Contourlet watermarking algorithm based on Arnold scrambling and singular value decomposition

A new digital watermarking algorithm based on the contourlet transform is proposed to improve the robustness and anti-attack performances of digital watermarking. The algorithm uses the Arnold scrambling technique and the singular value decomposition （SVD） scheme. The Arnold scrambling technique is used to preprocess the watermark, and the SVD scheme is used to find the best suitable hiding points. After the contourlet transform of the carrier image, intermediate frequency sub-bands are decomposed to obtain the singularity values. Then the watermark bits scrambled in the Arnold rules are dispersedly embedded into the selected SVD points. Finally, the inverse contourlet transform is applied to obtain the carrier image with the watermark. In the extraction part, the watermark can be extracted by the semi-blind watermark extracting algorithm. Simulation results show that the proposed algorithm has better hiding and robustness performances than the traditional contourlet watermarking algorithm and the contourlet watermarking algorithm with SVD. Meanwhile, it has good robustness performances when the embedded watermark is attacked by Gaussian noise, salt- and-pepper noise, multiplicative noise, image scaling and image cutting attacks, etc. while security is ensured.

The Singular Value Decomposition Analysis between Summer Precipitation in the Dongting Lake Region and the Global Sea Surface Temperature

By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation and their correlations with SST are analyzed.The coupling relationship between the anomalous distribution in summer precipitation and the variation of SST has between studied with the Singular Value Decomposition(SVD) analysis.The increase or decrease of summer precipitation in the Dongting Lake region is closely associated with the SST anomalies in three key regions.The variation of SST in the three key regions has been proved to be a significant previous signal to anomaly of summer rainfall in Dongting region.

DIRECT PERTURBATION METHOD FOR REANALYSIS OF MATRIX SINGULAR VALUE DECOMPOSITION

The perturbational reanalysis technique of matrix singular value decomposition is applicable to many theoretical and practical problems in mathematics, mechanics, control theory, engineering, etc.. An indirect perturbation method has previously been proposed by the author in this journal, and now the direct perturbation method has also been presented in this paper. The second-order perturbation results of non-repeated singular values and the corresponding left and right singular vectors are obtained. The results can meet the general needs of most problems of various practical applications. A numerical example is presented to demonstrate the effectiveness of the direct perturbation method.

PERTURBATION METHOD FOR REANALYSIS OF THE MATRIX SINGULAR VALUE DECOMPOSITION

The perturbation method for the reanalysis of the singular value decomposition (SVD) of general real matrices is presented in this paper. This is a simple but efficient reanalysis technique for the SVD, which is of great worth to enhance computational efficiency of the iterative analysis problems that require matrix singular value decomposition repeatedly. The asymptotic estimate formulas for the singular values and the corresponding left and right singular vectors up to second-order perturbation components are derived. At the end of the paper the way to extend the perturbation method to the case of general complex matrices is advanced.

Analysis of heart rate variability based on singular value decomposition entropy

Assessing the dynamics of heart rate fluctuations can provide valuable information about heart status. In this study, regularity of heart rate variability （HRV） of heart failure patients and healthy persons using the concept of singular value decomposition entropy （SvdEn） is analyzed. SvdEn is calculated from the time series using normalized singular values. The advantage of this method is its simplicity and fast computation. It enables analysis of very short and non-stationary data sets. The results show that SvdEn of patients with congestive heart failure （CHF） shows a low value （SvdEn： 0.056±0.006, p 〈 0.01） which can be completely separated from healthy subjects. In addition, differences of SvdEn values between day and night are found for the healthy groups. SvdEn decreases with age. The lower the SvdEn values, the higher the risk of heart disease. Moreover, SvdEn is associated with the energy of heart rhythm. The results show that using SvdEn for discriminating HRV in different physiological states for clinical applications is feasible and simple.

Detection and correction of level echo based on generalized S-transform and singular value decomposition

The echo of the material level is non-stationary and contains many singularities.The echo contains false echoes and noise,which affects the detection of the material level signals,resulting in low accuracy of material level measurement.A new method for detecting and correcting the material level signal is proposed,which is based on the generalized S-transform and singular value decomposition(GST-SVD).In this project,the change of material level is regarded as the low speed moving target.First,the generalized S-transform is performed on the echo signals.During the transformation process,the variation trend of window of the generalized S-transform is adjusted according to the frequency distribution characteristics of the material level echo signal,achieving the purpose of detecting the signal.Secondly,the SVD is used to reconstruct the time-frequency coefficient matrix.At last,the reconstructed time-frequency matrix performs an inverse transform.The experimental results show that the method can accurately detect the material level echo signal,and it can reserve the detailed characteristics of the signal while suppressing the noise,and reduce the false echo interference.Compared with other methods,the material level measurement error does not exceed 4.01%,and the material level measurement accuracy can reach 0.40%F.S.

