Boundary control for a constrained two-link rigid–flexible manipulator with prescribed performance

In this paper, we consider a boundary control problem for a constrained two-link rigid–flexible manipulator. The nonlinear system is described by hybrid ordinary differential equation–partial differential equation (ODE–PDE) dynamic model. Based on the coupled ODE–PDE model, boundary control is proposed to regulate the joint positions and eliminate the elastic vibration simultaneously. With the help of prescribed performance functions, the tracking error can converge to an arbitrarily small residual set and the convergence rate is no less than a certain pre-specified value. Asymptotic stability of the closed-loop system is rigorously proved by the LaSalle's Invariance Principle extended to infinite-dimensional system. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller.     

去除乘性噪声的非局部扩散模型

提出了一种基于非局部扩散的去除乘性噪声的模型。该模型根据图像噪声为高斯噪声的假设建立图像恢复的能量泛函,由变分法得到偏微分方程。通过人工合成图像和真实图像的实验结果可知,本文提出的模型在去噪效果方面优于基于有界变差的乘性噪声模型。     

小能量点火脉冲爆震发动机DDT过程数值模拟

模拟了以小能量点火触发爆震的脉冲爆震发动机工作过程。采用有限速率化学反应模型,通过二阶迎风格式差分逼近二维欧拉方程,模拟以丙烷和空气为可爆混合物的脉冲爆震起爆和传播。采用CFD软件中spark ignition模型模拟实验中电火花塞点火。在模拟过程中可以清楚地观察到DDT过程。通过与CEA程序计算结果比较,发现两者C-J值误差小于4%,说明所采用的计算方法和网格生成方法可以用于小能量点火触发爆震的多循环数值模拟。     

一种基于分数阶偏微分方程的图像放大算法

针对传统图像放大算法的不足之处,将物理意义鲜明的分数阶偏微分理论引入到图像放大算法中,提出一种新的基于分数阶偏微分方程的图像放大算法,使得放大图像的轮廓更加清晰,同时能够有效保留放大图像的细节边缘特征。仿真实验结果表明,该方法对比传统图像放大算法在放大图像的同时也增强图像的清晰度和对比度。     

连续性约束下基于样例的图像修复算法*

为了提高图像修复效果,提出了一种连续性约束下基于样例的图像修复模型。通过建立能量函数,引入一种新的偏微分方程约束,优化了修复顺序,能够克服传统的基于样例的修复算法在结构性较强的图像修复过程中造成的结构断接现象,在修复纹理的同时很好的保持了结构。实验表明,该算法可以更好的修复大尺度缺损的图像。     

Image deblurring with filters learned by extreme learning machine

Image deblurring is a basic and important task of image processing. Traditional filtering based image deblurring methods, e.g. enhancement filters, partial differential equation (PDE) and etc., are limited by the hypothesis that natural images and noise are with low and high frequency terms, respectively. Noise removal and edge protection are always the dilemma for traditional models.In this paper, we study image deblurring problem from a brand new perspective—classification. And we also generalize the traditional PDE model to a more general case, using the theories of calculus of variations. Furthermore, inspired by the theories of approximation of functions, we transform the operator-learning problem into a coefficient-learning problem by means of selecting a group of basis, and build a filter-learning model. Based on extreme learning machine (ELM) [1], [2], [3] and [4], an algorithm is designed and a group of filters are learned effectively. Then a generalized image deblurring model, learned filtering PDE (LF-PDE), is built.The experiments verify the effectiveness of our models and the corresponding learned filters. It is shown that our model can overcome many drawbacks of the traditional models and achieve much better results.     

Robust adaptive neural observer design for a class of nonlinear parabolic PDE systems

A robust adaptive neural observer design is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and bounded disturbances. The modal decomposition technique is initially applied to the PDE system to formulate it as an infinite-dimensional singular perturbation model of ordinary differential equations (ODEs). By singular perturbations, an approximate nonlinear ODE system that captures the dominant (slow) dynamics of the PDE system is thus derived. A neural modal observer is subsequently constructed on the basis of the slow system for its state estimation. A linear matrix inequality (LMI) approach to the design of robust adaptive neural modal observers is developed such that the state estimation error of the slow system is uniformly ultimately bounded (UUB) with an ultimate bound. Furthermore, using the existing LMI optimization technique, a suboptimal robust adaptive neural modal observer can be obtained in the sense of minimizing an upper bound of the peak gains in the ultimate bound. In addition, using two-time-scale property of the singularly perturbed model, it is shown that the resulting state estimation error of the actual PDE system is UUB. Finally, the proposed method is applied to the estimation of temperature profile for a catalytic rod.     

基于数值微分的图像融合方法

提出一种基于数值微分的图像融合方法。用精确求解离散数据导数的数值微分方法取代传统的邻域差分来求解图像梯度,将求解得到的图像梯度应用到基于偏微分方程的图像融合模型中,改进基于偏微分方程的图像融合数值化方案。将改进前后的方法进行对比实验,结果表明,应用改进方法得到的融合图像的质量指标和图像收敛性较优。     

基于MATLAB的流体润滑求解和可视化研究

讨论了如何利用MATLAB中PDE工具箱和窗口函数 ,进行流体润滑问题的求解和可视化。把润滑问题转化为MATLAB中的标准函数形式 ,然后利用PDE工具箱和主窗口函数以及少量编程 ,采用三角形单元划分 ,对无量纲雷诺方程进行有限元求解 ,获得了油膜压力、压力梯度和其他静特性。经验表明 ,利用MATLAB中PDE工具箱和主窗口函数 ,能方便而高效地进行某些润滑问题的求解 ,并对求解结果进行求解可视化。     

PM6 and DFT study of free radical scavenging activity of morin

Flavonoids have long been recognised for their general health-promoting properties, of which their antioxidant activity may play an important role. In this work, we have studied the properties of flavonoid morin using semiempirical and density functional theory (DFT) methods in order to validate the application of the recently developed parametric method 6 (PM6). Reaction enthalpies related to mechanisms of free radical scavenging by flavonoid morin were calculated by DFT and PM6 methods in gas-phase, water, DMSO and benzene. It has been shown that fast semiempirical PM6 method can mimic results obtained by means of more accurate time consuming DFT calculations. Thermodynamically favoured mechanism depends on reaction medium: SPLET (sequential proton loss electron transfer) is preferred in water and DMSO, and HAT (hydrogen atom transfer) is predominant in gas-phase. In benzene these two mechanisms are competitive.