Piecewise linear recursive convolution FDTD method for magnetized plasmas

The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method greatly improves accuracy over the original recursive convolution （RC） FDTD approach but retains its speed and efficiency advantages. A PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time is presented, enabled the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations the reflection and transmission coefficients through a magnetized plasma layer. The results show that the PLRC-FDTD method has significantly improved the accuracy over the original RC method.

3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization

Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model.Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations.Instead,the minimum cut on a special designed graph need to be computed.The method is tested on data with complicated structures.It is rather stable with respect to initial value and the algorithm is nearly parameter free.Experiments show that it can solve large problems much faster than traditional approaches.

A Revised Piecewise Linear Recursive Convolution FDTD Method for Magnetized Plasmas

The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method improves accuracy over the original recursive convolution （RC） FDTD approach and current density convolution （JEC） but retains their advantages in speed and efficiency. This paper describes a revised piecewise linear recursive convolution PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations of the reflection and transmission coefficients through a magnetized plasma layer. The results show that the revised PLRC-FDTD method has improved the accuracy over the original RC FDTD method and JEC FDTD method.

An Improved Mumford-Shah Model and Its Applications to Image Processing with the Piecewise Constant Level Set Method

为快分割并且降噪，提高 penalization 学期的古典 Mumford-Shah (MS ) 模型需要，即增加 penalization 参数，它导致目标的渐渐的消失。在这份报纸，我们建议一个改进 Mumford-Shah (IMS ) 模型避免现象，并且采用 piecewise 常数水平集合方法(PCLSM ) 和坡度降下方法解决最小化问题。数字实验被给显示出新模型和算法的效率和优点。

Analytical Approach to Differential Equations with Piecewise Continuous Arguments via Modified Piecewise Variational Iteration Method

In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique provides a sequence of functions which converges to the exact solution of the problem. Moreover, this method reduces the volume of calculations because it does not need discretization of the variables, linearization or small perturbations. The results seem to show that the method is very reliable and convenient for solving such equations.

Harmonics analysis of the ITER poloidal field converter based on a piecewise method

Poloidal field（PF） converters provide controlled DC voltage and current to PF coils. The many harmonics generated by the PF converter flow into the power grid and seriously affect power systems and electric equipment. Due to the complexity of the system, the traditional integral operation in Fourier analysis is complicated and inaccurate. This paper presents a piecewise method to calculate the harmonics of the ITER PF converter. The relationship between the grid input current and the DC output current of the ITER PF converter is deduced. The grid current is decomposed into the sum of some simple functions. By calculating simple function harmonics based on the piecewise method, the harmonics of the PF converter under different operation modes are obtained.In order to examine the validity of the method, a simulation model is established based on Matlab/Simulink and a relevant experiment is implemented in the ITER PF integration test platform.Comparative results are given. The calculated results are found to be consistent with simulation and experiment. The piecewise method is proved correct and valid for calculating the system harmonics.

A Gas Dynamics Method Based on the Spectral Deferred Corrections (SDC) Time Integration Technique and the Piecewise Parabolic Method (PPM)

We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to define edge-averaged quantities, which are then used to evaluate numerical flux functions. The SDC technique is used to integrate solution in time. This kind of approach was first taken by Anita et al in [1]. However, [1] is problematic when it is implemented to certain shock problems. Here we propose significant improvements to [1]. The method is fourth order (both in space and time) for smooth flows, and provides highly resolved discontinuous solutions. We tested the method by solving variety of problems. Results indicate that the fourth order of accuracy in both space and time has been achieved when the flow is smooth. Results also demonstrate the shock capturing ability of the method.

Adaptive Single Piecewise Interpolation Reproducing Kernel Method for Solving Fractional Partial Differential Equation

It is well-known that using the traditional reproducing kernel method(TRKM) for solving the fractional partial differential equation(FPDE) is very intractable. In this study, the adaptive single piecewise interpolation reproducing kernel method(ASPIRKM) is determined to solve the FPDE. This improved method not only improves the calculation accuracy, but also reduces the waste of time. Two numerical examples show that the ASPIRKM is a more time-saving numerical method than the TRKM.

