Singularity detection of the thin bed seismic signals with wavelet transform

The location of singularities may be detected by local maxima of the wavelet transform modulus. The digital modeling and focusing process to wavelet transform of the reflecting seismic signals have been done. It has been found that the locations of singularities after wavelet transform are only affected by two factors, their original locations and the seismic wavelet length, which says it does not matter with what shape the wavelet will be. The wavelet length can be determined according to the wavelet transform results and be eliminated thereafter so that we are able to detect thin bed seismic signal with resolution of l/32 wavelength. The singularities have been recovered with improved resolution of the seismic section by real data processing.

Study on Singularity of Chaotic Signal Based on Wavelet Transform

Based on the variations of wavelet transform modulus maxima at multi-scales, the singularity of chaotic signals are studied, and the singularity of these signals are measured by the Lipschitz exponent.In the meantime, a nonlinear method is proposed based on the higher order statistics, on the other aspect, which characterizes the higher order singular spectrum (HOSS) of chaotic signals. All computations are done with Lorenz attractor, Rossler attractor and EEG(electroencephalogram) time series and the comparisions among these results are made. The experimental results show that the Lipschitz exponents and the higher order singular spectra of these signals are significantly different from each other, which indicates these methods are effective for studing the singularity of chaotic signals.

An Improved Singularity Computing Algorithm Based on Wavelet Transform Modulus Maxima Method

In order to reduce the hidden danger of noise which can be charactered by singularity spectrum, a new algorithm based on wavelet transform modulus maxima method was proposed. Singularity analysis is one of the most promising new approaches for extracting noise hidden information from noisy time series . Because of singularity strength is hard to calculate accurately, a wavelet transform modulus maxima method was used to get singularity spectrum. The singularity spectrum of white noise and aluminium interconnection electromigration noise was calculated and analyzed. The experimental results show that the new algorithm is more accurate than tradition estimating algorithm. The proposed method is feasible and efficient.

On Wavelet Transform General Modulus Maxima Metric for Singularity Classification in Mammograms

Continuous wavelet transform is employed to detect singularities in 2-D signals by tracking modulus maxima along maxima lines and particularly applied to microcalcification detection in mammograms. The microcalcifications are modeled as smoothed positive impulse functions. Other target property detection can be performed by adjusting its mathematical model. In this application, the general modulus maximum and its scale of each singular point are detected and statistically analyzed locally in its neighborhood. The diagnosed microcalcification cluster results are compared with health tissue results, showing that general modulus maxima can serve as a suspicious spot detection tool with the detection performance no significantly sensitive to the breast tissue background properties. Performed fractal analysis of selected singularities supports the statistical findings. It is important to select the suitable computation parameters-thresholds of magnitude, argument and frequency range-in accordance to mathematical description of the target property as well as spatial and numerical resolution of the analyzed signal. The tests are performed on a set of images with empirically selected parameters for 200 μm/pixel spatial and 8 bits/pixel numerical resolution, appropriate for detection of the suspicious spots in a mammogram. The results show that the magnitude of a singularity general maximum can play a significant role in the detection of microcalcification, while zooming into a cluster in image finer spatial resolution both magnitude of general maximum and the spatial distribution of the selected set of singularities may lead to the breast abnormality characterization.

A New Feature Space for Partial Discharge Signal Separation Based on DWT Coefficient Variance

In this paper, a new feature space for PD （partial discharge） signal separation is presented. Three typical PD defects were experimentally reproduced in a laboratory for obtaining independent PD sources. Signals were acquired with a digital storage oscilloscope and then post-processed with DWT （discrete Wavelet transform） for de-noising. The new feature space for PD source separation was constructed with the variance of each Wavelet coefficient vector and was compared with an established feature space for PD source separation; based on the energy of DWT coefficient vectors. After a space reduction by mean of PCA （principal components analysis）, the separation capability among them was measured by comparing the final classification error after training a neural network Results showed that with this new feature space it is possible to separate different sources of PD signals. Later, the feature space proposed was used to separate two PD sources from a real equipment tested. Further analysis on the reduced feature space has shown the band location of PD signals information for separating purpose.

Theoretical analysis of adaptive harmonic window and its application in frequency extraction of vibration signal

The goal of this paper is to find an excellent adaptive window function for extracting the weak vibration signal and high frequency vibration signal under strong noise.The relationship between windowing transform andfiltering is analyzed first in the paper.The advantage of adjustable time-frequency window of wavelet transform is introduced.Secondly the relationship between harmonic wavelet and multiple analytic band-pass filter is analyzed.The coherence of the multiple analytic band-pass filter and harmonic wavelet base function is discussed,and the characteristic that multiple analytic band-pass filter included in the harmonic wavelet transform is founded.Thirdly,by extending the harmonic wavelet transform,the concept of the adaptive harmonic window and its theoretical equation without decomposition are put forward in this paper.Then comparing with the Hanning window,the good performance of restraining side-lobe leakage possessed by adaptive harmonic window is shown,and the adaptive characteristics of window width changing and analytical center moving of the adaptive harmonic window are presented.Finally,the proposed adaptive harmonic window is applied to weak signal extraction and high frequency orbit extraction of high speed rotor under strong noise,and the satisfactory results are achieved.The application results show that the adaptive harmonic window function can be successfully applied to the actual engineering signal processing.

