Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

基于SVD-CWT和CNN的水轮发电机转子故障识别

水轮发电机转子振动故障识别是水电站运维的重难点问题,为此提出一种基于转子振动信号的故障识别方法。首先针对发电机转子的非平稳和非线性振动信号,采用奇异值分解(SVD)并结合能量差分谱理论进行降噪预处理;对预处理数据使用连续小波变换(CWT)转换为时频图并形成图像数据集;然后将该图像数据集作为卷积神经网络(CNN)输入,通过CNN多层池化及卷积形成分布式故障特征表达,最终实现发电机转子故障模式识别和分类。经实验验证,该方法准确率达到99.5%以上,能有效识别出发电机转子的故障类型。

基于向量残差SVD的混凝土超声测试温度效应研究

为研究温度对混凝土超声测试尾波信号的影响规律;将信号向量间的归一化夹角作为波动指标,反映温度效应引起的信号变化;通过向量残差矩阵SVD获得表征温度效应大小的特征向量,建立向量空间映射和温度差的数学关系。在实验室采集混凝土梁尾波信号进行验证,结果表明,随温度升高尾波信号的波形发生后移,文中方法可分段线性量化温度效应;基于量化结果,得到常温下超声尾波信号最敏感的温度区间;任意4.5℃范围内,可去除74%~90%的温度效应。

基于DK-SVD的深度学习电阻抗块稀疏成像方法研究

针对电阻抗层析成像逆问题的病态性和非线性,提出一种基于DK-SVD的电阻抗块稀疏图像重建方法。该算法通过多层感知器为每组测量数据提供最优的模型参数,以适应数据集的多样性,进一步提高成像质量,并在稀疏编码阶段采用迭代收缩阈值算法加快收敛速度。仿真实验结果表明DK-SVD算法重建图像的结构相似性可达到0.95以上,误差可控制在0.1左右,平均重建速度为0.034 s,有效地提高了电阻抗层析成像的质量和效率,且经进一步实验证明了该算法具有良好的噪声鲁棒性和实际应用价值。

基于自适应动态粒子群优化的RAK-SVD方法

K均值奇异值分解(K-SVD)算法是一种行之有效的地震资料去噪方法,但由于其稀疏分解存在不确定性,需要引入正则项对其改进。为此,在常规粒子群算法的基础上,提出了一种自适应动态粒子群算法优化正则化参数的正则化近似K-SVD(RAK-SVD)去噪方法。首先通过修改字典原子和相关参数,解决了由于常规粒子群算法的惯性参数固定不变,导致后期搜索效率下降的问题;其次将正则化系数引入近似K-SVD(AK-SVD)方法,明显提升了去噪效果;最后利用自适应动态粒子群算法自动优选AK-SVD方法中的正则化参数,提高了稀疏分解的确定性,在对强反射信号进行去噪的同时加强了对弱信号的保护。模型测试和实际应用均表明,该方法有利于弱信号的提取和识别,不仅能够显著改善弱地震信号的去噪效果,还提升了计算效率。该方法具有一定的实际应用价值。

基于SVD-ILMD的暂态电能质量扰动定位检测方法

为实现对电网非平稳扰动信号的快速、准确分析,提出了融合SVD(奇异值分解)与ILMD(优化局部均值分解)的暂态电能质量扰动定位检测方法。首先,通过ILMD与模糊隶属度函数阈值处理噪声信息,削弱噪声干扰;然后,构造差值信号并利用滑窗SVD增强扰动特征,进一步抑制噪声干扰;最后,基于特征增强信号提出一种自适应阈值截断的暂态电能质量扰动定位检测方法。经仿真分析与算法对比,验证了所提方法定位准确、抗噪性强、计算量小,对过零与微弱扰动也有较好的定位效果。

Multi-resolution graph-based clustering analysis for lithofacies identifi cation from well log data: Case study of intraplatform bank gas fi elds, Amu Darya Basin

In this study, we used the multi-resolution graph-based clustering （MRGC） method for determining the electrofacies （EF） and lithofacies （LF） from well log data obtained from the intraplatform bank gas fields located in the Amu Darya Basin. The MRGC could automatically determine the optimal number of clusters without prior knowledge about the structure or cluster numbers of the analyzed data set and allowed the users to control the level of detail actually needed to define the EF. Based on the LF identification and successful EF calibration using core data, an MRGC EF partition model including five clusters and a quantitative LF interpretation chart were constructed. The EF clusters 1 to 5 were interpreted as lagoon, anhydrite flat, interbank, low-energy bank, and high-energy bank, and the coincidence rate in the cored interval could reach 85%. We concluded that the MRGC could be accurately applied to predict the LF in non-cored but logged wells. Therefore, continuous EF clusters were partitioned and corresponding LF were characteristics ＆different LF were analyzed interpreted, and the distribution and petrophysical in the framework of sequence stratigraphy.

