Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

A novel method for gamma spectrum analysis of low-level and intermediate-level radioactive waste

The uncertainty of nuclide libraries in the analysis of the gamma spectra of low-and intermediate-level radioactive waste(LILW)using existing methods produces unstable results.To address this problem,a novel spectral analysis method is proposed in this study.In this method,overlapping peaks are located using a continuous wavelet transform.An improved quadratic convolution method is proposed to calculate the widths of the peaks and establish a fourth-order filter model to estimate the Compton edge baseline with the overlapping peaks.Combined with the adaptive sensitive nonlinear iterative peak,this method can effectively subtracts the background.Finally,a function describing the peak shape as a filter is used to deconvolve the energy spectrum to achieve accurate qualitative and quantitative analyses of the nuclide without the aid of a nuclide library.Gamma spectrum acquisition experiments for standard point sources of Cs-137 and Eu-152,a segmented gamma scanning experiment for a 200 L standard drum,and a Monte Carlo simulation experiment for triple overlapping peaks using the closest energy of three typical LILW nuclides(Sb-125,Sb-124,and Cs-134)are conducted.The results of the experiments indicate that(1)the novel method and gamma vision(GV)with an accurate nuclide library have the same spectral analysis capability,and the peak area calculation error is less than 4%;(2)compared with the GV,the analysis results of the novel method are more stable;(3)the novel method can be applied to the activity measurement of LILW,and the error of the activity reconstruction at the equivalent radius is 2.4%;and(4)The proposed novel method can quantitatively analyze all nuclides in LILW without a nuclide library.This novel method can improve the accuracy and precision of LILW measurements,provide key technical support for the reasonable disposal of LILW,and ensure the safety of humans and the environment.

Research on Auto-detection for Remainder Particles of Aerospace Relay Based on Wavelet Analysis

Aerospace relay is one kind of electronic components which is used widely in national defense system and aerospace system. The existence of remainder particles induces the reliability declining, which has become a severe problem in the development of aerospace relay. Traditional particle impact noise detection （PIND） method for remainder detection is ineffective for small particles, due to its low precision and involvement of subjective factors. An auto-detection method for PIND output signals is proposed in this paper, which is based on direct wavelet de-noising （DWD）, cross-correlation analysis （CCA） and homo-filtering （HF）, the method enhances the affectivity of PIND test about the small particles. In the end, some practical PIND output signals are analysed, and the validity of this new method is proved.

Applications of Wavelet Analysis in Differential Propagation Phase Shift Data De-noising

Using numerical simulation data of the forward differential propagation shift （ΦDP） of polarimetric radar,the principle and performing steps of noise reduction by wavelet analysis are introduced in detail.Profiting from the multiscale analysis,various types of noises can be identified according to their characteristics in different scales,and suppressed in different resolutions by a penalty threshold strategy through which a fixed threshold value is applied,a default threshold strategy through which the threshold value is determined by the noise intensity,or a ΦDP penalty threshold strategy through which a special value is designed for ΦDP de-noising.Then,a hard-or soft-threshold function,depending on the de-noising purpose,is selected to reconstruct the signal.Combining the three noise suppression strategies and the two signal reconstruction functions,and without loss of generality,two schemes are presented to verify the de-noising effect by dbN wavelets：（1） the penalty threshold strategy with the soft threshold function scheme （PSS）; （2） the ΦDP penalty threshold strategy with the soft threshold function scheme （PPSS）.Furthermore,the wavelet de-noising is compared with the mean,median,Kalman,and finite impulse response （FIR） methods with simulation data and two actual cases.The results suggest that both of the two schemes perform well,especially when ΦDP data are simultaneously polluted by various scales and types of noises.A slight difference is that the PSS method can retain more detail,and the PPSS can smooth the signal more successfully.

