Study of the Functions of Wavelet Packet Transform （WPT） and Continues Wavelet Transform （CWT） in Recognizing the Damage Specification

Modem and efficient methods focus on signal analysis and have drawn researchers＇ attention to it in recent years. These methods mainly include Continuous Wavelet and Wavelet Packet transforms. The main advantage of the application of these Wavelets is their capacity to analyze the signal position in different occasions and places. However, in sites with high frequencies its resolution becomes much more difficult. Wavelet packet transform is a more advanced form of continuous wavelets and can make a perfect level by level resolution for each signal. Although very few studies have been done in the field. In order to do this, in the present study, f^st there was an attempt to do a modal analysis on the structure by the ANSYS finite elements software, then using MATLAB, the wavelet was investigated through a continuous wavelet analysis. Finally the results were displayed in 2-D location-coefficient figures. In the second form, transient-dynamic analysis was done on the structure to find out the characteristics of the damage and the wavelet packet energy rate index was suggested. The results indicate that suggested index in the second form is both practical and applicable, and also this index is sensitive to the intensity of the damage.

Performance of Continuous Wavelet Transform over Fourier Transform in Features Resolutions

This study presents a comparative analysis of two image enhancement techniques, Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT), in the context of improving the clarity of high-quality 3D seismic data obtained from the Tano Basin in West Africa, Ghana. The research focuses on a comparative analysis of image clarity in seismic attribute analysis to facilitate the identification of reservoir features within the subsurface structures. The findings of the study indicate that CWT has a significant advantage over FFT in terms of image quality and identifying subsurface structures. The results demonstrate the superior performance of CWT in providing a better representation, making it more effective for seismic attribute analysis. The study highlights the importance of choosing the appropriate image enhancement technique based on the specific application needs and the broader context of the study. While CWT provides high-quality images and superior performance in identifying subsurface structures, the selection between these methods should be made judiciously, taking into account the objectives of the study and the characteristics of the signals being analyzed. The research provides valuable insights into the decision-making process for selecting image enhancement techniques in seismic data analysis, helping researchers and practitioners make informed choices that cater to the unique requirements of their studies. Ultimately, this study contributes to the advancement of the field of subsurface imaging and geological feature identification.

CEEMD-FastICA-CWT联合瞬态响应阶次的电驱总成噪声源识别

以某增程式电驱动总成为研究对象,提出基于联合算法的噪声分离识别模型。首先,采用互补集合经验模态分解(complementary ensemble empirical mode decomposition,CEEMD)联合快速独立分量分析(fast independent component analysis,FastICA)方法提取纯电模式稳态工况下单一通道噪声信号特征,利用复Morlet小波变换及FFT对各分量信号时频特性进行识别。其次,采用阶次分析法和声能叠加法对稳态分量信号对应的各瞬态响应阶次能量进行对比分析,并结合皮尔逊积矩相关系数(Pearson product moment correlation coefficient,PPMCC)相似性识别确定不同噪声激励源贡献度。结果表明:减速齿副啮合噪声对该增程式电驱总成纯电模式运行噪声整体贡献度最大。

基于CWT-sCARS的土壤铜含量高光谱反演

光谱变量的有效程度与土壤铜含量的反演精度密切相关。基于原始反射率以及不同分解尺度下的小波系数,本研究采用连续小波变换(CWT)算法、稳定性竞争自适应重加权采样(sCARS)算法和随机森林(RF)算法对土壤铜含量进行了反演与验证。研究结果表明:连续小波变换可以有效提高光谱特征与土壤铜含量之间的相关性,不同分解尺度对应的最大相关系数中,最大值位于Scale 8分解尺度下1343 nm处,相关系数为0.60;使用sCARS算法可以显著减少特征变量的数量,结合CWT变换和sCARS算法可以显著减轻数据冗余,提高土壤Cu含量的反演精度。该研究可为利用高光谱遥感技术,快速、高精度反演土壤Cu含量提供重要参考。

