Matrix valued adaptive cross approximation

A new variant of the Adaptive Cross Approximation (ACA) for approximation of dense block matrices is presented. This algorithm can be applied to matrices arising from the Boundary Element Methods (BEM) for elliptic or Maxwell systems of partial differential equations. The usual interpolation property of the ACA is generalised for the matrix valued case. Some numerical examples demonstrate the efficiency of the new method. The main example will be the electromagnetic scattering problem, that is, the exterior boundary value problem for the Maxwell system. Here, we will show that the matrix valued ACA method works well for high order BEM, and the corresponding high rate of convergence is preserved. Another example shows the efficiency of the new method in comparison with the standard technique, whilst approximating the smoothed version of the matrix valued fundamental solution of the time harmonic Maxwell system. Copyright © 2016 John Wiley & Sons, Ltd.     

An adaptive wavelet space‐time SUPG method for hyperbolic conservation laws

This article concerns with incorporating wavelet bases into existing streamline upwind Petrov‐Galerkin (SUPG) methods for the numerical solution of nonlinear hyperbolic conservation laws which are known to develop shock solutions. Here, we utilize an SUPG formulation using continuous Galerkin in space and discontinuous Galerkin in time. The main motivation for such a combination is that these methods have good stability properties thanks to adding diffusion in the direction of streamlines. But they are more expensive than explicit semidiscrete methods as they have to use space‐time formulations. Using wavelet bases we maintain the stability properties of SUPG methods while we reduce the cost of these methods significantly through natural adaptivity of wavelet expansions. In addition, wavelet bases have a hierarchical structure. We use this property to numerically investigate the hierarchical addition of an artificial diffusion for further stabilization in spirit of spectral diffusion. Furthermore, we add the hierarchical diffusion only in the vicinity of discontinuities using the feature of wavelet bases in detection of location of discontinuities. Also, we again use the last feature of the wavelet bases to perform a postprocessing using a denosing technique based on a minimization formulation to reduce Gibbs oscillations near discontinuities while keeping other regions intact. Finally, we show the performance of the proposed combination through some numerical examples including Burgers’, transport, and wave equations as well as systems of shallow water equations.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2062–2089, 2017     

基于改进的PSO-SVM的音频信号特征识别和分类

针对音频信号准确性分类的问题,提出一种基于改进的的粒子群优化算法(PSO)的支持向量机(SVM)音频信号分类的方法,简称IPSO-SVM.首先用Mel倒谱系数法对4种音频信号进行特征提取.其次在PSO中引入自适应变异因子,能够成功地跳出局部极小值点;然后对PSO中的惯性权重进行了改进,将惯性权重由常数变为指数型递减函数.随着迭代的进行,使权重逐渐减小,这样做有利于粒子进行局部寻优.最后用改进的PSO不断优化SVM中的惩罚因子c和核函数参数g来提高预测精度.实验结果表明,与传统的SVM、PSO-SVM、GA-SVM相比,我们提出的IPSO-SVM算法分类结果更精确.     

带有不确定参数的一类混沌金融系统的广义投影同步

针对带有不确定参数的一类混沌金融系统,提出了实现驱动系统和响应系统广义投影同步的自适应控制策略,并基于Lyapunov稳定性理论给出和验证了广义投影同步稳定性判据.数值仿真验证了控制策略和理论分析的有效性.     

一种结构故障的振动诊断法

文章分析了振动参数对结构故障的敏感度，选取对故障比较敏感、又能反映结构动力特性的频响函数，作为诊断故障的参数，采用了最小二乘辨识、卡尔曼滤波、自适应滤波等方法，进行故障诊断、仿真试验的结果表明，本文提出的方法可行，且有一定精度，实物试验结果表明，当局部刚度下降5%时，运用本文方法可诊断出故障。     

采用MRAC的气－液联合多通道协调加载控制系统的研究

气压系统与液压系统的特性存在着较大的差异，本文研究了该系统的自适应控制方法。根据气－液控制系统的技术特点，作者提出了采用参考模型自适应控制的策略，并解决了控制器设计、实现中的一系列技术问题。经过试验，证明本文的研究是成功的。     