基于能量阈值的双参数阈值函数在生理信号降噪中的应用

针对弱生理信号在采集过程中易被噪声淹没,传统小波去噪算法存在去噪效果差和信号提取失真的问题,根据小波系数的能量分布特点,提出一种改进的小波阈值去噪算法。通过计算各层小波系数的能量来确定阈值,避免阈值计算的不平衡性,同时提高自适应性和弱信号的保真度;采用一种改进的可调节的双参数阈值函数对小波系数进行处理,在小波系数压缩程度可控的同时可以自由调节阈值函数的变化趋势。实验结果表明:改进的小波阈值去噪算法相较于两种传统去噪算法(经验模态分解算法和滤波器算法)以及12种传统小波阈值和阈值函数组合算法,在信噪比、均方根百分比和均方根误差上都具有明显的优势,并且在实测生理信号中取得了最小的平均相对误差和最小的波动性。

采煤工作面水流声的降噪算法研究

采煤工作面水害事故发生前伴有水流声出现,为减小常见机械设备噪声对水流声识别的影响,提出了一种改进小波阈值降噪法。为了补偿水流声在采集过程中高频信号的损失,对其进行了预加重、分帧、加窗等预处理;采用小波软、硬阈值函数折衷法对阈值函数进行改进,避免了信号处理后带来的附加振荡问题;在固定阈值中引入了分解层数j,变化的阈值可最大程度分离水流声信号与噪声信号。结果表明,改进小波阈值降噪法相较于谱减法、子空间法和小波阈值法的硬阈值函数,输出信噪比提高了1 dB以上,降噪性能提升了15%左右;相较于小波阈值法的软阈值函数,当输入信噪比大于0 dB时,输出信噪比提高1 dB以上,可有效降低水流声信号中的机械设备噪声干扰。

基于谱图小波的神经精神疾病患者脑功能网络多尺度分析

基于图信号处理,针对神经精神病患者的脑功能网络展开研究,采用谱图小波变换对脑功能网络进行多尺度分析,根据实验数据构建图拉普拉斯矩阵,从中选取最大特征值对谱图小波变换滤波器进行设计。之后结合血氧水平依赖对比度信号计算出受试者各脑区的谱图小波系数,对其进行多尺度组间差异分析,发现脑功能网络在不同频段下的能量分布存有异常,并对对应的异常脑区予以明确。所采用的谱图小波变换是目前针对不规则数据域中信号展开多尺度分析的最有效方法之一,对其他疾病患者脑功能网络多尺度分析研究具有重要的现实意义。

奇异性信号检测时小波基的选择

奇异性信号往往带有一些重要信息，小波是奇异性检测的一种有力工具．本文研究了几种常用小波对不同奇异性信号的检测效果，通过对比分析，对不同的奇异性信号，推荐出了优先选用的小波基，并实际应用于刀具磨损时切削力信号的分析．

小波变换在突变信号识别中的应用

小波变换具有识别转动机械振动突变信号的特性。小波变换改进的单子带算法能有效识别第一类突变点,但对于第二类突变点却无法有效识别。进一步的研究发现,单子带改进算法对一些不需要的点作置零运算时,由于没有合理的过渡,使得对置零后的信号再进行傅里叶反变换时带入了许多噪音,造成对第二类突变信号无法有效识别。针对该问题,通过引入过渡函数,提出了进一步完善的单子带重构改进算法,解决了第二类突变信号的识别问题,并应用相关实例——泵刚度突变仿真数据进行分析,验证了方法的有效性。

基于小波变换奇异信号检测的研究

奇异信号中的奇异点及不规则的突变部分经常携带有比较重要的信息 ,它是信号重要的特征之一。用李氏指数 (Lipschitz)来描述信号的局部奇异性。证明了小波变换确实能用来检测信号的局部奇异性。而利用小波变换模的局部极大值和信号奇异点之间的关系 ,同样可以对信号的局部奇异性进行分析 ,而且运算量较小。证明了小波变换模极大值能够检测信号奇异性 ;分析了奇异信号检测时小波基的选择的条件。最后给出实例分析的结论 :为了有效地检测奇异信号的各种奇异性特征 。

