NEW METHOD FOR WEAK FAULT FEATURE EXTRACTION BASED ON SECOND GENERATION WAVELET TRANSFORM AND ITS APPLICATION

A new time-domain analysis method that uses second generation wavelettransform (SGWT) for weak fault feature extraction is proposed. To extract incipient fault feature,a biorthogonal wavelet with the characteristics of impact is constructed by using SGWT. Processingdetail signal of SGWT with a sliding window devised on the basis of rotating operation cycle, andextracting modulus maximum from each window, fault features in time-domain are highlighted. To makefurther analysis on the reason of the fault, wavelet package transform based on SGWT is used toprocess vibration data again. Calculating the energy of each frequency-band, the energy distributionfeatures of the signal are attained. Then taking account of the fault features and the energydistribution, the reason of the fault is worked out. An early impact-rub fault caused by axismisalignment and rotor imbalance is successfully detected by using this method in an oil refinery.

SAR image despeckling based on edge detection and nonsubsampled second generation bandelets

To preserve the sharp features and details of the synthetic aperture radar （SAR） image effectively when despeckling, a despeckling algorithm with edge detection in nonsubsampled second generation bandelet transform （NSBT） domain is proposed. First, the Canny operator is utilized to detect and remove edges from the SAR image. Then the NSBT which has an optimal approximation to the edges of images and a hard thresholding rule are used to approximate the details while despeckling the edge-removed image. Finally, the removed edges are added to the reconstructed image. As the edges axe detected and protected, and the NSBT is used, the proposed algorithm reaches the state-of-the-art effect which realizes both despeckling and preserving edges and details simultaneously. Experimental results show that both the subjective visual effect and the mainly objective performance indexes of the proposed algorithm outperform that of both Bayesian wavelet shrinkage with edge detection and Bayesian least square-Gaussian scale mixture （BLS-GSM）.

Adaptive Wavelets Based on Second Generation Wavelet Transform and Their Applications to Trend Analysis and Prediction

In order to make trend analysis and prediction to acquisition data in amechanical equipment condition monitoring system, a new method of trend feature extraction andprediction of acquisition data is proposed which constructs an adaptive wavelet on the acquisitiondata by means of second generation wavelet transform ( SGWT), Firstly, taking the vanishing momentnumber of the predictor as a constraint, the linear predictor and updater are designed according tothe acquisition data by using symmetrical interpolating scheme. Then the trend of the data isobtained through doing SGWT decomposition , threshold processing and SGWT reconstruction. Secondly,under the constraint of the vanishing moment number of the predictor, another predictor based on theacquisition data is devised to predict the future trend of the data using a non-symmetricalinterpolating scheme, A one-step prediction algorithm is presented to predict the future evolutiontrend with historical data. The proposed method obtained a desirable effect in peak-to-peak valuetrend analysis for a machine set in an oil refinery.

Extension of covariant derivative(Ⅲ): From classical gradient to shape gradient

This paper further extends the generalized covari ant derivative from the first covariant derivative to the sec ond one on curved surfaces. Through the linear transforma tion between the first generalized covariant derivative and the second one, the second covariant differential transformation group is set up. Under this transformation group, the sec ond class of differential invariants and integral invariants on curved surfaces is made clear. Besides, the symmetric struc ture of the tensor analysis on curved surfaces are revealed.

Feature Extraction of Bearing Vibration Signals Using Second Generation Wavelet and Spline-Based Local Mean Decomposition

In order to extract the fault feature frequency of weak bearing signals,we put forward a local mean decomposition(LMD)method combining with the second generation wavelet transform.After performing the second generation wavelet denoising,the spline-based LMD is used to decompose the high-frequency detail signals of the second generation wavelet signals into a number of production functions(PFs).Power spectrum analysis is applied to the PFs to detect bearing fault information and identify the fault patterns.Application in inner and outer race fault diagnosis of rolling bearing shows that the method can extract the vibration features of rolling bearing fault.This method is suitable for extracting the fault characteristics of the weak fault signals in strong noise.