Research on runoff variations based on wavelet analysis and wavelet neural network model： A case study of the Heihe River drainage basin （1944-2005）

The Heihe River drainage basin is one of the endangered ecological regions of China. The shortage of water resources is the bottleneck, which constrains the sustainable development of the region. Many scholars in China have done researches concerning this problem. Based on previous researches, this paper analyzed characteristics, tendencies, and causes of annual runoff variations in the Yingluo Gorge （1944-2005） and the Zhengyi Gorge （1954-2005）, which are the boundaries of the upper reaches, the middle reaches, and the lower reaches of the Heihe River drainage basin, by wavelet analysis, wavelet neural network model, and GIS spatial analysis. The results show that： （1） annual runoff variations of the Yingluo Gorge have principal periods of 7 years and 25 years, and its increasing rate is 1.04 m^3/s.10y; （2） annual runoff variations of the Zhengyi Gorge have principal periods of 6 years and 27 years, and its decreasing rate is 2.25 m^3/s.10y; （3） prediction results show that： during 2006-2015, annual runoff variations of the Yingluo and Zhengyi gorges have ascending tendencies, and the increasing rates are respectively 2.04 m^3/s.10y and 1.61 m^3/s.10y; （4） the increase of annual runoff in the Yingluo Gorge has causal relationship with increased temperature and precipitation in the upper reaches, and the decrease of annual runoff in the Zhengyi Gorge in the past decades was mainly caused by the increased human consumption of water resources in the middle researches. The study results will provide scientific basis for making rational use and allocation schemes of water resources in the Heihe River drainage basin.

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage, This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform （WPT）. The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum （WPES） has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

ELECTROCHEMICAL NOISE ANALYSIS OF PURE ALUMINUM IN SODIUM CHLORIDE SOLUTION WITH WAVELET TRANSFORM TECHNIQUE

Wavelet transforms (WT) are proposed as an alternative tool to overcome the limitations of Fourier transforms (FFT) in the analysis of electrochemical noise (EN) data. The most relevant feature of this method of analysis is its capability of decomposing electrochemical noise records into different sets of wavelet coefficients, which contain information about the time scale characteristic of the associated corrosion event. In this context, the potential noise fluctuations during the free corrosion of pure aluminum in sodium chloride solution was recorded and analyzed with wavelet transform technique. The typical results showed that the EN signal is composed of distinct type of events, which can be classified according to their scales, i.e. their time constants. Meanwhile, the energy distribution plot (EDP) can be used as 'fingerprints' of EN signals and can be very useful for analyzing EN data in the future.

Application of Wavelet Analysis toInterference Elimination for Geochemical Hydrocarbon Exploration

Interference in the data of geochemical hydrocarbon exploration is a large obstacle for anomaly recognition. The multiresolution analysis of wavelet analysis can extract the information at different scales so as to provide a powerful tool for information analysis and processing. Based on the analysis of the geometric nature of hydrocarbon anomalies and background, Mallat wavelet and symmetric border treatment are selected and data pre-processing (logarithm-normalization) is established. This approach provide good results in Shandong and Inner Mongolia, China. It is demonstrated that this approach overcome the disadvantage of backgound variation in the window (interference in window), used in moving average, frame filtering and spatial and scaling modeling methods.

SIGNAL FEATURE EXTRACTION BASED UPON INDEPENDENT COMPONENT ANALYSIS AND WAVELET TRANSFORM

It is an important precondition for machine fault diagnosis that vibrationsignal can be extracted effectively. Based on the characteristic of noise interfused during thecourse of sampling vibration signal, independent component analysis (ICA) method is combined withwavelet to de-noise. Firstly, The sampled signal can be separated with ICA, then the function offrequency band chosen with multi-resolution wavelet transform can be used to judge whether thestochastic disturbance singular signal is interfused. By these ways, the vibration signals can beextracted effectively, which provides favorable condition for subsequent feature detection ofvibration signal and fault diagnosis.

Wavelet analysis of coastal-trapped waves along the China coast generated by winter storms in 2008

This study applies the wavelet analysis to the tidal gauge records, alongshore winds, atmospheric temperature and pressure along the China coast in winter 2008. The analysis results show three events of sea level oscillations （SLOs） on the shelf induced by winter storms. The first event occurred from January 9 to 21. The SLO periods were double-peaked at 1.6-5.3 and 7.0-16.0 d with the power densities of 0.04-0.05 and 0.10-0.15 m^2.d, respectively. The second event occurred from February 5 to 18. The SLO period was single-peaked at 2.3-3.5 d with power density of 0.03-0.04 m^2.d. The third event occurred from February 20 to March 8. The SLO periods were double- peaked at 1.5-4.3 and 6.1-8.2 d with the power densities of 0.08-0.11 and 0.02-0.08 me.d, respectively. The SLOs propagated along the coast from Zhejiang in north to Guangdong in south. The phase speeds ranged about 9-29 m/s from Kanmen to Pingtan, 5-11 m/s from Xiamen to Huizhou and 11-22 m/s from Huizhou to Shuidong. The dispersion relation of the SLOs shows their nature of coastal-trapped wave.

