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.

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.

VARIATIONAL DATA ASSIMILATION USING WAVELET BACKGROUND ERROR COVARIANCE: INITIALIZATION OF TYPHOON KAEMI (2006)

Background error covariance plays an important role in any variational data assimilation system, because it determines how information from observations is spread in model space and between different model variables. In this paper, the use of orthogonal wavelets in representation of background error covariance over a limited area is studied. Based on the WRF model and its 3D-VAR system, an algorithm using orthogonal wavelets to model background error covariance is developed. Because each wavelet function contains information on both position and scale, using a diagonal correlation matrix in wavelet space gives the possibility to represent some anisotropic and inhomogeneous characteristics of background error covariance. The experiments show that local correlation functions are better modeled than spectral methods. The formulation of wavelet background error covariance is tested with the typhoon Kaemi (2006). The results of experiments indicate that the subsequent forecasts of typhoon Kaemi’s track and intensity are significantly improved by the new method.

AMicroseismic Signal Denoising Algorithm Combining VMD and Wavelet Threshold Denoising Optimized by BWOA

The denoising of microseismic signals is a prerequisite for subsequent analysis and research.In this research,a new microseismic signal denoising algorithm called the Black Widow Optimization Algorithm(BWOA)optimized VariationalMode Decomposition(VMD)jointWavelet Threshold Denoising(WTD)algorithm(BVW)is proposed.The BVW algorithm integrates VMD and WTD,both of which are optimized by BWOA.Specifically,this algorithm utilizes VMD to decompose the microseismic signal to be denoised into several Band-Limited IntrinsicMode Functions(BLIMFs).Subsequently,these BLIMFs whose correlation coefficients with the microseismic signal to be denoised are higher than a threshold are selected as the effective mode functions,and the effective mode functions are denoised using WTD to filter out the residual low-and intermediate-frequency noise.Finally,the denoised microseismic signal is obtained through reconstruction.The ideal values of VMD parameters and WTD parameters are acquired by searching with BWOA to achieve the best VMD decomposition performance and solve the problem of relying on experience and requiring a large workload in the application of the WTD algorithm.The outcomes of simulated experiments indicate that this algorithm is capable of achieving good denoising performance under noise of different intensities,and the denoising performance is significantly better than the commonly used VMD and Empirical Mode Decomposition(EMD)algorithms.The BVW algorithm is more efficient in filtering noise,the waveform after denoising is smoother,the amplitude of the waveform is the closest to the original signal,and the signal-to-noise ratio(SNR)and the root mean square error after denoising are more satisfying.The case based on Fankou Lead-Zinc Mine shows that for microseismic signals with different intensities of noise monitored on-site,compared with VMD and EMD,the BVW algorithm ismore efficient in filtering noise,and the SNR after denoising is higher.

Weighted Variational Minimization Model for Wavelet Domain Inpainting with Primal-Dual Method

To preserve the edges and details of the image,a new variational model for wavelet domain inpainting was proposed which contained a non-convex regularizer. The non-convex regularizer can utilize the local information of image and perform better than those usual convex ones. In addition, to solve the non-convex minimization problem,an iterative reweighted method and a primaldual method were designed. The numerical experiments show that the new model not only gets better visual effects but also obtains higher signal to noise ratio than the recent method.

Discrete Wavelet Multi-scale Decomposition of the Temporal Gravity Variations in North China

On the basis of the absolute and relative gravity observations in North China,spatial dynamic variation of regional gravity fields is obtained. A multi-scale decomposition technique is used to separate anomalies at different depths,and give some explanation to gravity variation at different time space scales. Gravity variation trends in North China are improved. Based on this result and the analysis of wavelet power spectrum,the images of the depth of wavelet approximation and detail are obtained. The results obtained are of scientific significance for the deep understanding of potential seismic risk in North China from gravity variations in different time space scales.

Study of marine geomagnetic diurnal variation correction based on Wavelet Transform

Based on the existing geomagnetic diurnal variation theory and correction method,this paper makes a comprehensive analysis of the international geomagnetic quiet diurnal variation by Fourier Transform and one-dimensional Continuous Wavelet Transform.The frequency band greater than 0.2 Hz is the embodiment of the geomagnetic disturbance field in the frequency domain.Discrete Wavelet Transform is used to separate the variation,thus improving accuracy of the existing geomagnetic diurnal variation correction method.According to the characteristics of variation and Discrete Wavelet Decomposition,Sym8 wavelet is selected as the basic wavelet to decompose the data at 7 layers.The long-term and short-term variation of geomagnetic diurnal variation are effectively separated from the geomagnetic disturbance part under the condition of ensuring the fidelity.Compared with the results of Fourier Series decomposition and low-pass filter,the processing effect of Discrete Wavelet Transform is better.The effective separation and correction of short-term,long-term variation and geomagnetic disturbances can improve the quality of diurnal variation correction in marine geomagnetic measurement,reduce the error accumulation in the process of marine geomagnetic data processing,and improve the scientificity and accuracy of the current diurnal variation correction methods.

