The Lifting Scheme Based on the Second Generation Wavelets

The lifting scheme is a custom design construclion of Biorthogonal wavelets, a fast and efficient method to realize wavelet transform,which provides a wider range of application and efficiently reduces the computing time with its particular frame. This paper aims at introducing the second generation wavelets, begins with traditional Mallat algorithms, illustrates the lifting scheme and brings out the detail steps in the construction of Biorthogonal wavelets. Because of isolating the degrees of freedom remaining the biorthogonality relations, we can fully control over the lifting operators to design the wavelet for a particular application, such as increasing the number of the vanishing moments.

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.

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.

Second Generation Wavelet Finite Element and Rotor Cracks Quantitative Identification Method

The presence of cracks in the rotor is one of the most dangerous and critical defects for rotating machinery. Defect of fatigue cracks may lead to long out-of-service periods, heavy damages of machines and severe economic consequences. With the method of finite element, vibration behavior of cracked rotors and crack detection was received considerable attention in the academic and engineering field. Various researchers studied the response of a cracked rotor and most of them are focused on the crack detection based on vibration behavior of cracked rotors. But it is often difficult to identify the crack parameters quantitatively. Second generation wavelets （SGW） finite element has good ability in modal analysis for singularity problems like a cracked rotor. Based on the fact that the feature of SGW could be designed depending on applications, a multiresolution finite element method is presented. The new model of SGW beam element is constructed. The first three natural frequencies of the rotor with different crack location and size were solved with SGW beam elements, and the database for crack diagnosis is obtained. The first three metrical natural frequencies are employed as inputs of the database and the intersection of the three frequencies contour lines predicted the normalized crack location and size. With the Bently RK4 rotor test rig, rotors with different crack location and size are tested and diagnosed. The experimental results denote the cracks quantitative identification method has higher identification precision. With SGW finite element method, a novel method is presented that has higher precision and faster computing speed to identify the crack location and size.

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.

An Improved Algorithm for Image Edge Detection Based on Lifting Scheme

Wavelet transform is an ideal way for edge detection because of its multi-scale property, localization both in time and frequency domain, sensitivity to the abrupt change of signals, and so on. An improved algorithm for image edge detection based on Lifting Scheme is proposed in this paper. The simulation results show that our improved method can better reflect edge information of images.

A Study on Wavelet Data Compression of a Real-Time Monitoring System for Large Hydraulic Machines

The general concept of data compression consists in removing the redundancy existing in data to find a more compact representation. This paper is concerned with a new method of compression using the second generation wavelets based on the lifting scheme, which is a simple but powerful wavelet construction method. It has been proved by its successful application to a real-time monitoring system of large hydraulic machines that it is a promising compression method.

A New OFDM System Based on Lifting Wavelet Transform for Wireless Channel

It is well known that the Orthogonal Frequency Division Multiplexing （ OFDM ） system has a high ability to overcome the effect of multipath and can obtain high spectral efficiency in the wireless communication channel. However, avoid Interchannel Interference （ICI） and Intersymbol Interference （ISI） in wireless channel, a guard interval longer than channel delay is used in conventional OFDM system, which cause the efficiency of bandwidth usage reduced. Due to the superior spectral containment of wavelets, this paper proposed a new OFDM system based on Lifting Wavelet Transform （LWT-OFDM）, which adopts lifting wavelet transform to replace the conventional Fourier transform. This new OFDM system doesn＇t need the Cyclic Prefix （CP） so its structure is more simply than FFT-OFDM and its algorithm is as simply as FFT-OFDM. The new LWT-OFDM system can mitigates some disadvantages of FFT-OFDM system, such as a relatively large peak-to-average power ratio, more sensitive to carrier frequency offset and phase noise. Simulations show that the LWT-OFDM system is more effective and attractive than conversional FFT-OFDM in wireless channel.