Multi-resolution image segmentation based on Gaussian mixture model

Mixture model based image segmentation method, which assumes that image pixels are independent and do not consider the position relationship between pixels, is not robust to noise and usually leads to misclassification. A new segmentation method, called multi-resolution Ganssian mixture model method, is proposed. First, an image pyramid is constructed and son-father link relationship is built between each level of pyramid. Then the mixture model segmentation method is applied to the top level. The segmentation result on the top level is passed top-down to the bottom level according to the son-father link relationship between levels. The proposed method considers not only local but also global information of image, it overcomes the effect of noise and can obtain better segmentation result. Experimental result demonstrates its effectiveness.

Winter wheat identification by integrating spectral and temporal information derived from multi-resolution remote sensing data

Timely crop acreage and distribution information are the basic data which drive many agriculture related applications.For identifying crop types based on remote sensing,methods using only a single image type have significant limitations.Current research that integrates fine and coarser spatial resolution images,using techniques such as unmixing methods,regression models,and others,usually results in coarse resolution abundance without sufficient detail within pixels,and limited attention has been paid to the spatial relationship between the pixels from these two kinds of images.Here we propose a new solution to identify winter wheat by integrating spectral and temporal information derived from multi-resolution remote sensing data and determine the spatial distribution of sub-pixels within the coarse resolution pixels.Firstly,the membership of pixels which belong to winter wheat is calculated using a 25-m resolution resampled Landsat Thematic Mapper(TM)image based on the Bayesian equation.Then,the winter wheat abundance(acreage fraction in a pixel)is assessed by using a multiple regression model based on the unique temporal change features from moderate resolution imaging spectroradiometer(MODIS)time series data.Finally,winter wheat is identified by the proposed Abundance-Membership(AM)model based on the spatial relationship between the two types of pixels.Specifically,winter wheat is identified by comparing the spatially corresponding 10×10 membership pixels of each abundance pixel.In other words,this method takes advantage of the relative size of membership in a local space,rather than the absolute size in the entire study area.This method is tested in the major agricultural area of Yiluo Basin,China,and the results show that acreage accuracy(Aa)is 93.01%and sampling accuracy(As)is 91.40%.Confusion matrix shows that overall accuracy(OA)is 91.4%and the kappa coefficient(Kappa)is 0.755.These values are significantly improved compared to the traditional Maximum Likelihood classification(MLC)and Random Forest classification(RFC)which rely on spectral features.The results demonstrate that the identification accuracy can be improved by integrating spectral and temporal information.Since the identification of winter wheat is performed in the space corresponding to each MODIS pixel,the influence of differences of environmental conditions is greatly reduced.This advantage allows the proposed method to be effectively applied in other places.

基于SVD和1DCNN的滚动轴承故障诊断

为实现轴承故障的诊断,本文提出一种基于奇异值分解(SVD)和一维卷积神经网络(1DCNN)的分类算法,即将一维信号转为二维数据并重构,建立检测模型,将重构信号和原始信号分别输入1DCNN模型检测,最后通过混淆矩阵和准确率评估模型。结果显示,SVD结合1DCNN模型比传统1DCNN模型在不同工况下的准确率提高了1.57%和0.4%,具有一定参考价值。

Multi-sensor image registration using multi-resolution shape analysis

Multi-sensor image registration has been widely used in remote sensing and medical image field, but registration performance is degenerated when heterogeneous images are involved. An image registration method based on multi-resolution shape analysis is proposed in this paper, to deal with the problem that the shape of similar objects is always invariant. The contours of shapes are first detected as visual features using an extended contour search algorithm in order to reduce effects of noise, and the multi-resolution shape descriptor is constructed through Fourier curvature representation of the contour’s chain code. Then a minimum distance function is used to judge the similarity between two contours. To avoid the effect of different resolution and intensity distribution, suitable resolution of each image is selected by maximizing the consistency of its pyramid shapes. Finally, the transformation parameters are estimated based on the matched control-point pairs which are the centers of gravity of the closed contours. Multi-sensor Landsat TM imagery and infrared imagery have been used as experimental data for comparison with the classical contour-based registration. Our results have been shown to be superior to the classical ones.