基于小波奇异性检测的高压断路器故障诊断

高压断路器机械故障的出现不仅会引起振动冲击事件的时移 ,而且会引起时域波形中一些波峰形态的变化。基于小波变换的信号奇异性检测理论 ,可以求取振动信号包络的奇异性指数 ,作为特征参数用于故障诊断。对高压断路器合闸振动信号进行了分析 ,取得了较好的效果。

一种利用子波变换多尺度分辨特性的信号消噪技术

本文基于传统信号处理方法对非平稳信号的局限性，利用子波变换下奇异信号和随机噪声在多尺度空间中不同的模极大值传播特性设计了一种实用的子波消噪方法，对不同信号的仿真结果表明该方法既能提取一定的信噪比改善增益，同时又能保持对突变信息的良好分辨率，适合于一类非平稳信号进行时变处理．

小波分析在信号奇异性探测及瞬态信号检测中的应用

近年来,小波技术越来越成为一种有效的信号处理手段。本文介绍了小波的时频局部化和多尺度特性以及它在信号奇异性探测、瞬态信号检测领域中的应用。并以ECG信号分析为例,较全面地说明了小波在信号处理中的实现手段。最后,对小波可进一步应用的领域作了展望。

基于峰值信噪比和小波方向特性的图像奇异值去噪技术

提出一种利用小波变换子图像不同的方向特性和峰值信噪比进行奇异值分解的图像去噪算法。由于图像经过小波变换后,低频子图像集中了原图像的大部分能量噪声,故仅作简单维纳滤波;而噪声则主要集中在小波域中的三个不同方向的高频子图中,且系数较小,因此可以利用奇异值分解进行去噪处理,即用较大的奇异值和对应的特征向量重构出去噪图像,然而由于奇异值分解固有的行列方向性,对于高频对角线子图重构出的图像去噪效果不理想,故采取旋转至行列方向后再进行常用的奇异值滤波;最后将去噪后的低频和高频子图进行小波反变换重构出最终的去噪图像,其中重构所需的奇异值个数由图像的峰值信噪比确定。实验结果表明,该方法在有效去噪的同时较好的保留了原有的高频细节信息。

心音信号检测的一种新方法

本文为实现第一心音（Ｓ＿１）和第二心音（Ｓ＿２）的定位提出了一种新方法。对心音图（ＰＣＧ）信号进行预处理后，再利用小波变换原理检测信号的奇异点．达到准确定位的目的。这一检测方法已在心功能仪上成功地应用于测试Ｑ～Ｓ＿１和Ｑ～Ｓ＿２间期。

小波变换对突变信号峰值奇异点的精确检测

研究了小波变换对突变信号峰值奇异点的精确检测机理和方法,采用了离散小波变换的直接算法,避免了塔式算法在本检测方法中的某些局限性。通过模拟算例和应用实例的验证,证明即使在有严重噪声干扰的情况下,该方法也很容易实现对突变信号峰值奇异点的准确检测和精确定位,具有相当高的定位精度(其误差不大于1个采样点)和分析精度(不存在累积误差),同时具有较高的实时性。

基于新阈值函数的二进小波变换信号去噪研究

由于二进小波变换的小波基函数存在着一定的冗余,基于二进小波变换的去噪效果要好于离散小波变换的信号去噪·噪声阈值的准确估计和阈值函数的选择对去噪精度有着显著的影响·在分析高斯噪声的二进小波变换特性基础上,提出了一种改进的二进小波变换去噪方法·采用一种新的阈值函数,克服了Donoho软阈值方法中估计小波系数与分解小波系数存在恒定偏差的缺陷·仿真结果表明,改进的二进小波去噪方法不仅可以有效地抑制信号奇异点处的pseudo-Gibbs现象,而且消噪精度高于传统的软硬阈值方法·

爆破震动信号的小波分析与HHT变换

以实测的爆破震动信号为例,分别应用小波分析和HHT(Hilbert-Huang Transform)变换从不同方面进行对比分析,讨论了爆破震动信号的特征提取和时频分布。结果表明:小波分析和HHT变换都是处理非平稳信号的两种好方法,都能很好地提取信号的主要特征信息和进行滤波、消噪。然而,小波分析存在选择小波基的困难,而HHT变换不需要预先选择基函数,其EMD(empirical mode decomposition)得到的IMF(intrinsic mode function)能反映原始信号的固有特性,通常具有实际物理意义;小波谱的能量在频率范围内分布较宽,而Hilbert能量谱能清晰地表明能量随时频的具体分布,大部分能量都集中在有限的能量谱线上;小波分析中时间、频率分辨率受Heisenberg测不准原理的限制,而HHT变换中时间分辨率不变且精度很高,其频率分辨率则可随信号内在的特性进行自适应调节。分析表明:HHT变换在分析非平稳信号时较小波分析更具适应性,在岩石中波的传播、衰减规律、结构动态响应特征和爆破震动破坏等研究中有着广阔的应用前景。