Model order reduction of MIMO bilinear systems by multi-order Arnoldi method

In this paper, we present a time domain model order reduction method for multi-input multi-output (MIMO) bilinear systems by general orthogonal polynomials. The proposed method is based on a multi-order Arnoldi algorithm applied to construct the projection matrix. The resulting reduced model can match a desired number of expansion coefficient terms of the original system. The approximate error estimate of the reduced model is given. And we also briefly discuss the stability preservation of the reduced model in some cases. Additionally, in combination with Krylov subspace methods, we propose a two-sided projection method to generate reduced models which capture properties of the original system in the time and frequency domain simultaneously. The effectiveness of the proposed methods is demonstrated by two numerical examples.     

基于修正变分法开孔板和加强板结构的自由振动分析

为研究船舶开孔板和加强板结构的振动特性,用1阶剪切变形板理论描述各向同性板的位移场,并采用修正变分原理和区域分解方法建立板的离散动力学模型.每一块子域板的位移和转角分量通过第一类切比雪夫正交多项式展开.针对加强板模型,将该方法获得的结果与已经发表的文献和有限元商用软件计算结果进行对比,验证该方法的收敛性和正确性.基于修正变分法探讨多种开孔和加强板模型的自由振动特性,充分说明该数理模型和半解析方法是一种适合处理复杂板结构问题的数值工具.     

改进十字链表的存储方法在短路电流计算中的应用

节点导纳矩阵是一个稀疏矩阵,短路电流计算需要对导纳矩阵数据进行查询。为了既能保持快速按行列查询元素数值,又进一步提高按数值查询其所在行列的效率,以便于存储调用及后续矩阵的处理,提出构建高度平衡二叉树的改进十字链表方法,即在十字链表存储的基础上,拓展存储数据结点指针域,形成平衡二叉树,将高度维持在(O(log2n)),平均查找长度也可维持在(O(log2n)),大大降低操作时间复杂度,提高数值查询效率。同时,为保证测试结果的公平性,把构建高度平衡二叉树的时间计入总时间,以进行对比。通过相应算例,验证了该改进方法的高效性。     

Universal instability modes in internal and external flows

Two prototypical external and internal flows have been studied which display linear temporal instability followed by nonlinear saturation taking the flows to a new equilibrium state. Direct simulation results are obtained using a specific formulation and numerical methods with very high accuracy. These results are analyzed via proper orthogonal decomposition (POD), which reveal similar modes for flow past a circular cylinder and flow inside a lid-driven cavity, indicating universality of such modes. Unlike many other efforts on reduced order modeling via POD, here the emphasis has been on understanding the physical aspect of the flow instability which requires very high accuracy of the simulation. Then, the obtained POD modes are related to the instability modes (in the classical sense of defining the latter) and new generic types of instability modes are identified in the studied external and internal flows. These new modes have been reported for flow past a circular cylinder [Sengupta TK, Singh N, Suman VK. Dynamical system approach to instability of flow past a circular cylinder. J Fluid Mech 2010;656:82–115] which help one in understanding the instability sequence and the relative importance of these modes in the flow evolution starting from an impulsive start. Present comparative study, furthermore, reveals universality of such instability modes by showing their presence for the flow inside a lid-driven cavity as well. Despite seeming dissimilarities between these two flows, similarities between the instability portrait of these two flows suggest universality of such modes. From the equilibrium amplitude of vorticity time-series, we establish the presence of multiple modes and multiple bifurcation sequences for these flows in parameter space. Existing theory due to Landau and Stuart that considers only a single dominant mode and its self-interaction does not explain all these features. We invoke a multi-modal interaction model in the cited reference above, termed as Landau–Stuart–Eckhaus (LSE) equation in recognition of Eckhaus’ work in modifying the classical Stuart–Landau equation. We also show that the new instability modes do not follow either the classical Stuart–Landau or the newly proposed LSE model equations and for this reason we call these as anomalous modes. Two specific classes of anomalous modes are identified and classified in the present work. Empirical expressions for the evolution of these anomalous modes are presented and their unambiguous role during instabilities is discussed.     

基于互信息的颅脑MR影像序列的三维配准

医学图像配准具有重要的临床应用价值,并一直是医学图像处理领域的热点研究问题。基于互信息的配准方法由于自动化程度高和配准精度高的优点而被广泛应用于三维医学图像配准;但是,也存在着数据量大、计算速度慢的问题。采用归一化互信息测度,并将一种新的正交优化技术应用于颅脑MR影像序列的三维配准,旨在缩短处理时间。将该方法与使用传统优化算法的配准方法作了比较,实验结果表明,提出的方法能够显著提高配准速度,且不降低配准精度。     

一种深度图像中的表面曲率估计算法

曲率估计在深度图像分析中占有重要地位,传统的有限差分或局部拟合方法未考虑到表面上可能出现的不连续性,因而会不可避免地出现错误,为了得到有效可靠的曲率估计,本文提出了基于自适应局部表面拟合和鲁棒最大似然的估计的曲率估计算法,首先,提出曲面是分片光滑的假设,表面曲率需从该像素所属的光滑曲面片来估计,其次,定义了能量函数来度量拟合窗的平滑度,在局部表面拟合时,依据最小化能量函数的原则来自适应移动拟合窗的中心,以使拟合窗达到最“光滑”,最后,采用鲁棒最大似然估计以消除仍然存在的“局外点”的影响,理论分析和实验结果证明估计算法是稳健,可靠,有效的且计算复杂度小。     

RBF网学习的进化优选算法

讨论了用正交最小二乘算法训练ＲＢＦ网的不足之处,然后引入了选择路径的概念,在此基础上,提出了ＲＢＦ网隐层节点选取的进化优选算法,仿真结果表明,在不同的精度要求下,用进化优选算法均能设计出比正交最小二乘算法更小的ＲＢＦ网。     

基于正交小波变换的信号降噪算法研究

提出了一种基于正交小波变换的信号降噪方法,深入研究了小波变换中的信号分解与重构的Mallat算法,详细介绍了正交小波变换中阈值的选取,并进行了实验研究。实验结果表明,该方法可以取得较好的去噪效果。     

现代密码学上的弹性函数综述

本文介绍了在容错分布、量子密码学中的密钥分配以及流密码中的随机序列产生等领域都有着广泛应用的一类多输出布尔函数——弹性函数。弹性函数和0,1上多维空间的正交分划(一个正交矩阵组)是一致的。在此基础上,介绍了弹性函数的正交分划的递归构造方法和简单计数。