Variational Modeling of Free-form Curve and Surface Using Wavelet Basis Functions

Variational modeling approach is often used to interactively design free-form curves and surfaces. Traditionally, a variational problem can be transformed to the optimization of control points. Unfortunately, as the number of basis functions grows, the local support property of B-spline often makes the computation of an optimization system time-consuming. To solve this problem, wavelet basis instead of B-spline basis is used to represent the curves or surfaces. Because the wavelet basis is a hierarchical basis with multiresolution property, the coarse wavelet basis can be used to describe the overall shape of the curves/surfaces, while the finer wavelet basis used to describe the details of the curves/surfaces. Thus, the computing speed of the optimization system can be raised greatly.

Synergistic effects of multiple driving factors on the runoff variations in the Yellow River Basin,China

River runoff plays an important role in watershed ecosystems and human survival,and it is controlled by multiple environmental factors.However,the synergistic effects of various large-scale circulation factors and meteorological factors on the runoff on different time-frequency scales have rarely been explored.In light of this,the underlying mechanism of the synergistic effects of the different environmental factors on the runoff variations was investigated in the Yellow River Basin of China during the period 1950-2019 using the bivariate wavelet coherence(WTC)and multiple wavelet coherence(MWC)methods.First,the continuous wavelet transform(CWT)method was used to analyze the multiscale characteristics of the runoff.The results of the CWT indicate that the runoff exhibited significant continuous or discontinuous annual and semiannual oscillations during the study period.Scattered inter-annual time scales were also observed for the runoff in the Yellow River Basin.The meteorological factors better explained the runoff variations on seasonal and annual time scales.The average wavelet coherence(AWC)and the percent area of the significant coherence(PASC)between the runoff and individual meteorological factors were 0.454 and 19.89%,respectively.The circulation factors mainly regulated the runoff on the inter-annual and decadal time scales with more complicated phase relationships due to their indirect effects on the runoff.The AWC and PASC between the runoff and individual circulation factors were 0.359 and 7.31%,respectively.The MWC analysis revealed that the synergistic effects of multiple factors should be taken into consideration to explain the multiscale characteristic variations of the runoff.The AWC or MWC ranges were 0.320-0.560,0.617-0.755,and 0.819-0.884 for the combinations of one,two,and three circulation and meteorological factors,respectively.The PASC ranges were 3.53%-33.77%,12.93%-36.90%,and 20.67%-39.34%for the combinations one,two,and three driving factors,respectively.The combinations of precipitation,evapotranspiration(or the number of rainy days),and the Arctic Oscillation performed well in explaining the variability in the runoff on all time scales,and the average MWC and PASC were 0.847 and 28.79%,respectively.These findings are of great significance for improving our understanding of hydro-climate interactions and water resources prediction in the Yellow River Basin.

Variations of the temperature and solar activity in China

In this paper we analyze daily mean, minimum, and maximum temperature data collected at 119 meteorological stations over five regions of China during the period 1951-2010. The series of minimum, maximum, and mean temperatures from each climatic region have similar signatures, but there are differences among the five regions and the countrywide average. The results indicate that the periods of faster warming were not synchronous across the regions studied： warming in northeast China and Tibet began in 1986, while in central-east, southeast, and northwest China the warming emerged in 1995. Furthermore, central-east and northwest China, and Tibet, have warmed continuously since 2000, but the temperature has decreased during this period in southeast China. We evaluated the evolution of these temperature series using a novel nonlinear filtering technique based on the concept of the lifetime of temperature curves. The decadal to secular evolution of solar activity and temperature variation had similar signatures in the northeast, southeast, and northwest re- gions and the average across the whole country, indicating that solar activity is a significant control on climate change over secular time scales in these regions. In comparison with these regions, the signatures were different in central-east China and Tibet because of regional differences （e.g., landforms and elevation） and indirect effects （e.g., cloud cover influencing the radiation balance, thereby inducing climate change）. Furthermore, the results of wavelet analysis indicated that the El Nino Southem Oscillation （ENSO） has had a significant impact on climate change, but at different times among the regions, and these changes were most probably induced by differing responses of the atmospheric system to solar forcing.