基于CWT-CNN的离心泵轴承故障识别方法

针对传统的轴承故障诊断方法在面对强噪声和非平稳信号识别时特征提取过度依赖先验知识和专家经验等问题,结合传统的信号处理方法和深度学习算法提出一种基于CWT-CNN的离心泵轴承故障识别方法。连续小波变换(CWT)将原始的1D振动信号转化为故障特征信息更丰富的2D时频图,2D时频图再输入到卷积层完成特征的自动提取,最后SoftMax层完成故障识别。经过西储大学公开轴承数据集和实验室搭建的离心泵振动轴承采集实验台验证,该方法的故障识别准确率均能达到90%以上。

DETECTION OF INCIPIENT LOCALIZED GEAR FAULTS IN GEARBOX BY COMPLEX CONTINUOUS WAVELET TRANSFORM

As far as the vibration signal processing is concerned, composition ofvibration signal resulting from incipient localized faults in gearbox is too weak to be detected bytraditional detecting technology available now. The method, which includes two steps: vibrationsignal from gearbox is first processed by synchronous average sampling technique and then it isanalyzed by complex continuous wavelet transform to diagnose gear fault, is introduced. Twodifferent kinds of faults in the gearbox, i.e. shaft eccentricity and initial crack in tooth fillet,are detected and distinguished from each other successfully.

PARAMETERS OPTIMIZATION OF CONTINUOUS WAVELET TRANSFORM AND ITS APPLICATION IN ACOUSTIC EMISSION SIGNAL ANALYSIS OF ROLLING BEARING

Morlet wavelet is suitable to extract the impulse components of mechanical fault signals. And thus its continuous wavelet transform （CWT） has been successfully used in the field of fault diagnosis. The principle of scale selection in CWT is discussed. Based on genetic algorithm, an optimization strategy for the waveform parameters of the mother wavelet is proposed with wavelet entropy as the optimization target. Based on the optimized waveform parameters, the wavelet scalogram is used to analyze the simulated acoustic emission （AE） signal and real AE signal of rolling bearing. The results indicate that the proposed method is useful and efficient to improve the quality of CWT.

脉冲相干激光测风FFT和fCWT融合算法的研究

在脉冲相干激光雷达测风中,广泛使用的FFT算法运算简便快速,但测风的距离分辨率难以进一步提高,而连续小波变换(CWT)等时频分析方法具有时频精细分析能力,但计算实时性差,提出了一种结合FFT和快速连续小波变换(fCWT)优势的融合算法,算法继承了CWT精细分析能力,而运算速度显著加快。通过对融合算法以及CWT、FFT算法就雷达测风仿真数据及实测数据进行对比,融合算法及CWT和FFT算法绘制的风速曲线趋势一致,但具有更丰富细节,融合算法计算时间相比CWT算法减少了45%以上。此融合算法为提高脉冲相干激光测风雷达测风性能提供了一种新思路。

基于CWT和CNN-BiLSTM的散绕同步电机定子绕组短路故障检测方法

近年来,基于脉冲频率响应法(impulse frequency response analysis,IFRA)的神经网络模型已被证实能够有效检测定子绕组故障。然而,这些模型普遍具有鲁棒性不强、抗噪能力差等特点,究其原因是大多数的模型采用简单的神经网络架构且常规的IFRA普遍采用快速傅里叶变换(fast Fourier transform,FFT)对暂态信号进行时频变换,而FFT并不适合处理暂态突变的非平稳信号。文中以散绕结构的同步电机定子绕组为检测对象,采用连续小波变换(continual wavelet transform,CWT)代替FFT处理IFRA的暂态信号,并基于一维卷积神经网络(convolutional neural networks,CNN)和双向长短时记忆网络(bi-directional long short-term memory,BiLSTM)构建CNN-BiLSTM模型对采用CWT变换之后的信号进行故障检测。实验结果表明:采用CWT处理后的频域序列作为该模型的输入,相较于其它结构单一的模型,其平均准确率最优且高达99.01%。噪声对比实验表明:采用CWT变换后的数据能使故障诊断模型的鲁棒性及泛化性更强。

