GpoSolver: a Matlab/C++ toolbox for global polynomial optimization

Global polynomial optimization can be a powerful tool when applied to engineering problems. One of the most successful methods for solving such problems is based on convex linear matrix inequality (LMI) relaxations. Software implementations of this approach can be found for example in Matlab toolboxes GloptiPoly and YALMIP. Matlab language makes it very easy when it comes to modelling polynomial problems. However, when using these toolboxes, Matlab is also required for the problem solving. GpoSolver aims at bridging this gap by providing a Matlab-based problem modelling toolbox supplemented by a problem-solving back end in a form of a C++ template library. Once a problem is conveniently modelled and parametrized in Matlab, a C++ class is automatically generated by GpoSolver. This class can be easily included into an existing codebase and used to solve different instances of the problem based on the supplied parameters.     

Two general integral inequalities and their applications to stability analysis for systems with time‐varying delay

Integral inequalities have been widely used in stability analysis for systems with time‐varying delay because they directly produce bounds for integral terms with respect to quadratic functions. This paper presents two general integral inequalities from which almost all of the existing integral inequalities can be obtained, such as Jensen inequality, the Wirtinger‐based inequality, the Bessel–Legendre inequality, the Wirtinger‐based double integral inequality, and the auxiliary function‐based integral inequalities. Based on orthogonal polynomials defined in different inner spaces, various concrete single/multiple integral inequalities are obtained. They can produce more accurate bounds with more orthogonal polynomials considered. To show the effectiveness of the new inequalities, their applications to stability analysis for systems with time‐varying delay are demonstrated with two numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

基于相关系数的决策树优化算法

通过分析ID3算法的基本原理及其多值偏向问题,提出了一种基于相关系数的决策树优化算法。首先通过引进相关系数对ID3算法进行改进,从而克服其多值偏向问题,然后运用数学中泰勒公式和麦克劳林公式的性质,对信息增益公式进行近似简化。通过具体数据的实例验证,说明优化后的ID3算法能够解决多值偏向问题。标准数据集UCI上的实验结果表明,在构建决策树的过程中,既提高了平均分类准确率,又降低了构建决策树的复杂度,从而还缩短了决策树的生成时间,当数据集中的样本数较大时,优化后的ID3算法的效率得到了明显的提高。     

A coarse-to-fine IP-driven registration for pose estimation from single ultrasound image

A fast registration making use of implicit polynomial (IP) models is helpful for the real-time pose estimation from single clinical free-hand Ultrasound (US) image, because it is superior in the areas such as robustness against image noise, fast registration without enquiring correspondences, and fast IP coefficient transformation. However it might lead to the lack of accuracy or failure registration.In this paper, we present a novel registration method based on a coarse-to-fine IP representation. The approach starts from a high-speed and reliable registration with a coarse (of low degree) IP model and stops when the desired accuracy is achieved by a fine (of high degree) IP model. Over the previous IP-to-point based methods our contributions are: (i) keeping the efficiency without requiring pair-wised correspondences, (ii) enhancing the robustness, and (iii) improving the accuracy. The experimental result demonstrates the good performance of our registration method and its capabilities of overcoming the limitations of unconstrained freehand ultrasound data, resulting in fast, robust and accurate registration.     

基于马尔科夫链残差修正的EMD-MELM混凝土坝位移预测模型

基于经验模态分解(EMD)、改进的极限学习机(MELM)以及马尔科夫链,提出了一种新的混合模型。由于混凝土坝的变形可看成静水压力、环境温度和时间效应而产生的变形,前两者体现总变形中的周期性分量,后者体现为总变形中的趋势性分量,所以在数据预处理阶段,利用经验模态分解技术将坝体总位移序列分解为趋势分量位移和周期分量位移,选择多项式函数预测趋势分量位移,提出了一种改进的极限学习机,即均值学习机集成(MELM),采用MELM模型对周期分量进行预测。再使用马尔科夫链修正模型对两个模型的拟合残差进行修正预测,叠加各预测值得到最终预测值。在某混凝土坝的应用表明,该组合模型的拟合及预测精度明显优于传统模型,具有操作简便、预测精度高、训练速度快等优点。     

隐式多项式曲线的信息相似性分析研究

隐式多项式曲线用来描述数据点集合轮廓具有良好的性质,并已经获得广泛的应用。研究一般商业数据的特点,将一维商业数据变换成二维商业数据,使用隐式多项式曲线对其进行拟合描述,计算这些隐式多项式曲线的相似性,进而实现对商业数据的相似性计算分析。实验结果证明了算法的有效性。     

自动微分在隐式曲线绘制中的应用

自动微分是用于计算多变量函数的导数和偏导数的一种微分技术,在给定一个多变量光滑函数值的程序代码后,可以很容易地利用自动微分来实现有关导数和偏导数的精确计算。将自动微分技术与泰勒方法相结合应用到计算机图形学领域隐式函数曲线绘制的细分算法中,并与未使用自动微分技术前的隐式曲线绘制方法作比较和分析,展示了自动微分方法在绘制隐式曲线方面的优势。     

黑河中游试验区不同分辨率LAI数据处理、分析和尺度转换

008年开展的黑河综合遥感联合试验获取了大量野外实测叶面积指数(LAI)数据以及遥感LAI产品。在利用LAI地面点观测数据对遥感影像进行验证或者不同分辨率遥感产品相互比较的过程中存在由于地表异质性引起的尺度效应,导致无法直接进行验证、比较,需要进行尺度转换。以基于泰勒级数展开的尺度转换模型为基础,研究不同源LAI之间的尺度转换方法。包括两部分内容：① 以高分辨率影像为辅助数据将地面实测点尺度的LAI转换到中、低分辨率遥感像元尺度;② 利用高分辨率影像作为亚像元信息对低分辨率LAI产品进行尺度纠正。结果表明,利用泰勒级数展开模型进行尺度转换是一种简单可行的方法,经尺度转换的地面实测点尺度LAI可用作像元尺度数据比较验证的参考。     

一种高速正弦信号发生器的设计

文章提出了基于高速DSP芯片TMS320C5402实现正弦信号发生器的设计原理与方法,介绍了所设计的正弦信号发生器的硬件结构电路图和软件程序结构图。结合DSP硬件特性,通过使用泰勒级数展开法得到设定参数的正弦波波形输出,从而达到设计目的。     

Taylor series approach to fuzzy multiobjective linear fractional programming

This paper presents the use of a Taylor series for fuzzy multiobjective linear fractional programming problems (FMOLFP). The Taylor series is a series expansion that a representation of a function. In the proposed approach, membership functions associated with each objective of fuzzy multiobjective linear fractional programming problem transformed by using a Taylor series are unified. Thus, the problem is reduced to a single objective. Practical applications and numerical examples are used in order to show the efficiency and superiority of the proposed approach.