分数阶对称平移不变过完备小波的构造及其在轴承故障诊断中的应用

提出了一种分数阶的对称性近似平移不变过完备小波的构造方法.首先,给出一种构造具有对称性且具有最小长度的低通滤波器方法.其次,通过拓普利兹矩阵分解法求出对应的具有近似平移不变性的高通滤波器,此方法比其他分解方法具有更低的计算复杂度.此外,利用此构造方法,也得到具有更高阶消失矩的分数阶过完备小波变换.最后,将构造出的分数阶对称平移不变过完备小波应用到轴承故障诊断中.实验结果表明,提出的小波变换能有效地提取出轴承的故障特征.     

基于小波不变矩和保局投影的表面缺陷识别方法

提出了一种基于小波矩不变量和保局投影(LPP)的特征提取方法,并应用于中厚板表面缺陷自动识别.首先对图像做三级小波变分解,将中厚板表面图像的细节分解到各个尺度的各个分量中并利用小波阈值收缩法降噪;然后对各分量的傅里叶幅值谱提取Hu不变矩作为原始特征向量,并利用LPP将该特征向量的维数从77维降到8维;最后利用AdaBoost分类器对样本进行分类识别.实验结果表明,本文提出的特征提取方法适用于中厚板表面缺陷分类,识别率达到91.60%.     

基于形态非抽样小波和S变换的轧机振动信号分析

为了确定板带连轧中多台轧机振动的起振顺序,首先在形态非抽样小波一般框架的基础上,构造了一种基于多尺度平均滤波器的形态非抽样小波.然后通过仿真实验,得到此形态非抽样小波尺度与频率之间的关系.最终利用基于多尺度平均滤波器的形态非抽样和S变换的方法对轧机振动信号进行分析,成功提取了故障频率的起振时间,确定了轧机的起振顺序.     

带钢缺陷图像局域方差相异度的融合规则研究

当前应用在带钢表面缺陷图像的基于单个系数点的融合规则和基于区域系数特征的融合规则存在片面性、容易使融合图像失真等问题.针对以上问题,给出了一种新的融合规则.该融合规则在对小波分解后的高频子带进行融合时,充分考虑待融合图像的局域方差的相异度,并利用阈值来选择合适的融合规则.实验结果表明,该方法可以更好地保留图像的细节特征,且在冷轧带钢表面缺陷图像融合中有较好的适用性,具有一定的工程应用价值.     

互为Hilbert变换对的正交小波构造及其应用

提出一种互为Hilbert变换对的小波代数构造方法.这种互为Hilbert变换对的小波基的构造是从构造小波的充要条件入手,利用延迟滤波器的思想,把问题化为代数方程组求解.该方法可以避免进行谱分解.经实验证实:由基于本文构造的小波对的对偶树复小波变换可以得到比离散小波变换更好的特征提取效果.     

小波在分析流态化系统多尺度动态行为中的应用

利用小波分解方法,对用激光相位多普勒颗粒分析仪（ＰＤＰＡ）、光纤探针及压差传感器同时测得的二维循环流化床中的信号进行了分解,并对分解信号和三种原始信号进行了比较。研究表明：将动态过程分解为三种尺度是合理的,ＰＤＰＡ信号包含了循环流化床所有尺度的全部信息。分解后三种尺度信号均具有混沌性态,但可预测性比原始信号好,为增加对动态过程的认知和建立较好的动态表达模型提供了途径。     

基于小波变换的闪烁背光LCD响应时间估算

为了更准确、方便地估算闪烁背景光下的LCD液晶响应时间,利用小波变换法对测量得到的LCD亮度响应曲线进行滤波.通过实际测量连续背景光下五级灰度之间的液晶响应以及闪烁背景光的背景光响应,构造了闪烁背景光下的LCD亮度响应,利用小波变换滤波方法,通过小波分解、阈值处理、逆变换重构,还原了液晶响应信号,将估算得到的响应时间与真实值以及移动窗口积分方法的估算值进行比较.根据计算,移动窗口积分法的平均估算误差为7.535 5%,而小波变换滤波法的平均估算误差仅为1.966 5%.结果表明,小波变换滤波法对闪烁背景光技术下LCD液晶响应时间的估计比移动窗口积分法更加准确,而且应用简单,适应面广.     