On Inversion of Continuous Wavelet Transform

This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, wavelet’s dual is assumed to be a reconstruction wavelet or a localized function. This study finds that wavelet’s dual can be a harmonic which is not local. This finding leads to new CWT inversion formulas. It also justifies the concept of normal wavelet transform which is useful in time-frequency analysis and time-frequency filtering. This study also proves a law for CWT inversion: either wavelet or its dual must integrate to zero.

一种基于优化VMD-CWT-CNN的柱塞泵配流盘磨损状态识别方法

为解决一维振动信号难以充分挖掘表达状态特征信息以及柱塞泵配流盘磨损早期识别问题,基于卷积神经网络(Convolutional neural networks,CNN)优秀的图像处理能力,提出了一个优化VMD-CWT-CNN模型。首先,采用连续小波变换(Continuous wavelet transform,CWT)对信号进行预处理,得到信号的二维时频图,作为CNN模型的一路输入,将状态识别问题转化为CNN图像识别问题。其次,基于相关系数对变分模态分解(Variational mode decomposition,VMD)参数优化后,利用优化VMD对振动信号进行预处理,再以相关系数和峭度值最大为优选原则,甄选出三组蕴含故障特征的本征模态函数(Intrinsic mode function,IMF),将其重组为三通道一维信号,作为CNN模型的另一路输入。最后,在CNN模型中将两路信息汇聚并得到柱塞泵配流盘磨损状态识别分类结果。实验中,此方法分别采用优化VMD和CWT对振动信号预处理,再结合CNN对磨损状态进行分类。实验结果表明,该方法对于配流盘磨损的三种状态的识别效果显著优于单路输入的CNN模型以及典型的深度学习方法和机器学习分类器。因此,优化的VMD-CWT-CNN方法可以更准确地实现柱塞泵配流盘磨损状态识别。

小波包融合CWT的运动想象脑电信号识别算法

针对传统时频分析方法处理运动想象脑电信号时存在时频分辨率差和分类正确率低的问题,提出一种基于小波包变换(WPT)并优化连续小波变换(CWT)的特征提取算法。对原始信号进行4层小波包分解,提取与运动想象执行时事件相关同步/去同步(ERD/ERS)显著频段的小波能量特征,重构该频段数据作为CWT的输入数据,利用CWT得到最优时段下的时频特征,通过支持向量机(SVM)对提取的特征集进行分类,对比验证单特征与融合特征在整个时段和最优时段的平均识别率。在BCI Competition Ⅱ的Data Ⅲ数据集中,该方法在最优时段的平均识别率为89.04%,最高识别率达到91.68%,验证了小波包融合CWT特征提取算法的有效性。

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

The Continuous Wavelet Transform Associated with a Dunkl Type Operator on the Real Line

We consider a singular differential-difference operator Λ on R which includes as a particular case the one-dimensional Dunkl operator. By using harmonic analysis tools corresponding to Λ, we introduce and study a new continuous wavelet transform on R tied to Λ. Such a wavelet transform is exploited to invert an intertwining operator between Λ and the first derivative operator d/dx.

COMPUTATION OF CONTINUOUS WAVELET TRANSFORM AT DYADIC SCALES BY SUBDIVISION SCHEME

A new algorithm to compute continuous wavelet transforms at dyadic scales is proposed here. Our approach has a similar implementation with the standard algorithme a trous and can coincide with it in the one dimensional lower order spline case.Our algorithm can have arbitrary order of approximation and is applicable to the multidimensional case.We present this algorithm in a general case with emphasis on splines anti quast in terpolations.Numerical examples are included to justify our theorerical discussion.