The piecewise constant method in gait design through optimization

The objective of this paper is to introduce the piecewise constant method in gait design of a planar,under actuated,five-link biped robot model and to discuss the advantages and disadvantages.The piecewise constant method transforms the dynamic optimal control problem into a static problem.

Breakage Distribution Estimation of Bauxite Based on Piecewise Linearized Breakage Rate

Laboratory tests were carried out to study the breakage kinetics of diasporic bauxite and determine its breakage distribution function. Non-first order breakage with different deceleration rates for different size intervals is found, which is most probably caused by the heterogeneity of the ore. Piecewise linearization method is proposed to describe the non-first order breakage according to its characteristics. In the method, grinding time is divided into several intervals and breakage is assumed to be first order in each interval. So, the breakage rates are calculated by taking the product of the last interval as feed and then established as a function of particle size and grinding time. Based on the predetermined breakage rate function, the breakage distribution of the ore is back-calculated from the experimental data using the population balance model (PBM). Finally, the obtained breakage parameters are validated and the simulated data are in good agreement with the experimental data. The obtained breakage distribution and the method for breakage rate description are both significant for modeling the full scale ball milling process of bauxite.

ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS

This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.

具有局部阻尼的二维Mindlin-Timoshenko板系统的镇定

该文研究了具有局部阻尼的二维Mindlin-Timoshenko板系统,首先将原系统转化成抽象柯西问题,运用算子半群理论得到了系统的适定性.借助系统频域稳定性结果,通过引入几何光学条件结合乘子技巧得到了系统的一致指数稳定性.

基于MLMD的电能质量扰动检测方法

针对局部均值分解(Local Mean Decomposition,LMD)算法应用于电能质量扰动检测时存在“端点效应”与滑动平均收敛速度慢,严重影响测量精度的问题,提出一种改进局部均值分解方法(Modified LMD,MLMD)。通过分段三次Hermite插值取代滑动平均法,有效改善LMD收敛慢、受平滑长度影响的弊端。为避免延拓长度不够而导致的“延拓失败”情形,在镜像延拓法的基础上结合“奇延拓”方法提出改进镜像延拓法。针对“直接法”求频率存在“毛刺现象”的弊端,文中改用希尔伯特变换(Hilbert Transform,HT)求取瞬时频率。最后,将MLMD分别应用于单一扰动信号与复合谐波信号的检测,相较传统的经验模态分解方法(Empirical Mode Decomposition,EMD),MLMD方法可有效抑制“端点效应”,同时能更准确的定位扰动信号的起止时刻,并且对高次谐波信号有更好的提取能力。

夏季日峰降温电力负荷预测灰色模型及其应用

基于2017—2020年石家庄市逐15分钟电力负荷及同期气象资料,计算人体舒适度指标有效温度和温湿指数,考虑基准负荷存在周期性和增长性,提出采用灰色模型GM(1,1)并结合滤波法、相关分析等方法,建立日峰降温电力负荷与人体舒适度指标分段回归模型。结果表明:石家庄电力负荷具有明显的逐年增长趋势;剥离出的日降温负荷曲线呈“W”型分布;分别对模型进行一次、二次和分段函数拟合,对3种预测模型进行检验发现分段函数预测精度较高,平均相对误差在4.8%~5.2%,有效温度和温湿指数的分段函数误差在-10%~10%所占比例分别为88.1%和90.5%;考虑了温度、湿度和风速的有效温度较温湿指数的夏季日峰降温电力负荷预测模型预测准确率更高,回归模型分段点为26.2℃,对电网“迎峰度夏”时期电力调度具有参考价值。

分段光滑机械振动系统亚谐振动的复杂分岔

以一类单自由度分段光滑机械振动系统为研究对象.数值计算两参数平面上亚谐振动的模式及分布区域,利用延拓打靶法对亚谐包含域内亚谐振动的分岔特征、稳定性及转迁规律进行了详细研究.结果表明:弹性碰撞振动系统中擦边分岔是连续可逆的.在亚谐包含域内,倍化型擦边分岔普遍存在,鞍结型擦边分岔和亚临界周期倍化分岔使系统响应发生跳跃和迟滞.高频亚谐包含域内多吸引子共存,混沌吸引子发生边界激变而突然消失.

