Numerical simulation and convergence analysis for a system of nonlinear singularly perturbed differential equations arising in population dynamics

In this article, we consider a system of nonlinear singularly perturbed differential equations with two different parameters. To solve this system, we develop a weighted monotone hybrid scheme on a nonuniform mesh. The proposed scheme is a combination of the midpoint scheme and the upwind scheme involving the weight parameters. The weight parameters enable the method to switch automatically from the midpoint scheme to the upwind scheme as the nodal points start moving from the inner region to the outer region. The nonuniform mesh in particular the adaptive grid is constructed using the idea of equidistributing a positive monitor function involving the solution gradient. The method is shown to be second order convergent with respect to the small parameters. Numerical experiments are presented to show the robustness of the proposed scheme and indicate that the estimate is optimal.     

A simplified adaptive Cartesian grid system for solving the 2D shallow water equations

This paper presents a new simplified grid system that provides local refinement and dynamic adaptation for solving the 2D shallow water equations (SWEs). Local refinement is realized by simply specifying different subdivision levels to the cells on a background uniform coarse grid that covers the computational domain. On such a non‐uniform grid, the structured property of a regular Cartesian mesh is maintained and neighbor information is determined by simple algebraic relationships, i.e. data structure becomes unnecessary. Dynamic grid adaptation is achieved by changing the subdivision level of a background cell. Therefore, grid generation and adaptation is greatly simplified and straightforward to implement. The new adaptive grid‐based SWE solver is tested by applying it to simulate three idealized test cases and promising results are obtained. The new grid system offers a simplified alternative to the existing approaches for providing adaptive mesh refinement in computational fluid dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

This paper studies an (n+4)-dimensional nonlinear virus dynamics model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, B cells and cytotoxic T lymphocyte (CTL) cells. Both viral and cellular infections have been incorporated into the model. The infected-susceptible and virus-susceptible infection rates as well as the generation and removal rates of all compartments are described by general nonlinear functions. Five threshold parameters are computed, which insure the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established, which is sufficient to investigate the global dynamics of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.     

阿尔茨海默病诊断的自适应BP神经网络模型

阿尔茨海默病(AD)和轻度认知功能损伤(MCI)具有患者多、诊断难的特点,改进BP神经网络,提出自适应BP神经网络(ABP)进行100次AD和MCI诊断模拟,ABP神经网络的诊断正确率显著高于BP和RBF神经网络.采用留一法将101例正常人、200例MCI和90例AD患者的样本分为训练集和检测集,用ABP神经网络对其进行诊断模拟,总正确率达到73.91%.     

An improved ensemble learning machine for biological activity prediction of tyrosine kinase inhibitors

Boosting is one of the most important strategies in ensemble learning because of its ability to improve the stability and performance of weak learners. It is nonparametric, multivariate, fast and interpretable but is not robust against outliers. To enhance its prediction accuracy as well as immunize it against outliers, a modified version of a boosting algorithm (AdaBoost R2) was developed and called AdaBoost R3. In the sampling step, extremum samples were added to the boosting set. In the robustness step, a modified Huber loss function was applied to overcome the outlier problem. In the output step, a deterministic threshold was used to guarantee that bad predictions do not participate in the final output. The performance of the modified algorithm was investigated with two anticancer data sets of tyrosine kinase inhibitors, and the mechanism of inhibition was studied using the relative weighted variable importance procedure. Investigating the effect of base learner's strength reveals that boosting is only successful using the classification and regression tree method (a weak to moderate learner) and does not have a significant effect using the radial basis functions partial least square method (a strong base learners). Copyright © 2015 John Wiley & Sons, Ltd.     

基于FPGA的电容式编码器数据采集系统的设计与实现

电容式编码器是一种新型、耐用、可靠和准确的编码器。由于电容式编码器编码的原理不同于传统的光学式和电磁式编码器,其输出的位置信息是经过两路激励信号调制后的正弦波形,与传统的正余弦(和)和方波(PWM)输出方式差异较大,因此其信号检测技术也和传统的编码器有很大的差别。为了精确地获取电容式编码器输出信号中所携带的位置信息,本文设计了一套基于现场可编程门阵列(FPGA)的电容式编码器数据采集系统。文中介绍了带通滤波器、同步正交解调、低通滤波器和Cordic等算法,并详细分析了系统的稳定性和误差。实验结果表明,系统能够实时的获取转子的位置信息,同时具有较好的分辨率和精度。     

Switching adaptive controllers to control fractional‐order complex systems with unknown structure and input nonlinearities

This article investigates the chaos control problem for the fractional‐order chaotic systems containing unknown structure and input nonlinearities. Two types of nonlinearity in the control input are considered. In the first case, a general continuous nonlinearity input is supposed in the controller, and in the second case, the unknown dead‐zone input is included. In each case, a proper switching adaptive controller is introduced to stabilize the fractional‐order chaotic system in the presence of unknown parameters and uncertainties. The control methods are designed based on the boundedness property of the chaotic system's states, where, in the proposed methods the nonlinear/linear dynamic terms of the fractional‐order chaotic systems are assumed to be fully unknown. The analytical results of the mentioned techniques are proved by the stability analysis theorem of fractional‐order systems and the adaptive control method. In addition, as an application of the proposed methods, single input adaptive controllers are adopted for control of a class of three‐dimensional nonlinear fractional‐order chaotic systems. And finally, some numerical examples illustrate the correctness of the analytical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 211–223, 2015     

基于自适应模糊控制的节能装置研究

针对凹版印刷干燥设备,设计节能装置,该装置利用压缩机换热原理,对余热进行再循环利用。设计自适应模糊PID节能控制系统,完成对压缩机,调功器,变频器的实时控制。利用组态软件完成系统界面设计,人机交互简洁,操作方便。控制算法采用自适应模糊PID控制,依靠数据信息来调整模糊逻辑系统的参数,通过在线计算得到最佳控制器参数,抑制不确定性对系统的影响。将节能装置应用到凹版印刷机,实验数据显示,系统耗能减少,效率得到提高,达到节能目的,证明了节能系统的有效性,具有较强的应用价值。