Spectroscopic Leaf Level Detection of Powdery Mildew for Winter Wheat Using Continuous Wavelet Analysis

Powdery mildew （Blumeria graminis） is one of the most destructive crop diseases infecting winter wheat plants, and has devastated millions of hectares of farmlands in China. The objective of this study is to detect the disease damage of powdery mildew on leaf level by means of the hyperspectral measurements, particularly using the continuous wavelet analysis. In May 2010, the reflectance spectra and the biochemical properties were measured for 114 leaf samples with various disease severity degrees. A hyperspectral imaging system was also employed for obtaining detailed hyperspectral information of the normal and the pustule areas within one diseased leaf. Based on these spectra data, a continuous wavelet analysis （CWA） was carried out in conjunction with a correlation analysis, which generated a so-called correlation scalogram that summarizes the correlations between disease severity and the wavelet power at different wavelengths and decomposition scales. By using a thresholding approach, seven wavelet features were isolated for developing models in determining disease severity. In addition, 22 conventional spectral features （SFs） were also tested and compared with wavelet features for their efficiency in estimating disease severity. The multivariate linear regression （MLR） analysis and the partial least square regression （PLSR） analysis were adopted as training methods in model mildew on leaf level were found to be closely related with the development. The spectral characteristics of the powdery spectral characteristics of the pustule area and the content of chlorophyll. The wavelet features performed better than the conventional SFs in capturing this spectral change. Moreover, the regression model composed by seven wavelet features outperformed （R2=0.77, relative root mean square error RRMSE=0.28） the model composed by 14 optimal conventional SFs （R2---0.69, RRMSE--0.32） in estimating the disease severity. The PLSR method yielded a higher accuracy than the MLR method. A combination of CWA and PLSR was found to be promising in providing relatively accurate estimates of disease severity of powdery mildew on leaf level.

Wavelet analysis and its application to signal processing

The construction of basic wavelet was discussed and many basic analyzing wavelets was compared. Acomplex analyzing wavelet which is continuous, smoothing, orthogonal and exponential decreasing was presented, andit was used to decompose two blasting seismic signals with the continuous wavelet transforms (CWT). The resultshows that wavelet analysis is the better method to help us determine the essential factors which create damage effectsthan Fourier analysis.

Wavelet analysis method of harmonics and electromagnetic interference in coal mines

In this study we propose an analytical method based on orthogonal wavelet transforms for detecting harmonic noise and Electromagnetic Interference (EMI) from power supply systems and equipment in coal mines. The method will separate interference from signals through wavelet packet decomposition and then accomplish wavelet packet synthesis towards decomposition results after filtering, to remove harmonic noise and electromagnetic interference. Detailed simulation experiments are presented to study power harmonics and Electrical Fast Transient Burst (EFT/B) interference and to validate the effectiveness of our proposed method. The experimental results show that the proposed method, suitable for mutant and non-stationary signal detection, can accurately analyze harmonic interference and EMI in coal mines, as well as establish EMI source models and perform underground Electromagnetic Compatibility (EMC) prediction analyses.

SAR image denoising based on wavelet-fractal analysis

Wavelet-fractal based SAR （synthetic aperture radar） image processing is one of the advanced technologies in image processing. The main concept of analysis is that after wavelet transformation, multifractal spectrum of the signal is different from that of noise. This difference is used to alleviate the noise produced by SAR image.The method to denoise SAR image using the process based on wavelet-fractai analysis is discussed in detail. Essentially, the present method focuses on adjusting the Hoelder exponent α of multifractal spectrum. After simulation, α should be adjusted to 1.72-1.73. The more the value of α exceeds 1.73, the less distinctive the edges of SAR image become. According to the authors denoising is optimal at α=1.72-1.73. In other words, when α =1.72-1.73, a smooth and denoised SAR image is produced.