Multi-time scale analysis of precipitation variation in Guyuan, China:1957-2005

Morlet wavelet transformation is used in this paper to analyze the multi time scale characteristics of pre cipitation data series from 1957 to 2005 in Guyuan region.The results showed that(1) the annual precipitation evo lution process had obvious multi time scale variation characteristics of 15 25 years,7 12 years and 3 6 years,and different time scales had different oscillation energy densities;(2) the periods at smaller time scales changed more frequently,which often nested in a biggish quasi periodic oscillations,so the concrete time domain should be ana lyzed if necessary;(3) the precipitation had three main periods(22 year,9 year and 4 year) and the 22 year period was especially outstanding,and the analysis of this main period reveals that the precipitation would be in a relative high water period until about 2012.

Excitations of length-of-day seasonal variations:Analyses of harmonic and inharmonic fluctuations

Geophysical excitations of length-of-day(LOD)variations is of great significance in understanding changes in the Earth’s spin rate and interactions between geophysical fluids and the solid Earth,as well as validating the reliability of atmospheric,oceanic and hydrological models.In this study seasonal excitations of LOD variation during 06.30,1987-06.30,2017 are investigated using both harmonic and inharmonic analyses.We examined the agreements between the IERS EOP 14C04ΔLOD series and that from the previous version EOP08C04,and analyzed contributions of atmospheric,oceanic,hydrological and sea level angular momenta to seasonal excitations of LOD variations on the bases of the ESMGFZ products.We found that the sea level angular momentum plays an important role in global mass conservation and can bring better agreements between the geophysical and geodetic excitations.

基于特征图像组合与改进ResNet-18的电能质量扰动识别方法

针对传统电能质量扰动(power quality disturbance,PQD)识别体系中单一图像特征信息受限与算法识别能力不足等问题,依据特征融合的思想,提出一种基于特征图像组合与改进ResNet-18的PQD识别方法。首先,对PQD信号进行变分模态分解(variational mode decomposition,VMD)得到一系列固有模态函数(intrinsic mode functions,IMFs)与残差分量;其次,将IMFs、残差分量、原始扰动信号与Subtract分量纵向拼接成分量矩阵,利用信号-图像转化方法生成特征分量彩色图;再次,对原始扰动信号进行连续小波变换(continuous wavelet transform,CWT)生成小波时-频图;最后,将特征分量彩色图与小波时-频图组合输入改进的六通道ResNet-18中训练学习并完成扰动识别。通过仿真对PQD识别方法进行分析并将其与目前常用识别体系进行比较。结果表明,所提方法具有较好的抗噪性能并且能够更好地提取PQD特征信息,达到更高的识别准确率。

基于POA-VMD-WT的MEMS去噪方法

针对MEMS传感器所测得的加速度和角速度输出信号噪声较大问题,提出一种基于鹈鹕优化算法(pelican optimization algorithm,POA)的变分模态分解(variational mode decomposition,VMD)结合小波阈值(wavelet threshold,WT)的去噪方法。首先利用POA对VMD的参数组合进行优化选择,然后应用POA-VMD将含噪信号自适应、非递归地分解为一系列本征模态函数(intrinsic mode function,IMF)。再通过计算每个IMF的余弦相似度对IMFs进行分类,根据计算结果将IMFs分为噪声主导分量与信号主导分量,对分类后的噪声主导分量进行改进小波阈值去噪处理,最后对处理后的噪声分量与信号主导分量进行重构,获得降噪后的MEMS传感器信号。静态和动态实验结果表明,该方法去噪处理后信号的信噪比分别提高12和10 dB,均方误差分别降低75.5%和46.6%,去噪效果显著,能够提高MEMS传感器的精度。

加权核范数最小化和改进小波阈值函数的图像去噪算法

针对加权核范数最小化算法存在结构残余噪声以及无法较好地保持图像边缘结构的问题,提出基于加权核范数最小化和改进小波阈值函数的图像去噪算法。利用全变分模型对噪声图像进行初步去噪,使用噪声图像与初步去噪后的图像进行差分运算,对差分后得到的噪声残差图像使用改进的小波阈值函数去噪,将小波去噪后的残差图像与初步去噪图像叠加,将叠加后的图像使用基于残余噪声水平迭代的加权核范数最小化算法进行二次去噪。相较于当下主流去噪算法,经该算法处理后的图像的PSNR和SSIM值均有所提升,能够更好地保持图像的纹理结构,且在高噪声环境下效果更佳。