多分辨小波控制器在轧辊偏心控制中的应用

提出了一种用于轧辊偏心控制的多分辨小波控制器,它利用小波对轧制力信号进行多分辨分解.机架的轧制力中包含着许多潜在因素的累积影响,比如压下环节的动特性、轧辊偏心、测量噪声、外部干扰等,这些影响体现在不同的尺度上.通过小波的多分辨分解,这些不同尺度上的信息被区分开来,然后在控制中对轧辊偏心进行补偿.仿真实验表明该方法是有效的.     

小波分析在钢筋混凝土梁损伤识别中的应用

为识别钢筋混凝土简支梁的损伤状况,对简支梁进行了逐级加载实验,每级加荷后卸荷,观测梁的裂缝,并测定梁的动力反应.将钢筋混凝土简支梁作为无限自由度体系,并对该体系的动力方程进行小波变换,得到多尺度下的结构动力响应表达式.信号经多尺度分解后,包含了信号中更多的结构损伤信息.基于此,用DASP信号处理系统对钢筋混凝土简支梁各损伤阶段的动态信号进行二进制小波分解,通过分析各频段的波形,确定了梁的损伤.     

形态小波在中厚板表面裂纹缺陷检测中的应用

中厚板表面裂纹缺陷在图像中容易受背景噪声和氧化铁皮的影响,传统的图像处理方法很难将裂纹缺陷从图像中检测出来.提出了将形态小波变换应用于中厚板表面裂纹缺陷检测的方法.该方法利用小波分解对突变信号的检测能力,结合裂纹缺陷在形态上近似于直线的性质,将裂纹缺陷从图像中准确提取出来.实验证明形态小波用来检测中厚板表面裂纹缺陷比用其他方法更有效.     

Bias in mean frequency estimation of Doppler signals due to wall clutter filters

Wall clutter filters used in Doppler ultrasound systems give rise to a bias in the mean frequency estimation. This effect has been explored for two second order filters: the initialised infinite impulse response (IIR)-type filter, and the finite impulse response (FIR) echo-canceller filter. These are used in conjunction with two mean frequency estimation algorithms: the FFT-based intensity-weighted-mean algorithm, and the autocorrelation algorithm. The bias is shown to be caused by the finite settling times of the filters. The IIR filter, although having a much better frequency response than the FIR filter, has a greater bias associated with it. A compromise between bias and frequency response is suggested and a simple method of bias correction is described.     

多分辨率小波极限学习机

针对一类具有空间不均匀性的辨识和回归问题,提出了基于小波分析的极限学习机方法.从多分辨率分析的思想出发,构造一簇紧支撑正交小波作为隐层激活函数,并利用改进的误差最小化极限学习机训练输出层权重,避免了新加入高分辨率子网络后的重新训练.同时,由一维多分辨分析的张量积构造了二维多分辨小波极限学习机.进而通过脊波变换将小波学习机扩展到高维空间,对脊波函数的伸缩、方向和位置参数进行优化计算.对具有奇异性的函数仿真结果证明,与标准极限学习机相比,小波极限学习机由于其聚微性能在极短的训练时间内更好地逼近目标.一些实际基准回归问题上的测试验证了脊波极限学习机在其中大部分问题上达到更高的训练和泛化精度.     

Random Field Representation in a Biorthogonal Wavelet Basis

This paper develops a new representation scheme for random fields, which can be used in a variety of mechanics applications, based upon the projection onto a biorthogonal wavelet basis. The merits of such a scheme can be shown to result from the relaxation of the condition of orthonormality, while still requiring compact support of the basis functions. Earlier methods have relied on the diagonalization properties of wavelets to demonstrate how the Daubechies family of orthonormal wavelets is effective in weakening the correlation across scales for a large class of random processes. It is shown that biorthogonal processes achieve better decorrelation owing to the fact that fewer filter coefficients are needed to maintain the same support of basis functions when compared to the Daubechies family. Numerical examples of fields encountered in earthquake engineering and other applications are given.     

