Improved Variable Scale-Convex-Peak Method for Weak Signal Detection

Based on the rectification of detectable domain method and elimination of blind domain method, the variable scale-convex-peak method for the identification frequency of weak signal is improved. For the initial phase of weak signal to be detected, the analytic expression of chaotic threshold is obtained by using stochastic Melnikov method. The influence of phase on chaotic threshold is clarified, which leads to that the frequency of weak signal can be identified. Specifically, the initial phase in a period is divided into the detectable domain and the blind domain. In the detectable domain, when the frequency identification deviates, the rectification of detectable domain method is introduced. Specifically, the Newton interpolation method is used to give the calculation formula to rectify the deviation, which improves the accuracy of frequency identification. In the blind domain, the elimination of blind domain method is given by constructing the detection equations. The feasibility of the improved variable scale-convex-peak method is verified by numerical simulation and circuit experiment. Furthermore, by comparing the identified frequency value with the theoretical fault frequency value, the fault location of the wheelset bearing of high-speed train is determined. The improved variable scale-convex-peak method is applied when the initial phase is in the frequency detectable domain or the blind domain, respectively. The accuracy of the detection effect can be 96.69%, and the minimum signal-to-noise ratio(SNR) can be - 50.8757dB.