Natural frequencies and damping estimation based on continuous wavelet transform

The continuous wavelet transform(CWT)based method was improved for estimating the natural frequencies and damping ratios of a structural system in this paper.The appropriate scale of CWT was selected by means of the least squares method to identify the systems with closely spaced modes.The important issues related to estimation accuracy such as mode separation and end effect,were also investigated.These issues were associated with the parameter selection of wavelet function based on the fitting error of least squares.The efficiency of the method was confirmed by applying it to a simulated 3dof damped system with two close modes.

基于CWT-CNN-LSTM的配电网单相接地故障选线方法分析

阐述配电网单相接地故障特征提取难点,分析现有选线方法、选线精度不高的问题,提出一种连续小波变换(Continuous wavelet transform,CWT)和CNN-LSTM的故障选线方法。首先对零序暂态电流进行连续小波变换获取对应的时频灰度图像,然后CNN自适应提取时频灰度图像的局部特征,LSTM层从CNN层学到的局部特征中学习上下文依赖关系,最后通过SoftMax层实现故障选线。仿真结果表明,所提方法的选线精度为99.65%,与CWT-CNN等方法相比,具有较强的鲁棒性。

基于DT-CWT和SVD的变电站直流系统接地故障检测技术研究

变电站直流系统的状态直接关系到变电站的正常运行,为了对变电站直流系统出现的接地故障快速、准确定位,提出了一种双树复小波变换(DT-CWT)和奇异值分解(SVD)相结合的变电站直流系统接地故障检测新方法。该方法首先利用DT-CWT对支路电流信号进行分解来构建Hankel矩阵;然后对Hankel矩阵进行SVD分解,得到一系列奇异特征值;再次,利用相邻奇异值差值构建奇异值差分谱,通过奇异值差分谱最大峰值来保留有效的奇异值个数;最后,利用保留的奇异值来重构低频信号。算例分析结果表明,该方法能够准确地从支路电流信号中提取出低频交流信号,可以对变电站直流系统接地故障进行准确定位,很大程度上减小对地电容对检测精度的影响。

The Time-Frequency Energy Attenuation Factor and Its Application on the Basis of Gauss Linear Frequency-Modulated Continuous Wavelet Transform

Based on the Gauss linear frequency modulated wavelet transform, a new characteristic index is presented, namely time frequency energy attenuation factor which can reflect the difference features of waveform in earthquake focus mechanism, wave traveling path and its attenuation characteristics in focal area or near field. In order to test its validity, we select the natural earthquakes and explosion or collapse events whose focus mechanisms vary obviously,and some natural earthquakes located at the same site or in a very small area. The study indicates that the time frequency energy attenuation factors of the natural earthquakes are obviously different with that of explosion or collapse events, and the change of the time frequency energy attenuation factors is relatively stable for the earthquakes under the normal seismicity background. Using the above mentioned method, it is expected to offer a useful criterion for strong earthquake prediction by continuous earthquake observation.

基于CWT-HHT的玉米叶片铜离子污染信息探测

为了准确探测农作物在不同浓度重金属污染下叶片光谱间微弱的畸变信息,本研究通过设置不同浓度铜离子(Cu2+)胁迫下的玉米盆栽实验,在采集了不同梯度下玉米叶片光谱并测定同期叶片Cu2+含量的基础上,采用连续小波变换(CWT)结合希尔伯特-黄变换(HHT)的方法,构建CWT-HHT算法以探测玉米叶片光谱重金属污染信息,同时与红边位置(REP)、红边归一化指数(NDVI705)和红边植被胁迫指数(RVSI)等常规的植被指数监测方法进行对比分析。结果表明:基于CWT-HHT探测方法提取的瞬时能量峰值呈现先升高、后降低的趋势,与玉米叶片Cu2+含量变化趋势一致。而且通过与植被指数监测农作物重金属污染的方法对比,证明CWT-HHT探测结果最优,表明CWT-HHT方法在玉米叶片重金属Cu2+污染信息探测方面具有可行性。