The Wavelet Analysis And Its Application In Fault Diagnosis Of Gear Box

As a fast delveloping signal processing algorithm, the wavelet transform has been widelyused in many areas such as fault diagnosis successfully. In order to improve its accuracy, anew method is presented in this paper. For improving the accuracy of the threshold in thewavelet threshold denoising algorithm, a new algorithm based on coefficients correction isproposed. An algorithm used to extract the stationary modulation component and the impactcomponent in the signal is presented to improve the accuracy of fault diagnosis.By analyzing the characteristic of the wavelet filter, the cause of the distortion isdetermined. A new method is presented to rectify the distortion and improve the accuracy. Inthis method, a splitting operator is used to split the convolution results into two parts beforedown-sampling, which are processed by an imported transferring factor to the same frequencyband so that they can be added directly. By this, the coefficients are corrected. Theoretically,the maximum error could be reduced from50%to25%with one time compensationcalculation. The influences of the correcting times on the accuracy and the complexity of thealgorithm are analyzed. The results show that with two and four times compensationcalculations, the error is reduced to10%and2%respectively. The influence of the vanishingmoment is analyzed. The result shows that increasing the vanishing moment can effectivelyimprove the coefficient accuracy of the components far from the cutoff frequency. For thecomponents near the cutoff frequency, the effect is limited. The experiment result of thevibration signal of a roller bearing with outer ring fault shows that the proposed method caneffectively magnify the amplitude of the fault frequencies in practice.An improved wavelet threshold denoising algorithm is proposed based on the coefficientcorrecting method. In this algorithm, the wavelet transform coefficients are corrected by usingthe complementary characteristic of wavelet filters, then the threshold is calculated and usedfor denosing. The proposed algorithm is used to process the Bumps and Heavy Sine signals ofdifferent SNR by using the soft and hard threshold functions. The results show that theimproved wavelet threshold denosing algorithm can effectively preserve the singularity of theoriginal signal. Compared with the results gotten by the standard wavelet threshold denoisingalgorithm, the maximum of the SNR is increased by3dB and the minimum is0.2dB. Theexperiment result shows that the improved method can suppress the noise and extract theuseful characteristic components effectively.A method for extracting the characteristic signals based on the inner product and wavelet isproposed. In this algorithm, the amplitude modulation signal and the real part of the Laplace wavelet are used as the basis functions of stationary modulation and impact modulation. Thechoices of basis functions have a clear physical meaning. The parameters of the stationarymodulation basis are determined by the frequency distribution of the signal. The naturalfrequency and the damping parameters are determined by using the Laplace wavelet filteringalgorithm. By doing this, the operation efficiency of the algorithm can be greatly improved.By determined the base functions according to the correlation between the signal and the basisfunctions, the signal is decomposed into different parts. The result of two kinds of simulationsignals and the transmission vibration signal show the algorithm can extract the twomodulation signals accurately.