基于状态转移矩阵逼近的椭圆球面波函数求解方法

该文针对现有椭圆球面波函数(PSWFs)求解算法存在的效率低、硬件实现复杂度高,尤其是精度不可控的问题,结合线性时变系统理论,提出一种基于微分方程状态转移矩阵逼近的PSWFs求解方法。该算法通过求解小区间上的状态转移矩阵来逼近整个时间区间上的状态转移矩阵,进而求得离散时间点上的系统运动轨迹,即PSWFs数值解。理论推导了求解误差并修正了算法,修正后算法具有简明的误差表达式,与Parr算法和Legendre多项式逼近算法在求解精度和复杂度上进行了对照分析。结果表明,该文算法求解精度高且可控,时间和空间复杂度低,易于硬件实现。     

基于伪逆算子的超分辨率信号处理方法研究

为了解决信号压缩过程中旁瓣串扰问题并提高参数估计时频率的估计精度,在研究超分辨信号处理理论的基础上,从框架理论入手,提出了可改善系统性能的恒噪声灵敏度分解算法。首先在基于矩阵表示的超分辨信号处理模型的基础上,采用矩阵伪逆算子,进行基于信号压缩的微波成像处理,讨论了伪逆算子应用于信号分解过程中的噪声性能;然后针对伪逆算子导致系统噪声增益增加的问题,通过根据信号处理的噪声指标要求设定处理门限,实现对信号的超分辨处理。仿真实验结果表明,该方法可消除匹配滤波类算法不可避免的旁瓣串扰问题,并可在一定程度上改善系统分辨率性能。     

基于提升框架的传统小波研究

提升框架的核心思想是通过有限步预测和更新来构造小波滤波器。由于传统小波的多相矩阵可以分解为多个矩阵的乘积,本文从原理上说明了这些矩阵可以看作是预测算子和更新算子,并给出了具体例子。在例子中,把小波分解变换与重建交换表示成提升框架的形式,说明了提升框架对传统离散小波变换具有包容性。     

基于矩阵分解和非凸秩近似的低秩表示算法

针对低秩表示模型的一般求解算法存在针对核范数存在近似矩阵秩不精确的问题,用矩阵分解技术与对数行列式函数替代矩阵核范数来近似矩阵秩函数。提出了基于矩阵分解和非凸秩近似的低秩表示模型,并设计了一种交替方向乘子法求解,最后用谱聚类方法进行聚类,通过数值实验对比,证明提出的算法有效性。     

系统矩阵表示的电磁场时域计算方法

为了进一步提高电磁场数值计算效率,把数字信号处理技术和计算电磁学的时域有限差分方法相结合,按照信号与系统理论的概念把求解区域看作一个线性系统,从有源区域的麦克斯韦方程组对称形式出发,推导了离散的时域差分方程组,给出了电磁场求解区域的系统矩阵表达形式.分析了求解差分方程组迭代过程的系统框图,以满足数字信号处理的形式要求.对空域上的微分算子进行矩阵分解,把无条件稳定的电磁场时域离散方程组,通过时间交错迭代格式来处理,给出无条件稳定的方程组的系统矩阵形式,实现电磁波传播过程的模拟.最后,通过一维高斯脉冲的传播、低通滤波器以及紧凑型带阻滤波器的仿真,验证了这种系统矩阵方法的有效性.     

用遗传算法求解时间表问题

通过对时间表问题的认识,设计了求解该问题的遗传算法,给出了矩阵编码,和针对矩阵行,列操作的遗传算子,并给出了一个实例。     

外场驱动下扩散过程中密度矩阵主方程的求解和应用

利用热纠缠态表象方法和有序算符积分技术,求 解了单模腔在振荡外场驱动下扩散过程中的 密度矩阵主方程。基于实模算符和虚模算符作用在热纠缠态上的等效关系,将密度矩阵主方 程转化为态矢 演化方程,给出了其形式解。进一步,导出了密度矩阵用Kraus算符无限和表示的解析解。 证明了Klaus 算符满足归一化条件。作为解的应用,计算了相干态和真空态在该模型中密度矩阵的演化。 计算结果表明:相干态和真空态在振荡外场驱动下扩散过程中都将演化为热场。     