自适应有限元局部P加密的面向对象程序实现

本文采用了面向对象的程序设计方法，以C 作为编程语言，构造了一个局部自适应有限元P加密程序。研究内容涉及从Serendipity函数的构造、单元的形成、自升阶算法以及误差估计和判断。最后采用C 的一系列类及成员函数实现了这些功能，并构造了相应的输入输出模块，使其成为一个完整的自适应有限元分析程序。文中给出的计算结果表明，在P加密有限元分析程序中，误差随着阶数的升高而下降。而且，局部P加密的区域也集中在应力奇异的部位。这验证了文中的理论推导及程序实现的正确性。     

一种改进的分块隐式数值方法

提出了一种改进的分块隐式数值方法，在贴体坐标和交错网格下以逆变速度分量和压力Ｕ，Ｖ，Ｗ，ｐ为基本求解变量，由此克服了原分块隐式数值方法求解复杂边界流动时的困难．９０°弯管流动数值计算初步表明，本文提出的方法合理、可行     

The automatic control of boundary-layer transition — Experiments and computation

In recent years there has been an increasing interest in the control of boundary-layer transition through the use of wall suction. In the current work suction is provided through one or more suction panels situated close to the leading edge of a plate. Experiments show that boundary-layer pressure fluctuation measurements can be used to identify the position of transition. Transition can be maintained at a desired location with minimum power consumption by employing an automatic adaptive feedback control loop which regulates the suction flow rates of two independent suction panels. This can be expressed as a constrained optimization problem. To allow the suction flow rates to be updated, a modified least mean squares algorithm is used within the control loop. Experimental measurements show that the control algorithm allows fast and stable convergence towards the optimum suction distribution for a double suction panel configuration. Numerical simulations have also been performed. The two-dimensional boundary layer was calculated allowing the viscous boundary layer to interact with the inviscid outer flow. Following linear stability theory the spatial growth rates are calculated by solving an Orr-Sommerfeld type eigenvalue problem, with the streamwise location of transition predicted via thee ^N -method. Applying the same optimization strategy as in the experiments, good qualitative agreement between computations and experiments was found. The optimization algorithm has been applied to computer models where the relation between suction flow rates and transition location is described by an empirical analytical function. This shows that the controller can in principle be applied to systems with more than two suction panels.Nomenclature b transition location with zero suction - d desired transition location - e(k) error signal - k iteration index - p rms pressure - p _ref reference rms pressure - r sum of the reference pressure - u streamwise velocity - u _e external velocity - inviscid external velocity - A wave amplitude - F( ) cost function - I identity matrix - N maximum amplification factor - P projection matrix - R Reynolds number - Re Reynolds number based on the boundary-layer thickness - R matrix of weights - Tu turbulence level - vector of suction flow rates - v normal velocity - v _wall suction velocity at the surface - x streamwise coordinates - x _m microphone location - x _T(k) measured transition location - y normal coordinate - y(k) sum of the measured pressures - w(k) noise - plate length - r +i _i - free stream velocity - * displacement thickness - gradient vector - Lagrange multiplier - controller gain - disturbance stream function - disturbance amplitude - wave frequency = complex wave number     

无刷直流力矩电机系统的自适应扰动力矩补偿研究

陀螺漂移测试转台无刷直流力矩电机系统中存在波动力矩和负载力矩振动，这严重地影响了转台速率平稳度。为提高转台速率状态位置跟踪精度，设计了一种自适应补偿方法。该方法包含一个参自适应律和等效PID控制律，它利用前馈补偿原理，来估计电机中未知参数以及波动力矩和负载力矩参数并给与补偿。该自适应补偿方法保证了闭环系统全局稳定性和对期望位置信号的渐进跟踪。仿真结果证明：该方法有效地提高了转台速率状态跟踪精度。