Digital mammography: M-channel quadrature mirror filters (QMFs) for microcalcification extraction

Multiresolution methods are reported for feature extraction in breast cancer screening using digital mammography. The initial application is directed at the detection of microcalcification clusters (MCCs). Quadrature mirror filter (QMF) banks, using both two and three channel are proposed for the first time for both multiresolution decomposition and reconstruction. These filters are specifically tailored for automatic extraction of MCCs. The QMF multiresolution methods are compared to two channel tree structured wavelet transforms (TSWTs) methods previously reported. The QMF filters are preceded by an advanced tree structured nonlinear filter for noise suppression, prior to feature extraction, in order to minimize the false positive (FP) detection rate in digital mammography. The relative performance of these methods were evaluated using both simulated images and fifteen representative digitized mammograms containing biopsy proven microcalcification clusters. Similar high sensitivity (true positive (TP) detection rate (100%) and high specificity (0.6 average false positive (FP) MCC's/image) were observed, substantially better than more traditional approaches using single scale filters. The three channel QMF method, however, demonstrated better detail preservation of MCC's extracted compared to the two channel method. Detail preservation is important for the characterization of MCC's or individual microcalcifications in cancer screening.     

Wavelet-Based Approach for Structural Damage Detection

A wavelet-based approach is proposed for structural damage detection and health monitoring. Characteristics of representative vibration signals under the wavelet transformation are examined. The methodology is then applied to simulation data generated from a simple structural model subjected to a harmonic excitation. The model consists of multiple breakable springs, some of which may suffer irreversible damage when the response exceeds a threshold value or the number of cycles of motion is accumulated beyond their fatigue life. In cases of either abrupt or accumulative damages, occurrence of damage and the moment when it occurs can be clearly determined in the details of the wavelet decomposition of these data. Similar results are observed for the real acceleration data of the seismic response recorded on the roof of a building during the 1971 San Fernando earthquake. Effects of noise intensity and damage severity are investigated and presented by a detectability map. Results show the great promise of the wavelet approach for damage detection and structural health monitoring.     

Denoising of the uterine EHG by an undecimated wavelet transform

We propose two original methods of denoising of the uterine electrohysterography (EHG) signal by wavelets. This external electrophysiological signal is corrupted by electronic, electromagnetic noises and by the remaining electrocardiogram of the mother. The interfering signals have overlapping spectra. Therefore, a classical filtering is unusable. Wavelets should be a very well-suited denoising tool. The first proposed method uses the algorithm "à trou" with nonsymmetrical filters. The computation is rapid and the results are satisfying compared to the classical denoising techniques. The second algorithm is an improvement of the first method. It uses orthogonal wavelets and the result of the thresholding corresponds to the average of all circulant shifts denoised by a decimated wavelet transform. Results are compared to traditional denoising algorithms by wavelet (orthogonal, maximally decimated). The proposed algorithms are more efficient on simulated signals as well as on uterine EHG.     

Optimally weighted wavelet transform based on supervised training for detection of microcalcifications in digital mammograms

We are developing a computer-aided diagnosis (CAD) scheme for detection of clustered microcalcifications in digital mammograms. The use of an empirically chosen wavelet and scale combination for detection of microcalcifications as an initial step of the CAD scheme has been reported by us previously. In this study, we developed a technique for optimizing the weights at individual scales in the wavelet transform to improve the performance of our CAD scheme based on the supervised learning method. In the learning process, an error function was formulated to represent the difference between a desired output and the reconstructed image obtained from weighted wavelet coefficients for a given mammogram. The error function was then minimized by modifying the weights for wavelet coefficients by means of a conjugate gradient algorithm. The Least Asymmetric Daubechies' wavelets were optimized with 297 regions of interest (ROIs) as a training set by a jackknife method. The performance of the optimally weighted wavelets was evaluated by means of receiver-operating characteristic (ROC) analysis by use of the above set of ROIs. The analysis yielded an average area under the ROC curve of 0.92, which outperforms the difference-image technique used in our existing CAD scheme, as well as the partial reconstruction method used in our previous study.     

基于自适应形态小波的轧机电气信号压缩方法

针对非线性、非平稳信号的数据压缩问题,提出了一种基于自适应形态小波的轧机电气信号压缩方法.结合电气信号的形态特征,采用中值算子作为形态小波的更新算子对信号进行分解,从而实现根据信号的局部形态特征,自适应地调整形态小波分解的更新算子.工业现场实际轧机电气信号的数据压缩实验证明:利用这种形态小波信号压缩方法,可以获得高压缩比的信号,并能保留信号的形态特征;同时,这种形态小波信号压缩方法运算量小,可以应用到实时性要求较高的在线监测系统中.