扩散过程中混沌场的演化

利用热纠缠态表象求解密度矩阵主方程的方法和有序算符内的积分技术,对扩散过程的密度矩阵主方程进行了求解,给出了主方程密度算符无限和表示的解的形式,导出了扩散过程混沌场密度算符的演化规律,并研究了平均光子数和光子数涨落的演化。研究结果表明:随着扩散过程的进行,混沌场密度算符的形式不变,仍然保持混沌场的性质,但其平均光子数随着扩散过程的进行线性增加,光子数涨落随扩散时间以二次函数形式扩大。     

二进制粒属性相关判定与应用

采用二进制粒表示信息系统中的离散化属性值,即对属性进行二进制粒化,定义了基于二进制信息粒的匹配、合取及析取算子,描述了二进制粒属性相关的定义,提出了基于二进制粒的属性相关性判定矩阵的算法,算法通过判定信息系统中属性的相关性,为属性约简及关联规则的求解提供一种新方法.如果相关属性同为条件属性,则可进行约简,选择其一;如果有决策属性,则可生成强关联规则;该算法在气象数据的仿真实验中验证了其实用性.     

基于鲁棒稀疏表示的人脸识别算法

提出了一种基于LBP算子和鲁棒稀疏表示的人脸识别方法。首先,提取训练样本和测试样本的LBP特征。其次,在原有稀疏表示分类器(SRC)的基础上添加一个权值矩阵W来解决l1正则化最小二乘问题。最后,利用鲁棒稀疏表示分类器(RSRC)分类测试人脸图像所属类别。在ATT人脸库上进行实验的结果表明,此方法是优于其他经典算法的。     

Physical interpretation of state assignment

The general operation of state reassignment is analysed using a method of Boolean matrix algebra. It is shown that state reassignment can be implemented by pre- and postmultiplication of a given (assigned) machine by a single operator. The physical interpretation of this operation is considered. Possible applications of this structure to the evaluation of optimal assignments are proposed.     

正交小波(包)变换的算子矩阵

本文采用纯数学的方式,构造性地直接证明了对于长度为2的整数次幂的有限长离散信号,它的有限支撑的正交小波(包)变换算子可以用一个大小与信号长度一样的正交矩阵来表示,并且给出了该矩阵构造的一般方法和规律.     

有限差分法解电磁场方程的共轭梯度法三角阵预处理器

通过考察电磁场微分方程经非均匀网格离散后的有限差分方程组矩阵,建立了函数偏微分运算与离散向量矩阵相乘运算的对应关系,给出了差分方程组矩阵对应于微分算子的分解式,并据此提出了共轭梯度法的三角阵预处理器。此外,还提出了对不同的边界条件、求解域内部边界、介质分界面和时谐场方程的处理技术以便应用该预处理器。数值计算结果验证了本文算法的正确性,展示了其十分明显的加速收敛效果,表明了本文算法有线性的存储复杂度和几乎线性的计算复杂度,可有较广泛的应用。本文中将算子细节和矩阵细节对应的基本思想对构造其它高效预处理器具有借鉴作用。     

基于Grover硬币算子的量子行走在商图上的演化算子

商图是利用图的对称性分析量子行走算法的一种重要数学工具.量子行走在商图上的演化算子由移位算子和硬币算子构成.本文以构造的方式给出了Grover硬币算子在超立方体的商图上对应的矩阵形式,并给出了其正确性证明.由于商图上的移位算子可由原图上的移位算子直接导出,从而确定了使用Grover算子作为硬币的量子行走在商图上的演化算子.     

