A fractional hilbert transform order optimization algorithm based de for bearing health monitoring

Bearings are widely used in various industries, especially in emerging industries such as un-manned aerial vehicles and so on. However, the higher failure rate and maintenance cost of bearing have become the most intractable problems in these applications. Mechanical failures of bearing leads to abnormal vibration signal and therefore, its condition and damage could be monitored and evaluated by analyzing the vibration signal. Fast Fourier transform (FFT) method can be used in the spectrum analysis of envelope signals, which could only give the global energy-frequency distributions and fail to reflect the details of a signal. So it is hard to analyze a signal effectively when the fault signal is weaker than the interfering signal. At present, the Hilbert Transform (HT) based envelope analysis has been widely used in bearing fault diagnosis and it could effectively extract envelope of the rolling element fault vibration signal. As a generalization of the HT, the Fractional Hilbert Transform (FHT) is defined in the frequency-domain based upon the modification of spatial filter with a fractional parameter, and it can be used to construct a new kind of fractional analytic signal. FHT can obtain more information than other analysis methods with the gained benefit directly affected by the selection of the fractional order. Unfortunately, it is rather difficult to fmd the best order of FHT. In this paper, an automated method is proposed to fmd the optimal order using Differential Evolution (DE) algorithm. DE is a simple and efficient evolutionary algorithm for global optimization, and has shown significant success in solving different numerical optimization problems. It is seen as a continuous optimization problem to search the optimal order of FHT. When weak faults occur on a bearing, some of the characteristic frequencies could clearly show by analyzing vibration signal with the optimal order of FHT. These characteristic frequencies can be used for bearing weak fault feature extraction. The effectiveness of the proposed method is verified through simulation and experiment data.