The Singular Value Decomposition as a Tool of Investigating Central MHD Instabilities in the HL-1M Tokamak

A variety of strong MHD instabilities are always resulted from MHD activity of Tokamak plasmas. Central MHD instabilities can be observed with pinhole cameras to record soft x-ray (SXR) emission from the plasma along many chords with a high temporal resolution. The investigation of MHD instabilities often necessitates an analysis on spatial-temporal signals. The method of Singular Value Decomposition (SVD) can split such signals into orthogonal spatial and temporal vectors. By this means, the repetition time and the characteristic radius of various MHD phenomena such as sawteeth and snake-like perturbation can be obtained. Moreover, the (1,1) MHD mode is analyzed in great detail by SVD and used to determine the radius of the q = 1 surface.

A TRUST-REGION METHOD FOR SOLVING TRUNCATED COMPLEX SINGULAR VALUE DECOMPOSITION

The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,etc.In this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et al.is presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence rate.Numerical experiments are provided to illustrate the efficiency of the proposed method.Comparisons with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach.

On the Application of Adomian Decomposition Method to Special Equations in Physical Sciences

The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations.

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。

基于SVD-K-means算法的软扩频信号伪码序列盲估计

针对通信中软扩频信号伪码序列盲估计困难的问题,提出一种奇异值分解(singular value decomposition,SVD)和K-means聚类相结合的方法。该方法先对接收信号按照一倍伪码周期进行不重叠分段构造数据矩阵。其次对数据矩阵和相似性矩阵分别进行SVD完成对伪码序列集合规模数的估计、数据降噪、粗分类以及初始聚类中心的选取。最后通过K-means算法优化分类结果,得到伪码序列的估计值。该算法在聚类之前事先确定聚类数目,大大减少了迭代次数。同时实验结果表明,该算法在信息码元分组小于5 bit,信噪比大于-10 dB时可以准确估计出软扩频信号的伪码序列,性能较同类算法有所提升。

二级减速器故障系统建模及SVD-MMSE劣化评估

为检测故障齿轮劣化程度并进行有效的程度评估,通过有限元法建立含有正常、裂纹和断齿等3种齿轮状态的二级直齿轮减速器系统模型。首先,分别计算3种状态的齿轮时变啮合刚度,并综合考虑轴承支撑刚度,得到了3种不同状态下的轴承振动响应;其次,引入多元多尺度样本熵(multivariate multiscale sample entropy,简称MMSE)对故障齿轮的劣化程度进行分析;最后,引进奇异值分解(singular value decomposition,简称SVD)算法进行预处理,以达到更好的诊断效果来综合评定故障齿轮生命周期的劣化程度。结果表明:齿轮发生故障时,主要导致时频域信号发生转频调制,时域存在有规律的冲击,频域出现边频带,且分布在输入轴的转频及其倍频和啮频及其倍频处;随着故障程度的增加,劣化越发明显,频率成分也发生改变,致使MMSE值也随之变化,且整体呈单调递减趋势;SVD-MMSE算法能有效地对齿轮故障程度进行判别,降低了噪声对于劣化程度检测准确性的影响。

DeepSVDNet:A Deep Learning-Based Approach for Detecting and Classifying Vision-Threatening Diabetic Retinopathy in Retinal Fundus Images

Artificial Intelligence(AI)is being increasingly used for diagnosing Vision-Threatening Diabetic Retinopathy(VTDR),which is a leading cause of visual impairment and blindness worldwide.However,previous automated VTDR detection methods have mainly relied on manual feature extraction and classification,leading to errors.This paper proposes a novel VTDR detection and classification model that combines different models through majority voting.Our proposed methodology involves preprocessing,data augmentation,feature extraction,and classification stages.We use a hybrid convolutional neural network-singular value decomposition(CNN-SVD)model for feature extraction and selection and an improved SVM-RBF with a Decision Tree(DT)and K-Nearest Neighbor(KNN)for classification.We tested our model on the IDRiD dataset and achieved an accuracy of 98.06%,a sensitivity of 83.67%,and a specificity of 100%for DR detection and evaluation tests,respectively.Our proposed approach outperforms baseline techniques and provides a more robust and accurate method for VTDR detection.

基于增广SVD-MWKF的激励识别与结构响应重构

针对传统卡尔曼滤波算法在结构响应重构应用中需要外部激励及测量噪声方差先验已知的问题,提出一种基于增广SVD-MWKF(Singular Value Decomposition-Moving Window Kalman Filter)的激励识别与结构响应重构方法。首先,引入奇异值分解降噪技术以优化移动窗口法对测量噪声方差的实时估计。随后使用基于增广状态空间方程的卡尔曼滤波算法并结合部分测点的加速度测量数据,实现对结构外部激励的识别及各位置的速度、加速度响应的重构。最后,对起重机桁架和简支梁分别进行数值模拟和试验分析,结果表明,相较于移动窗口法,所提方法对测量噪声方差估计更加准确,且对外部激励能进行有效识别。