Condition Assessment Approach of Hydraulic Brake for Large Crane Based on State Estimation Algorithm

Hydraulic brake was widely used for mechanical brake of port crane. The run-state of the brake affects the safety of the crane because of the sudden accident. Because of the complex structure and unsuited to use in real time of traditional assessment model, the condition assessment approach of hydraulic brake was constructed based on state estimation algorithm in this paper. The oil temperature, dynamic friction coefficient, spring stiffness coefficient, brake shoe clearance and contact area were chosen as the state components of the memory matrix based on the analysis of the structure and failure reasons of the brake. Considering the correlation between the state components, the Mahalanobis distance was chosen as the nonlinear operator of algorithm, and the uncertainty factors and random disturbances in state assessment were eliminated by the sliding window residual statistics method. The dynamics simulation of hydraulic brake was constructed for confirming the validity of the approach in this paper. The result shows that it can be accurately judged by the method if the brake is in abnormal state.     

Admissible Control of Linear Singular Delta Operator Systems

In this paper, we study the problem of state feedback admissible control for the linear singular delta operator systems that result from linear singular continuous systems. By introducing the concept of delta operator, for a given linear singular continuous system, we establish its corresponding delta operator model and this discrete model converges to its continuous counterpart as the sampling period decreases. Sufficient conditions for desirable controllers in terms of matrix inequalities and linear matrix inequalities are given, and the explicit expressions of the controllers are derived. Some examples as well as numerical simulations are provided to demonstrate the effectiveness of the proposed approaches.     

分数Fourier变换、矩阵群和时-频分析

本文从矩阵群的观点出发讨论了分数Fourier变换的数学描述并通过数字仿真直观地说明了它进行信号时-频分析的两个特点.结果表明,在矩阵描述下,经典的Fourier变换相当于一个置换矩阵;一般的分数Fourier变换相当于一个广义置换矩阵;分数Fourier变换全体构成的变换族可以用一个矩阵群来描述,多次变换运算完全转化为相应的矩阵乘法运算.最后,数字信号分数Fourier变换的仿真计算表明,分数Fourier变换具有独特的时-频分析性质.     

Fault Detection for Uncertain Fuzzy Systems Based on the Delta Operator Approach

This paper investigates the problem of designing a robust fault-detection for uncertain T-S fuzzy models based on the delta operator approach. By means of the T-S fuzzy delta operator systems, a fuzzy fault detection filter system is constructed via the delta operator approach. The worst case fault sensitivity has been formulated in terms of linear matrix inequalities. The proposed fault-detection filter not only ensures the H _?-gain from a fault signal to a residual signal greater than a prescribed value, but also guarantees the H _∞-gain from an exogenous input to a residual signal less than a prescribed value in terms of the solvability of linear matrix inequalities. The linear matrix inequalities can be solved by an effective algorithm. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.     

An Orthogonal Method for Measurement Matrix Optimization

Compressive sensing theory states that signals can be sampled at a much smaller rate than that required by the Nyquist sampling theorem, because the sampling of a signal in the former is performed as a relatively small number of its linear measurements. Thus, the design of a measurement matrix is important in compressive sensing framework. A random measurement matrix optimization method is proposed in this study based on the incoherence principle of compressive sensing, which requires the mutual coherence of information operator to be small. The columns with mutual coherence are orthogonalized iteratively to decrease the mutual coherence of the information operator. The orthogonalization is realized by replacing the columns with the orthogonal matrix \(\mathbf {Q}\) of their QR factorization. An information operator with smaller mutual coherence is acquired after the optimization, leading to an improved measurement matrix in terms of its relationship with the information operator. Results of several experiments show that the improved measurement matrix can reduce its mutual coherence with dictionaries compared with the random measurement matrix. The signal reconstruction error also decreases when the optimized measurement matrix is utilized.     

运用Kraus算子分析红宝石激光器中离子密度矩阵元的演化

红宝石激光器是一个三能级系统。本文基于Kraus算子理论,针对能级间同时存在吸收和辐射的情况,研讨密度矩阵元的演化特性。结果表明在粒子分别以大概率从基态跃迁到第二激发态和从第二激发态辐射到第一激发态过程中形成粒子数反转,为产生激光作准备;在粒子以大概率从第一激发态辐射到基态时,产生激光。