Periodic‐phase‐diagram similarity method for weak signal detection

The periodic‐phase‐diagram similarity method is proposed to identify the frequency of weak harmonic signals. The key technology is to find a set of optimal coefficients for Duffing system, which leads to the periodic motion under the influence of weak signal and strong noise. Introducing the phase diagram similarity, the influences of strong noise on the similarity of periodic phase diagram are discussed. The principle of highest similarity of periodic phase diagram with the same frequency is detected by discussing the persistence of similarity of periodic motion phase diagram under the strong noise and the periodic‐phase‐diagram similarity method is constructed. The weak signals of early fault and strong noise are input into Duffing system to obtain the identified system. The stochastic subharmonic Melnikov method is extended to obtain the conditions of the optimal coefficients for the identified system. Based on the results, the constructed frequency conversion harmonic weak signals are considered to form a datum periodic system. With the change of frequency in the datum periodic system, the phase diagram similarity of the two constructed systems can be calculated. Based on the periodic‐phase‐diagram similarity method, the frequency of weak harmonic signals can be identified by the principle of highest similarity of periodic phase diagram with the same frequency. The results of numerical simulation and the early fault diagnosis results of actual bearings verify the feasibility of the periodic‐phase‐diagram similarity method. The accuracy of the detection effect is 97%, and the minimum signal‐to‐noise ratio is −80.71 dB.