基于SVD-Schmidt正交化的压缩感知测量矩阵的优化

压缩感知(CS)理论中测量矩阵的性能优劣直接影响信号重构性能。为了优化测量矩阵提高其重构性能,本文提出了一种基于奇异值分解-施密特(SVD-Schmidt)正交化的CS测量矩阵优化方法。首先对测量矩阵进行奇异值分解(SVD)并选择最大的奇异值替换原来的奇异值形成新的矩阵,同时对其进行施密特正交化,对矩阵的列进行单位化,通过行和列不断循环交替自适应迭代优化得到优化后的测量矩阵。通过一维信号和二维图像的仿真实验验证所提方法的优越性。一方面,本文方法优化的测量矩阵互相关性明显降低;另一方面,实验仿真结果证明了测量矩阵经过优化之后提高了信号重构性能,本文方法重构性能优于现有的SVD法和特征值分解法。

基于改进TVF-EMD与SVD的轴承故障特征提取

滚动轴承早期故障信号微弱,故障特征难以提取。针对此问题,提出一种基于时变滤波经验模态分解(TVF-EMD)模态分量自适应融合与奇异值分解(SVD)降噪的轴承早期故障特征提取方法。为了降低故障信号的非线性和非平稳性,通过TVF-EMD将轴承信号分解为一系列本征模态函数(IMF)。为了克服TVF-EMD分解后IMF分量过多的不足,构造包络故障信息能量占比(EREFI)指标,通过EREFI对IMF分量进行降序排列,并依据包络故障信息能量占比递增原则对IMF分量依次进行融合,直至找到最优融合分量。最后,通过SVD对最优融合分量降噪,并提取故障特征。通过仿真信号以及2个实测轴承故障信号对所提方法性能进行了实验验证。实验结果表明:所提方法具有良好的敏感特征筛选融合能力和降噪能力,能更准确提取出轴承早期故障特征,实现故障类型的准确识别。

基于SVD-IACMD的GIS振动信号去噪算法

振动测量对发现气体绝缘开关设备(gas insulated switchgear,GIS)潜在性缺陷具有重要意义,但GIS本体振动信号易受基础振动、测量噪声以及环境噪声的影响,使得现场GIS振动带电检测和机械缺陷诊断的效果较差。针对此问题,提出一种基于奇异值分解(singular value decomposition,SVD)-改进自适应啁啾模态分解(improve adaptive chirp mode decomposition,IACMD)的现场振动信号降噪算法。该方法首先利用SVD对原始振动信号进行预处理,滤除低频基础振动和测量噪声,其次利用鱼鹰优化算法(osprey optimization algorithm,OOA)对处理后的信号进行自适应模态分解,得到分解后的固有模态(intrinsic mode functions,IMF)分量,再利用互相关系数筛选有效分量重构振动信号。模拟信号与现场信号测试结果表明:与OOA-自适应啁啾模态分解(adaptive chirp mode decomposition,ACMD)和SVD-变分模态分解(variational mode decomposition,VMD)相比,所提出的SVD-IACMD算法可以去除基础振动、测量噪声和环境噪声,保留GIS本体振动的基频和谐波分量,为GIS现场抗干扰振动检测和机械缺陷诊断提供技术支持。

基于SVD-SUKF的水下机器人电池SOC估计

荷电状态(SOC)的准确估计关系到水下机器人的电池使用效率与任务规划。针对传统SOC估计算法存在的准确性、稳定性和鲁棒性不足等问题,提出一种奇异值分解增强的球型无迹卡尔曼滤波(SVD-SUKF)SOC估计算法。建立2阶Thevenin电路模型,并使用遗忘因子递推最小二乘法对模型参数进行在线辨识;在无迹卡尔曼滤波算法的基础上引入球型无迹变换和奇异值分解,避免繁琐的调参过程、减少算法计算量以及解决算法的协方差矩阵非正定问题;采用城市道路循环工况对SVD-SUKF算法进行验证。结果表明:SVD-SUKF算法收敛速度较快,平均绝对值误差为0.006 8、均方根误差为0.005 6,算法相较于扩展卡尔曼滤波和无迹卡尔曼滤波有更高的估计精度、更好的稳定性和更强的鲁棒性。

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。

基于峭度原则的VMD-SVD微型电机声音信号降噪方法

微型电机运转时的声音信号包含丰富的状态信息,可用于生产线上电机的快速检测,但由于待测电机体积小、声音能量低,采集过程中声音信号易与环境噪声耦合,导致声音信号提取和检测不准确。该文通过研究电机组成结构,分析声音信号频率成分与成因,得到该文研究电机的声音信号3倍频谐波特点,提出一种基于峭度原则的VMDSVD算法对电机声音信号进行提纯降噪,该算法采用VMD分段原理,对各分段信号进行SVD分解,提取谐波特征,利用峭度原则优化VMD参数选取。首先通过仿真信号对比实验,验证了该文算法具有更好的降噪效果和降噪性能指标。而后,将该方法应用于微型电机实测声音信号,测试结果表明提出的基于峭度原则VMD-SVD算法具有良好降噪效果,能够显著提高原始信号信噪比,更利于后续特征提取和故障检测工作。