Solutions to the generalized Sylvester matrixequations by a singular value decomposition

In this paper, solutions to the generalized Sylvester matrix equations AX -XF = BY and MXN -X = TY with A, M ∈ R^n×n, B, T ∈ Rn×r, F, N ∈ R^p×p and the matrices N, F being in companion form, are established by a singular value decomposition of a matrix with dimensions n × （n ＋ pr）. The algorithm proposed in this paper for the euqation AX - XF = BY does not require the controllability of matrix pair （A, B） and the restriction that A, F do not have common eigenvalues. Since singular value decomposition is adopted, the algorithm is numerically stable and may provide great convenience to the computation of the solution to these equations, and can perform important functions in many design problems in control systems theory.

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.

Randomized Generalized Singular Value Decomposition

The generalized singular value decomposition(GSVD)of two matrices with the same number of columns is a very useful tool in many practical applications.However,the GSVD may suffer from heavy computational time and memory requirement when the scale of the matrices is quite large.In this paper,we use random projections to capture the most of the action of the matrices and propose randomized algorithms for computing a low-rank approximation of the GSVD.Serval error bounds of the approximation are also presented for the proposed randomized algorithms.Finally,some experimental results show that the proposed randomized algorithms can achieve a good accuracy with less computational cost and storage requirement.

Source-Generated Noise Suppression Using the Singular Value Decomposition

Source-generated noise, such as air, refracted, guided waves, near-surface multiples, and radial ground roll, is one of the most challenging problems in the land seismic method. The interference of the noise with reflection events often results in a distorted representation of the subsurface and gives rise to interpretation uncertainties. To suppress the noise, geophysicists have devised various techniques in both acquisition and processing stages. Conventional processing methods, such as high-pass, f - k and hyperbolic velocity filters, however, have certain disadvantages when handling actual seismic data. In this study, we present a new hybrid method combining singular value decomposition (SVD) with a special linear transformation of the common-shot gather. The method is aimed at effectively removing the noise while minimizing harm to the signal. As compared with other methods, the SVD-based one gives a denser approximation to source-generated noise before its subtraction from the seismic data, due to the use of more appropriate basis functions. The special transformation applied in advance to the data is intended to align the source-generated noise events horizontally and thus to benefit the subsequent SVD. The effectiveness of the method in suppressing source-generated noise is demonstrated with a synthetic data set. Emphasis is put on the comparison of the performance of the method with that of conventional f - k filtering.

Weak characteristic information extraction from early fault of wind turbine generator gearboxKeywords wind turbine generator gearbox, B-singular value decomposition, local mean decomposition, weak characteristic information extraction, early fault warning

Given the weak early degradation characteristic information during early fault evolution in gearbox of wind turbine generator, traditional singular value decomposition （SVD）-based denoising may result in loss of useful information. A weak characteristic information extraction based on μ-SVD and local mean decomposition （LMD） is developed to address this problem. The basic principle of the method is as follows： Determine the denoising order based on cumulative contribution rate, perform signal reconstruction, extract and subject the noisy part of signal to LMD and μ-SVD denoising, and obtain denoised signal through superposition. Experimental results show that this method can significantly weaken signal noise, effectively extract the weak characteristic information of early fault, and facilitate the early fault warning and dynamic predictive maintenance.

基于LDA/GSVD和支持向量机的人耳识别

针对人耳图像自身的特点并通过对现有方法的研究,提出了一种先利用LDA/GSVD算法对样本图像进行特征提取,然后运用SVM分类器对样本向量进行分类的人耳识别方法.此外,还对线性判别分析、广义奇异值分解和支持向量机的相关内容做了简要介绍.实验表明,LDA/GSVD很好地解决了在高维、小样本的情况下,使用Fisher线性鉴别分析的特征提取方法存在的病态奇异问题,把它与支持向量机有机地结合起来,构成了一种有效的人耳识别新方法.