基于APSO-SSD-SVD的特高压换流站OLTC振动信号降噪方法

随着中国特高压交直流换流站的大规模投运,有载分接开关(on-load tap changer, OLTC)已成为特高压换流站中发生故障较多的设备之一。针对强背景噪声环境下特高压换流站OLTC故障特征难以提取的问题,提出一种基于自适应粒子群算法优化奇异谱分解和奇异值分解的方法。首先,利用自适应粒子群优化(adaptive particle swarm optimization, APSO)算法对奇异谱分解算法中的模态参数进行优化,选取最优分解模态数。其次,基于最大峭度准则选取最佳奇异谱分量。然后,确定最佳重构阶数,通过奇异值分解重构信号,从而达到信号降噪的目的。将所提方法应用于仿真信号和实验信号,结果表明所提方法的信噪比达到23.302,均方根误差仅为0.004,并且波形相似参数高达0.998,优于其他降噪方法。所提方法能够更有效地实现对特高压换流站OLTC振动信号的降噪,为辅助运维人员诊断OLTC状态提供参考。

MULTI-RESOLUTION MOTION ESTIMATION AND COMPENSATION BASED ON ADJACENT PREDICTION OF FRAME DIFFERENCE IN WAVELET DOMAIN

Aiming at the higher bit-rate occupation of motion vector encoding and more time load of full-searching strategies, a multi-resolution motion estimation and compensation algorithm based on adjacent prediction of frame difference was proposed.Differential motion detection was employed to image sequences and proper threshold was adopted to identify the connected region.Then the motion region was extracted to carry out motion estimation and motion compensation on it.The experiment results show that the encoding efficiency of motion vector is promoted, the complexity of motion estimation is reduced and the quality of the reconstruction image at the same bit-rate as Multi-Resolution Motion Estimation(MRME) is improved.

Automatic target tracking on multi-resolution terrain

We propose a high-performance path planning algorithm for automatic target tracking in the applications of real-time simulation and visualization of large-scale terrain datasets, with a large number of moving objects （such as vehicles） tracking multiple moving targets. By using a modified Dijkstra＇s algorithm, an optimal path between each vehicle-target pair over a weighted grid-presented terrain is computed and updated to eliminate the problem of local minima and losing of tracking. Then, a dynamic path re-planning strategy using multi-resolution representation of a dynamic updating region is proposed to achieve high-performance by trading-off precision for efficiency, while guaranteeing accuracy. Primary experimental results showed that our algorithm successfully achieved l0 to 96 frames per second interactive path-replanning rates during a terrain simulation scenario with 10 to 100 vehicles and multiple moving targets.

Application of multi-resolution analysis in sonar image denoising

Sonar images have complex background, low contrast, and deteriorative edges; these characteristics make it difficult for researchers to dispose the sonar objects. The multi-resolution analysis represents the signals in different scales efficiently, which is widely used in image processing. Wavelets are successful in disposing point discontinuities in one dimension, but not in two dimensions. The finite Ridgelet transform （FRIT） deals efficiently with the singularity in high dimension. It presents three improved denoising approaches, which are based on FRIT and used in the sonar image disposal technique. By experiment and comparison with traditional methods, these approaches not only suppress the artifacts, but also obtain good effect in edge keeping and SNR of the sonar image denoising.

Multi-resolution EMD and classscatter matrix extracting of tank sound

The acoustic vibration signal of tank is disassembled into the sum of intrinsic mode function （IMF） by multi-resolution empirical mode decomposition （EMD） method. The instantaneous frequency is obtained, and feature transformation matrix is figured out by class scatter matrix. Multi- dimensional scale energy vector is mapped into low-dimensional eigenvector, and classification extraction is realized. This method sufficiently separates of different sound target features. The test result indicates that it is effective.