B-Spline Wavelet on Interval Finite Element Method for Static and Vibration Analysis of Stiffened Flexible Thin Plate

A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.

Wavelet analysis of ultrasonic A-scan signal of solid-state welded joints

In the ultrasonic nondestructive evaluation of the quality of solid state welded joints, such as friction bonding and diffusion bonding, the main difficulty is the identification of micro defects which are most likely to emerge in the welding process. The ultrasonic echo on the screen of a commercial ultrasonic detector due to a micro defect is so weak that it is completely masked by noise, and impossible to be pointed out. In the present paper, wavelet analysis (WA) is utilized to process A scan ultrasonic signals from weak bonding defects in friction bonding joints and porosity in diffusion bonding joints. First, perception of WA for engineers is given, which demonstrates the physical mechanism of WA when applied to signal processing. From this point of view, WA can be understood easily and more thoroughly. Then the signals from welding joints are decomposed into a time scale plane by means of WA. We notice that noise and the signal echo attributed to the micro defect occupy different scales, which make it possible to enhance the signal to noise ratio of the signals by proper selection and threshold processing of the time scale components of the signals, followed by reconstruction of the processed components.

Ultrasonic C-scan Detection for Stainless Steel Spot Welding Based on Wavelet Package Analysis

An ultrasonic test of spot welding for stainless steel is conducted. Based on wavelet packet decomposition, the ultrasonic echo signal has been analyzed deeply in time - frequency domain, which can easily distinguish the nugget from the corona bond. The 2D C-scan images produced by ultrasonic C scan which contribute to quantitatively calculate the nugget diameter for the computer are further analyzed. The spot welding nugget diameter can be automatically obtained by image enhancement, edge detection and equivalent diameter algorithm procedure. The ultrasonic detection values in this paper show good agreement with the metallographic measured values. The mean value of normal distribution curve is 0.006 67, and the standard deviation is 0.087 11. Ultrasonic C-scan test based on wavelet packet signal analysis is of high accuracy and stability.

THEORY AND APPLICATION OF WAVELET ANALYSIS INSTRUMENT LIBRARY

Some new theory and algorithms on wavelet analysis are proposed, including continuous wavelet transform （CWT）, discrete wavelet transform （DWT）, wavelet package transform （WPT）, wavelet denosing and mother wavelet selection, etc. Using the component-based hierarchy mode, the platform for virtual instrument （VI） is constructed, and the functions such as data sampling, data analysis and data present, etc are provided. Subsequently, the wavelet analysis library is designed and developed. The library consists of expert system, experienced database, development platform and abundant wavelet analysis functional module, which together implement general and special wavelet analysis in the field of mechanical engineering, energy source, transportation and biomedicine, etc. Finally, the wavelet analysis virtual instrument library is applied to detect fault called engine knock. Experimental result indicates that the wavelet analysis virtual instrument library can efficiently solve the engineering problem such as detecting engine knock.

APPLICATION OF WAVELET TIME-FR EQUENCY ANALYSIS TO IDENTIFICA-TION OF CRACKED ROTOR

Based on the simple hinge crack model and the local flexibility theorem, thecorresponding dynamic equation of the cracked rotor is modelled, the numerical simulation solutionsof the cracked rotor and the uncracked rotor are obtained. By the continuous wavelet time-frequencytransform, the wavelet time-frequency properties of the uncracked rotor and the cracked rotor arediscussed. A new detection algorithm that uses the wavelet time-frequency transform to identify thecrack is proposed. The influence of the sampling frequency on the wavelet time-frequency transformis analyzed by the numerical simulation research. The valid sampling frequency is suggested.Experiments demonstrate the validity and availability of the proposed algorithm in identification ofthe cracked rotor for engineering practices.

RESEARCH OF WAVELET TRANSFORM INSTRUMENT SYSTEM FOR SIGNAL ANALYSIS

After brief describing the Principle of wavelet transform (WT) of signals, a new signals analysis system based on wavelet transform is introduced. The design and development of the instryment of wavelet transform are described. A number of practical uses of this system demonstrate that wavelet transform system is specially functional in identifying and processing impulse, singular and non-smooth signals, so that it should be evaluated the most advanced signal analyzing system.