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The vibration signals of bearings and gears measured from rotating machinery usually have nonlinear, nonstationary characteristics. The local projection algorithm cannot only reduce the noise of the nonlinear system, but can also preserve the nonlinear deterministic structure of the signal. The influence of centroid selection on the performance of noise reduction methods is analyzed, and the multiscale local projection method of centroid was proposed in this paper. This method considers both the geometrical shape and statistical error of the signal in high dimensional phase space, which can effectively eliminate the noise and preserve the complete geometric structure of the attractors. The diagonal slice spectrum can identify the frequency components of quadratic phase coupling and enlarge the coupled frequency component in the nonlinear signal. Therefore, the proposed method based on the above two algorithms can achieve more accurate results of fault diagnosis of gears and rolling bearings. The simulated signal is used to verify its effectiveness in a numerical simulation. Then, the proposed method is conducted for fault diagnosis of gears and rolling bearings in application researches. The fault characteristics of faulty bearings and gears can be extracted successfully in the researches. The experimental results indicate the effectiveness of the novel proposed method.

In our model, firstly, we predict the residence of the offender based on the locations of the last crime scenes with three methods (distance analysis: the location that has the shortest distance to each crime site, circle fitting, probability theory); secondly, we predict the time of the next crime based on previous data with the method of fitting a straight line; next, we predict the location of the next crime based on the locations of the last crime scenes and the time predicted in the second step with the method of weighted average; finally, we generate a predicted location based on the three predicted locations with the method of weighted average.