Harmonic Wavelet With Applications In Machinery Fault Diagnosis

The existed methods of analyzing signals are imperfect in the aspect of detailed analysis on high frequency and the analysis on non-stationary and singularity signals. Therefore, it is necessary to develop new method of analyzing signals for extracting fault characteristic efficiently. The harmonic wavelet analysis discussed in this dissertation is one of this these new methods.With the launching on the spectrum of wavelet, the harmonic wavelet is structured, which has strict box-like spectrum and simple function expression. Through strict mathematic deducing, the dyadic fast algorithm of harmonic wavelet based on FFT is gained. According to the harmonic wavelet coefficients calculated by the above algorithm and Parseval theorem, the harmonic wavelet time-frequency grid plot, contour plot and profile plot are developed. By applying dyadic harmonic wavelet to analyze the fault gears' signals of some test-bed, on the basis of harmonic wavelet time-frequency grid plot, the contour plot and profile plot are constructed, the periodic impacting signals of breaking gear are diagnosed successfully, which proves that dyadic harmonic wavelet has great capacity of extracting characteristic signals.Dyadic harmonic wavelet is extended to generalized harmonic wavelet, which can select random frequency band as analyzing frequency band. Based on this advantage of generalized harmonic wavelet, we can do harmonic wavelet package analysis, the high frequency band and low frequency band of the signals can be both analyzed on the same high resolution. The analysis on a simulating signal by harmonic wavelet package proves that the algorithm of harmonic wavelet package is right and valid. By applying generalized harmonic to purify unbalanced axis orbit signals collected from some test-bed, the filtered axis orbit is obvious ellipse, which demonstrated that generalized harmonic wavelet has good filtering effect.The algorithm of generalized harmonic wavelet provides a way to compute the decomposition coefficients of wavelets with predetermined level parameters. How to select the level parameters (frequency band) and hence the wavelets however remains a problem. The adaptive harmonic wavelet transformation (AHWT) this dissertation proposed does the selection adaptively and overcomes the shortcomings effectively. By applying AHWT to analyze the fault gears' signals of some test-bed, the results prove that AHWT has a high frequency resolution and great capacity of extracting characteristic signals.