基于GSVD的核不相关辨别子空间与雷达目标识别

该文提出了一种基于广义奇异值分解的核不相关辨别子空间算法,并将其用于高分辨距离像雷达目标识别。新算法结合广义奇异值分解与核方法的优点,有效地解决了传统方法面临的矩阵奇异问题,同时进一步改善了目标的类可分性。其次,依据Fisher准则导出了距离像总散度矩阵零空间中不含有有用辨别信息的结论。利用这一结论,可以在求解核不相关最优辨别矢量之前对各散度矩阵进行预降维,以减小后续运算的计算复杂度。对3类飞机目标实测数据的识别结果表明了所提方法的有效性。

基于KDA／GSVD和支持向量机的人耳识别

在高维、小样本的情况下使用Fisher线性鉴别分析的特征提取方法存在病态奇异问题,学者们提出了许多解决此问题的方法。针对小样本问题,并通过对现有人耳识别方法的研究,提出了一种利用KDA/GSVD算法对图像数据进行降维,运用SVM分类器对样本进行判别的人耳识别方法。此外,还对线性判别分析、广义奇异值分解和支持向量机的基本理论等内容做了简要介绍。实验证明,KDA/GSVD很好地解决了由于小样本的问题而导致的LDA算法中类内离散度矩阵不可求逆的问题,把它与支持向量机有机地结合起来,构成了一种有效的人耳识别新方法。

MIMO双向中继GSVD线性预编码的功率优化算法

为优化多输入多输出双向中继系统的功率分配,应用广义奇异值分解方法对角化一对用户到中继的信道,并划分成两种传输模式:单向和双向中继传输模式.针对划分后的空间子信道采取矩阵置换的方法对齐中继节点处的链路信号.此外,相比传统的每个节点总功率约束,提出约束单链路下3节点总功率的方法来最大化系统平均总速率,获得功率优化的封闭解并降低计算的复杂度.仿真结果显示,所提功率算法具有和全局优化算法非常相近的性能,且在30dB处,天线规格从3-5-3到4-6-4再到5-7-5,能够带来近2bit/(s·Hz-1)的递增增益.

Generalized Inverse Eigenvalue Problem for (P,Q)-Conjugate Matrices and the Associated Approximation Problem

In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the least residual problem of the above generalized inverse eigenvalue problem is studied by using the canonical correlation decomposition（CCD）.The solutions to these problems are derived.Some numerical examples are given to illustrate the main results.

矩阵奇异值分解与非齐次线性方程组系数矩阵的广义逆求解

非齐次线性方程组在多数实际工程反演问题中较为常见,对其进行有效地求解是解决实际反演问题的关键,本文通过对方程组系数矩阵进行奇异值分解,推导非齐次线性方程组系数矩阵的广义逆求解过程,给出具体的求解方法和实现步骤,使得求解算法更容易进行计算机编程.

附参数约束的方程赋权值解法研究

针对附参数约束等式方程的函数模型解算问题,提出一种对约束方程赋权值再联合观测方程统一解算的约束方程赋权统一解法。为验证此方法的可靠性和效率,基于矩阵分析法推导了适用于附参数约束方程解算的正交三角分解法和广义奇异值分解法。通过算例对3种解算法进行比较分析,结果表明:当给约束方程附加合适范围内的权值时,约束方程赋权统一解法获得的参数估计值与矩阵分解算法的参数估计结果在要求的精度范围内一致;赋权统一解法与正交三角分解法的计算效率接近,广义奇异值分解法计算效率较低;约束方程赋权统一解法更符合参数模型统一表达和平差准则设定,有利于平差算法设计和误差特性分析和研究。

计及分布式电源接入的配电网状态估计

为适应分布式电源接入量测配置较少配电网的需要,基于风电和光伏发电系统的功率预测,提出将分布式电源预测有功功率和"虚拟"无功功率作为伪测量建立带等式约束条件的加权最小二乘状态估计模型。模型中计及异步风力发电机的无功-电压特性对雅克比矩阵进行修正,利用光伏发电系统零无功注入等式约束修正估计结果。基于奇异值分解求解建立的模型以保证状态估计的数值稳定性。通过对IEEE33节点算例的仿真计算,结果表明所建的模型将分布式电源自身特性与加权最小二乘状态估计有效融合,能够更准确反映分布式电源出力状态,从而在不增加量测装置情况下提高了状态估计精度。

基于正交搜索的粒子群优化测试用例生成方法

针对粒子群优化算法易出现早熟收敛的问题,本文提出一种基于正交搜索的粒子群优化测试用例生成方法.首先,利用奇异值分解来预测种群的进化方向,在其正交方向进行搜索,可避免已搜索过的区域,有助于跳出局部最优;然后,对粒子速度项进行改进,使其与正交方向保持一致,保证种群可持续受到正交方向的影响,有利于减少奇异值分解次数,降低时间消耗;最后,对每代最优个体进行局部搜索,以增强算法局部搜索能力.实验证明,本文方法在覆盖率、运行时间、进化代数等指标上均有优势.

