Variational Mode Decomposition-Informed Empirical Wavelet Transform for Electric Vibrator Noise Analysis

Electric vibrators find wide applications in reliability testing, waveform generation, and vibration simulation, making their noise characteristics a topic of significant interest. While Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) offer valuable support for studying signal components, they also present certain limitations. This article integrates the strengths of both methods and proposes an enhanced approach that integrates VMD into the frequency band division principle of EWT. Initially, the method decomposes the signal using VMD, determining the mode count based on residuals, and subsequently employs EWT decomposition based on this information. This addresses mode aliasing issues in the original method while capitalizing on VMD’s adaptability. Feasibility was confirmed through simulation signals and ultimately applied to noise signals from vibrators. Experimental results demonstrate that the improved method not only resolves EWT frequency band division challenges but also effectively decomposes signal components compared to the VMD method.

Landsat Image-Based Spatiotemporal Variation Analysis of Erosion and Deposition off the Qingshuigou of the Yellow River Delta from 1984 to 2021

Owing to climate change and human activity,the Qingshuigou of the Yellow River Delta(YRD)has undergone dynamic changes in erosion and deposition.Therefore,studying these changes is important to ensure ecological protection and sustainable development.In this study,the trend of erosion-deposition evolution in the Qingshuigou was investigated based on 38 coastline phases extracted from Landsat series images of the YRD at one-year intervals from 1984 to 2021.The periodicity of the scouring and deposition evolution was also analyzed using wavelet analysis.Results showed that the total area of the Qingshuigou was affected by deposition and erosion and that the fluctuation first increased and then decreased.The total area reached a maximum in 1993.The depositional area first increased and then decreased,whereas the overall erosion area decreased.Deposition and erosion areas showed periodic changes to some extent;however,the periodic signal intensity decreased.Furthermore,factors including channel morphological evolution and variations in water and sediment discharge affect the spatiotemporal dynamics of erosion and deposition processes.The application of nonconsistency tests finally revealed that deposition area and flushing magnitude exhibited non-stationarities,which are potentially attributed to impacts from climatic change drivers.

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.

Wavelet De-noising of Speech Using Singular Spectrum Analysis for Decomposition Level Selection

The problem of speech enhancement using threshold de-noising in wavelet domain was considered.The appropriate decomposition level is another key factor pertinent to de-noising performance.This paper proposed a new wavelet-based de-noising scheme that can improve the enhancement performance significantly in the presence of additive white Gaussian noise.The proposed algorithm can adaptively select the optimal decomposition level of wavelet transformation according to the characteristics of noisy speech.The experimental results demonstrate that this proposed algorithm outperforms the classical wavelet-based de-noising method and effectively improves the practicability of this kind of techniques.

Application of Wavelet Analysis in Signal De-noising of Blast Shock Wave Overpressure

It＇ s a problem to be solved how to de-noise the signal of blast shock wave overpressure. In the conventional methods, the high frequency of the signal is cut directly by some mathematics algorithms, such as Fourier Transform, but some of the useful signal will be cut together. We adopt a new method for the signal de-noising of shock wave overpressure by wavelet analysis, There are four steps in this method. Firstly, the original signal is de-compoed. Then the time-frequency features of the signal and noise are analyzed. Thirdly, the noise is separated from the signal by only cutting its frequency while the useful signal frequency is reserved as much as possible. Lastly, the useful signal with least loss of information is recovered by reconstruction process. To verify this method, a blast shock wave signal is de-noised with FFF to make a comparison. The results show that the signal de-noised by wavelet analysis approximates the ideal signal well.

Application of Wavelet Packet De-noising in Time-Frequency Analysis of the Local Wave Method

The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.

Theoretical research on structural damage alarming of long-span bridges using wavelet packet analysis

The state equation and observation equation of the structural dynamic systems under various analysis scales are derived based on wavelet packet analysis. The time-frequency properties of structural dynamic response under various scales are further formulated. The theoretical analysis results reveal that the wavelet packet energy spectrum （WPES） obtained from wavelet packet decomposition of structural dynamic response will detect the presence of structural damage. The sensitivity analysis of the WPES to structural damage and measurement noise is also performed. The transfer properties of the structural system matrix and the observation noise under various analysis scales are formulated, which verify the damage alarming reliability using the proposed WPES with preferable damage sensitivity and noise robusticity.

Integrated interpretation of dual frequency induced polarization measurement based on wavelet analysis and metal factor methods

In mineral exploration, the apparent resistivity and apparent frequency （or apparent polarizability） parameters of induced polarization method are commonly utilized to describe the induced polarization anomaly. When the target geology structure is significantly complicated, these parameters would fail to reflect the nature of the anomaly source, and wrong conclusions may be obtained. A wavelet approach and a metal factor method were used to comprehensively interpret the induced polarization anomaly of complex geologic bodies in the Adi Bladia mine. Db5 wavelet basis was used to conduct two-scale decomposition and reconstruction, which effectively suppress the noise interference of greenschist facies regional metamorphism and magma intrusion, making energy concentrated and boundary problem unobservable. On the basis of that, the ore-induced anomaly was effectively extracted by the metal factor method.

Automated Registration for Infrared Image Based on Wavelet Analysis

To develop a quick, accurate and antinoise automated image registration technique for infrared images, the wavelet analysis technique was used to extract the feature points in two images followed by the compensation for input image with angle difference between them. A hi erarchical feature matching algorithm was adopted to get the final transform parameters between the two images. The simulation results for two infrared images show that the method can effectively, quickly and accurately register images and be antinoise to some extent.

Study on Rhizome Crops by Fourier Transform Infrared Spectroscopy Combined with Wavelet Analysis

In order to distinguish 8 kinds of rhizome crops, the 40 samples were studied by Fourier transform infrared spectroscopy （FTIR） combined with wavelet transform （WT）, principal component analysis （PCA） and hieramhical cluster analysis （HCA）. The results showed that the infrared spectra were similar on the whole, but there were differences in peak position, peak shape and peak absorption intensity in the range of 1 800-700 cm-1. The infrared spectra in the range of 1 800-700 cm-1 were selected to perform continuous wavelet transform （CWT） and discrete wavelet transform （DWT）. The 15th-Ievel decomposition coefficients of CWT and the 5=-level detail coefficients of DWT were classified by PCA and HCA. The cumulative contri- bution rates of the first three principal components of CWT and DWT were 93.12% and 89.78%, respectively. The accurate recognition rates of PCA and HCA were all 100%. It is proved that FTIR combined with WT can be used to distinguish different kinds of rhizome crops.

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.

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.

Detecting Inhomogeneity in Daily Climate Series Using Wavelet Analysis

A wavelet method was applied to detect inhomogeneities in daily meteorological series, data which are being increasingly applied in studies of climate extremes. The wavelet method has been applied to a few well- established long-term daily temperature series back to the 18th century, which have been ＂homogenized＂ with conventional approaches. Various types of problems remaining in the series were revealed with the wavelet method. Their influences on analyses of change in climate extremes are discussed. The results have importance for understanding issues in conventional climate data processing and for development of improved methods of homogenization in order to improve analysis of climate extremes based on daily data.

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.

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 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.