Variety of nonlinear wave-breaking

We discuss the formation of typical (structurally stable) singularities in nonlinear wave breaking in stable and unstable media. The wake wave-break due to the inhomogeneity of the Langmuir frequency is accompanied by electron injection into the acceleration phase. In a wake wave excited behind a finite width laser pulse, the wave-breaking mechanism involves the increase, with the distance behind the pulse, of the curvature of the wake front, followed by the self-intersection of the electron trajectories. In the long wavelength limit, the Weibel instability which leads to the generation of a strong magnetic field, the relativistic self focusing and the Rayleigh-Taylor instability of a thin plasma slab provide examples of a common behavior with the rarefaction wave-breaking in unstable media. We present a solution of the Cauchy problem that describes the evolution of nonlinear perturbations of the Rayleigh-Taylor instability in terms of analytical functions of a complex variable.     

Dynamics analysis of distributed parameter system subjected to a moving oscillator with random mass, velocity and acceleration

The problem of calculating the response of a distributed parameter system excited by a moving oscillator with random mass, velocity and acceleration is investigated. The system response is a stochastic process although its characteristics are assumed to be deterministic. In this paper, the distributed parameter system is assumed as a beam with Bernoulli–Euler type analytical behaviour. By adopting the Galerkin's method, a set of approximate governing equations of motion possessing time-dependent uncertain coefficients and forcing function is obtained. The statistical characteristics of the deflection of the beam are computed by using an improved perturbation approach with respect to mean value. The method, useful to gathering the stochastic structural effects due to the oscillator–beam interaction, is simple and leads to results very close to Monte Carlo simulation for a wide interval of variation of the uncertainties.     

On the estimation of probability of error

This paper considers the problem of estimation of classification error in pattern recognition. A theorem is presented to obtain the changes in the eigenvalues and eigenvectors of matrices of the form S₂⁻¹ S₁, when there are changes of first order of smallness in the real symmetric matrices S_i, I = 1, 2. Based on this theory a computational algorithm is developed for the estimation of classification error of Fisher classifier, using leaving groups out method.     

有限精度混沌系统的m序列扰动实现

本文研究利用ｍ序列的扰动来实现有限精度混沌系统的方法，考察了扰动序列的周期，幅度以及扰动分布对混沌信号特性的影响，研究表明，扰动ｍ序列所需的阶数取决于混沌序列所需要达到的周期长度，扰动的位数取决于混沌映射的最大斜率，随着混沌系统实现粗度的提高，所需的扰动幅度呈指数减小。     

Adaptive control and stability analysis of nonlinear crane systems with perturbation

This paper presents an adaptive control approach using a model matching technique for 3-DOF nonlinear crane systems. The proposed control is linearly composed of two control frameworks: nominal PD control and corrective control. A nonlinear crane model is approximated by means of feedback linearization to design nominal PD control avoiding perturbation. We propose corrective control to compensate system error feasibly occurring due to perturbation, which is derived by using Lyapunov stability theory with bound of perturbation. Additionally, we achieve stability analysis for the proposed crane control system and analytically derive sufficient stability condition with respect to its perturbation. Numerical simulation is accomplished to evaluate our proposed control and demonstrate its reliability and superiority compared to traditional control method.     

微扰理论总结

电磁兼容数值仿真需要建立电子设备的仿真模型,但是实际电子设备模型比较复杂,包括有大量的微小结构,如各种安装凸台、凹槽等.如果按照实际的模型建立仿真模型会耗费大量的人力物力.同时复杂的模型会使计算量急剧的增加,过于复杂的模型也会导致网格的畸变,导致错误的仿真结果.因此在电磁兼容仿真建模过程中,必须对电子设备的仿真模型加以简化或等效处理.本文基于国内外对微扰问题研究,给出电子设备建模过程中模型简化的基本原理,即微扰理论.并对以后的研究提出相关的思路和方法.     

扩轧管电液伺服系统非线性建模与控制

为了研究阀控缸机构的非线性对电液伺服系统控制性能的影响,以钢管生产过程中的扩轧管电液伺服系统为背景,首先通过分析非对称比例(伺服)阀的电信号输入到阀芯位移和阀芯位移到非对称液压缸活塞位移输出过程的非线性特性,建立非对称阀控非对称缸机构的非线性数学模型以描绘实际系统;其次根据实际系统模型的级联性特点,提出了一种融合定量反馈控制理论和扰动估计理论的非线性控制策略,实现了对负载运动和负载压力非线性的分级控制;最后以常规PID控制为基础,对提出控制策略的有效性进行相应的仿真和实际控制对比.结果表明,该控制策略具有更好的系统稳态和动态响应性能,可应用于解决工程实际问题.     

复模态理论的摄动有限元法

本文借助状态空间,采用摄动有限元法对不定参数结构进行了动力分析.将复模态的二次特征值问题化为一次特征值问题,对不定参数在某一确定值邻域内的摄动,利用二阶摄动的有限元方法通过一次性计算得到了结构复特征值,状态特征向量的一、二阶摄动公式。     

发电机转子的非线振荡分析

本文应用奇异摄动理论分析了同步发电机转子的非线性振荡过程,得到了三重尺度下的二阶非线性近似解析解,并讨论了电力系统机电参数对发电机移子非线性振荡特性的影响。     

基于节点电纳摄动的通用配电网损耗分配方法

文中主要探讨配电网损耗的分配方法。针对含有转供和小电源的任意结构配电网，分析并给出了损耗分配的对象和基本要求。提出了一种基于节点电纳摄动改造配电网全节点导纳矩阵可逆性的方法。这种改造方法从损耗分配的合理性与潮流误差出发确定电纳摄动点和摄动值，使任意配电网的全节点阻抗矩阵能够可靠计算。最后基于全节点阻抗矩阵和交易的等值节点电流提出了一种通用的配电网损耗分配方法。这种分配方法既适用任意结构的配电网络和Pool与Bilateral交易，又满足电路定律、具有可加性和聚合不变性的经济特征。仿真结果验证了文中方法的有效性。