新小波阈值法与VMD相结合的滚动轴承特征提取

针对滚动轴承故障信号弱以及难提取等问题,提出了一种新小波阈值方法与VMD相结合的轴承故障信号特征提取方法。首先,利用一种改进的指数小波阈值函数来优化传统小波降噪方法,克服其存在间断点和恒定偏差等问题;然后,结合VMD提取滚动轴承的有效故障特征;最后,以6205-RS号轴承内圈故障数据作为原始信号进行实验验证。实验结果表明,该方法能够有效提高降噪信号的信噪比,降低均方根误差,保证滚动轴承微弱故障信号特征提取的完整性和有效性。

基于ZOA优化VMD-IAWT岩石声发射信号降噪算法

针对岩石破裂过程中产生的声发射(AE)信号夹杂大量噪声的问题,提出了一种基于斑马优化算法(ZOA)改进变分模态分解(VMD)并与改进的自适应小波阈值(IAWT)联合的声发射信号降噪算法。利用ZOA算法优选出影响VMD分解效果的模态个数K和二次惩罚因子α;通过相关系数将分解出的IMFs划分为有效分量、含噪分量和剔除分量;针对小波阈值(WT)降噪算法不具备自动调整小波基以及软、硬阈值函数存在偏差大和不连续的弊端,提出了IAWT算法去除IMFs中的噪声分量,并与有效分量合并重构,得到降噪后的AE信号。通过模拟和实测AE信号验证并与现有降噪算法对比,结果表明ZOA-VMD-IAWT降噪算法适合处理AE信号,信号的时频特征得以保留。研究结果可为岩石AE信号理论及实际工程应用提供参考。

大跨度单层柔性光伏支架结构气动阻尼的试验研究

大跨光伏支架结构轻柔,在风荷载作用下易产生显著气动效应。为研究该类结构的气动阻尼特征,对不同风速和张力工况下两种典型倾角(0°和10°)的大跨度柔性光伏支架结构开展气弹风洞试验。基于气弹模型风洞试验结果,分别利用经验小波变换(empirical wavelet transform,EWT)和变分模态分解(variational modal decomposition,VMD)结合改进的随机减量方法(random decrement technique,RDT)识别得到了柔性光伏支架结构在不同风速风向、组件倾角和拉索预张力下的气动阻尼比。研究结果表明,气动阻尼对风向角的变化较为敏感。当组件倾斜铺设时(10°倾角),大跨光伏结构气动阻尼在180°迎风向时会出现负值。张力增加可能导致高风速下平铺组件的气动阻尼比显著降低。气动阻尼比随风速的增加整体呈减小趋势,低风速下基本为正值,而高风速下可能出现负气动阻尼。不同方法识别出的气动阻尼比结果存在一定的差异,但反映出的气动阻尼的变化特征具有一致性。

融合T-分布小波变异的混沌鲸鱼优化算法

针对鲸鱼优化算法难以跳出局部最优导致收敛精度不足的问题,提出一种融合了T-分布小波变异和多项式差分学习策略的鲸鱼优化算法.该算法首先引入Circle混沌扩大搜索范围,提高收敛速度;然后采用T-分布小波变异策略平衡全局和局部搜索能力;最后采用多项式差分学习策略改进算法的优化精度.对3种改进策略作单一引入的仿真对比分析,并将改进的鲸鱼优化算法在12个可变维度的基准测试函数上进行仿真,对本文改进的鲸鱼优化算法与其他改进策略的鲸鱼优化算法以及其他几种智能算法进行比较.结果表明,基于T-分布小波变异和多项式差分学习策略的改进鲸鱼优化算法具有较好的稳定性,收敛速度和精度更好.

参数优化VMD结合改进小波包阈值的去噪方法

针对轴承信号故障特征容易被噪声淹没的问题,提出一种参数优化变分模态分解结合改进小波包阈值的去噪方法。首先,通过变分模态分解(Variational Mode Decomposition,VMD)结合改进粒子群算法(Improve Particle Swarm Optimization,IPSO)将含噪信号分解为若干本征模态分量(Intrinsic Mode Function,IMF)。以最大相关系数-相关峭度为准则,把IMF分为高值分量(High-value Intrinsic Mode Function,HIMF)和低值分量(Low-value Intrinsic Mode Function,LIMF)。再对LIMF进行改进小波包(Improved Wavelet Packet,IWP)阈值去噪。最后对重构信号进行包络解调,提取轴承故障特征频率,完成故障诊断。实验结果表明,该方法不仅能够避免“过扼杀”现象,并且可以得到信噪比更高的去噪信号。