paper presents a new method,which combines high efficiency and high precision blind domain elimination method with variable metric method.A set of parameters is used to analyze the effect of the initial phase on the detection effect.The results show that the proposed method is more accurate and more efficient than the previous methods.Finally,the Duffing equation is used to find the threshold of chaos by the change of phase diagram.Merlin Melnikov function is one of the analytical method for chaos threshold.The key of the problem lies in solving Melnikov function.In this paper,using the Melnikov method solved the Melnikov function in Duffing equation.