基于协方差矩阵同时对角化的盲信号分离算法

提出了基于自相关协方差矩阵同时对角化的两个盲源信号分离算法.利用广义奇异值分解(GSVD)算法,将源信号观测数据预白化后的零阶和一阶自相关协方差矩阵同时对角化,估算出两路源信号.与二阶盲识别(SO-BI)算法进行了比较,该算法具有计算简单且运算精度高的优点.在线性混合加噪模型下,计算机仿真表明该算法的有效性.

带状随机线性系统状态的估计问题

针对目前关于广义系统状态估计的研究现状 ,即几乎所有的讨论都集中在奇异矩阵为方阵的情况 ,讨论了广义逆矩阵和矩阵的奇异值分解问题。首次提出了带状随机系统的状态估计问题 ,利用矩阵的奇异分解理论给出了带状广义连续线性系统的奇异值标准形式。基于标准形式 ,利用广义逆矩阵的性质 ,在两种情况下将系统分解成两个子系统 ,通过估计子系统的状态 ,得到了该系统状态的最优预测和滤波递推方程。

矩阵的SVD分解性质及其在秩亏网平差中的应用

对矩阵的奇异值分解(SVD,Singular Value Decomposition)进行了分析。推导证明了奇异值分解和M-P广义逆矩阵之间的关系,得出奇异值分解的广义逆矩阵为矩阵的M-P广义逆;分析了奇异值分解和线性方程组最小范数最小二乘解的关系,推导了应用奇异值分解进行秩亏网平差解算的平差解算公式和精度估算公式;推导了加权最小二乘最小范数解的奇异值分解解算问题,扩展了奇异值分解求解未知参数最小范数最小二乘解;最后通过秩亏网算例进行了解算,验证了方法的正确性和矩阵分解的有效性。

基于广义S变换模时频矩阵的局部放电特高频信号去噪方法

为有效抑制局部放电特高频信号中的噪声干扰,提出一种基于广义S变换模时频矩阵的去噪方法。基于二维模时频矩阵,采用区域最大能量法提取周期性窄带干扰的特征量,并通过矩阵逆向分离将其去除;采用奇异值分解去噪方法抑制信号中的高斯白噪声。使用该方法对仿真信号和实验室实测信号进行去噪处理,并与传统方法去噪结果进行对比。结果表明,所提方法能有效抑制局部放电信号特高频信号中的噪声,同时更好地保留了原始局部放电信号特征。对现场实测信号进行去噪处理,与传统方法相比,该方法具有较高的噪声抑制比和较低的幅值衰减比,可以有效提取局部放电超高频信号。

基于广义奇异值分解的通用旁瓣消除算法

提出一种新的通用旁瓣消除器结构,它利用广义奇异值分解(Generalized singular value decomposition,GSVD)技术,通过广义奇异向量的变换间接估计声源到麦克风之间的传递函数。不同噪声环境下的实验结果表明,与现有的各种GSC算法相比,该算法能够更有效地抑制混响和噪声,并且增强后的语音失真最小。

矩阵奇异值分解与广义岭估计及其在测量中的应用

在测量等许多工程领域中，存在因函数模型结构差即设计矩阵病态、致使未知数的最小二乘估计偏差太大且不稳定的问题，因此，研究了使用矩阵奇异值分解和广义岭估计进行数据处理的方法。首先，简述了矩阵奇异值分解及广义岭估计的理论与性质；然后，重点比较研究了它们解算病态方程的思想、途径、对关键问题的处理、适应范围、工作量大小等；最后，通过摄影测量算例验证了所得结果。并且指出，奇异值分解方法应用于病态方程的参数解算，是一种易于操作、效果更好的方法，有重要的应用价值。