Magnetic-resonance image segmentation based on improved variable weight multi-resolution Markov random field in undecimated complex wavelet domain

To solve the problem that the magnetic resonance(MR)image has weak boundaries,large amount of information,and low signal-to-noise ratio,we propose an image segmentation method based on the multi-resolution Markov random field(MRMRF)model.The algorithm uses undecimated dual-tree complex wavelet transformation to transform the image into multiple scales.The transformed low-frequency scale histogram is used to improve the initial clustering center of the K-means algorithm,and then other cluster centers are selected according to the maximum distance rule to obtain the coarse-scale segmentation.The results are then segmented by the improved MRMRF model.In order to solve the problem of fuzzy edge segmentation caused by the gray level inhomogeneity of MR image segmentation under the MRMRF model,it is proposed to introduce variable weight parameters in the segmentation process of each scale.Furthermore,the final segmentation results are optimized.We name this algorithm the variable-weight multi-resolution Markov random field(VWMRMRF).The simulation and clinical MR image segmentation verification show that the VWMRMRF algorithm has high segmentation accuracy and robustness,and can accurately and stably achieve low signal-to-noise ratio,weak boundary MR image segmentation.

Fast image super-resolution algorithm based on multi-resolution dictionary learning and sparse representation

Sparse representation has attracted extensive attention and performed well on image super-resolution（SR） in the last decade. However, many current image SR methods face the contradiction of detail recovery and artifact suppression. We propose a multi-resolution dictionary learning（MRDL） model to solve this contradiction, and give a fast single image SR method based on the MRDL model. To obtain the MRDL model, we first extract multi-scale patches by using our proposed adaptive patch partition method（APPM）. The APPM divides images into patches of different sizes according to their detail richness. Then, the multiresolution dictionary pairs, which contain structural primitives of various resolutions, can be trained from these multi-scale patches.Owing to the MRDL strategy, our SR algorithm not only recovers details well, with less jag and noise, but also significantly improves the computational efficiency. Experimental results validate that our algorithm performs better than other SR methods in evaluation metrics and visual perception.

基于CRS-LMD和SVD的MMC-HVDC线路故障测距方法

直流输电线路故障行波波速不确定、波头提取困难以及噪声干扰等因素制约了直流电网中故障测距技术的应用。为了降低上述因素对定位准确性的影响,提出一种基于局部特征有理样条插值均值分解(LMD based on characteristic rational spline,CRS-LMD)和奇异值分解(singular value decomposition,SVD)的故障测距方法。首先,利用特征尺度选取最优极点系数,结合有理样条插值调节拟合曲线的松紧程度,实现对故障电压行波的局部均值分解。其次,采用奇异值分解对故障行波波头进行准确提取。最后,在PSCAD/EMTDC中搭建了张北±500 kV柔性直流电网的仿真模型,模拟各种故障情况并输出故障数据,利用Matlab对故障数据进行处理并验证定位算法。最后,仿真结果表明,所提故障测距算法在不同故障距离和故障类型下均能实现故障测距,且在叠加噪声和过渡电阻的情况下也能保障较高的精确性。

Convergence to Steady-State Solutions of the New Type of High-Order Multi-resolution WENO Schemes: a Numerical Study

A new type of high-order multi-resolution weighted essentially non-oscillatory(WENO)schemes(Zhu and Shu in J Comput Phys,375:659-683,2018)is applied to solve for steady-state problems on structured meshes.Since the classical WENO schemes(Jiang and Shu in J Comput Phys,126:202-228,1996)might suffer from slight post-shock oscillations(which are responsible for the residue to hang at a truncation error level),this new type of high-order finite-difference and finite-volume multi-resolution WENO schemes is applied to control the slight post-shock oscillations and push the residue to settle down to machine zero in steady-state simulations.This new type of multi-resolution WENO schemes uses the same large stencils as that of the same order classical WENO schemes,could obtain fifth-order,seventh-order,and ninth-order in smooth regions,and could gradually degrade to first-order so as to suppress spurious oscillations near strong discontinuities.The linear weights of such new multi-resolution WENO schemes can be any positive numbers on the condition that their sum is one.This is the first time that a series of unequal-sized hierarchical central spatial stencils are used in designing high-order finitedifference and finite-volume WENO schemes for solving steady-state problems.In comparison with the classical fifth-order finite-difference and finite-volume WENO schemes,the residue of these new high-order multi-resolution WENO schemes can converge to a tiny number close to machine zero for some benchmark steady-state problems.