重叠保留法教学探索与案例设计

分段卷积是DFT/FFT实现线性卷积的重要途径,主要有重叠保留法和重叠相加法,教学过程中发现,学生对于重叠保留法的学习往往忽略对算法原理的真正理解,导致计算结果不准确。该文基于圆周卷积与线性卷积的数学关系,推导重叠保留法计算误差出现的原因,得到重叠保留法的计算步骤;结合计算流程和具体实例,分析造成计算数据缺失的原因,并创新提出解决方法;随后分析基2-FFT算法下补零处理对重叠保留法的影响,得出采用重叠保留法和FFT算法计算线性卷积的优化步骤;最后,以调制光谱分析为例进行教学案例设计,并对重叠保留法给出相应的教学建议。

基于分段仿射阻抗模型的电压源变流器小扰动稳定域在线构造

近年来小扰动振荡事故频发,亟需建立能反映新能源并网系统全工况的在线稳定域。小扰动在线稳定域可以为时变性和波动性下新型电力系统的安全评估和控制优化提供强有力的支撑。因此,提出基于分段仿射阻抗模型的电压源变流器(voltage source converter,VSC)小扰动稳定域在线构造方法。首先,该方法使用电压、功率和频域因子作为分区变量,离线构建VSC的分段仿射阻抗模型。在线计算时根据运行工况可以快速定位运行分区并确定对应的线性仿射模型,从而极大地提高阻抗计算的效率。其次,提出VSC稳定域边界点的双层优化模型,利用改进的广义奈奎斯特判据和复合形法进行快速求解。然后,通过改变双层优化模型的求解方向搜索边界点,基于分段拟合获取准确的边界解析式。最后,仿真算例和实验结果表明,分段仿射阻抗模型与全阶阻抗模型误差小于1%;该方法可以准确和高效地构建在线稳定域。

拟周期激励下分段不对称振子的全局动力学

分段线性振子是一类强非线性系统,广泛存在于工程和数学领域.例如用永磁铁和悬臂梁构造分段线性能量阱,用分段线性模型逼近非线性振子,这类系统具有复杂的动力学行为.目前关于分段线性振子的研究主要考虑单频激励情形,对于拟周期激励系统研究较少.然而在实际工程中,外部激励通常为多频激励.文章通过广义的Melnikov方法,研究了拟周期激励下一类分段不对称振子的全局动力学,得到了同宿轨道横截相交的条件,由此给出了系统发生Smale马蹄型混沌的阈值.通过时间历程图、相图、Poincaré截面图和最大Lyapunov指数图验证了理论结果,并分析了阻尼、弹簧刚度及外激励幅值对系统混沌运动的影响.此外,发现了系统的拟周期吸引子经环面倍化路径和分形路径演化为奇异非混沌吸引子的特殊现象.奇异非混沌吸引子是一类具有分形几何结构,但最大Lyapunov指数非正的吸引子,这类吸引子可看作一种介于拟周期吸引子和混沌吸引子之间的特殊吸引子.对奇异非混沌吸引子的产生机理和拓扑结构的研究有助于更好地理解多频激励系统中的分岔和混沌现象.

限幅型非光滑吸振器模型的稳定性与周期运动研究

本文研究具有分段光滑特性的限幅型吸振器模型的稳定性与周期运动.建立一类限幅型非光滑吸振器的动力学模型,探讨模型容许平衡点的存在性,通过Liénard-Chipart稳定性准则,分析容许平衡点的稳定性.通过参数变换,将限幅型吸振器模型转化为具有两个切换流形的四维分段光滑系统.通过计算系统首次积分,获得四维含参分段光滑动力系统在其未扰系统存在一族周期轨条件下的Melnikov函数.探讨不同参数条件下系统周期轨的存在性及个数,并利用数值模拟方法给出其相图构型,验证理论结果的正确性.研究结果表明不同的间隙参数影响系统周期轨个数及相对位置.

基于供冷/热系统质-量调节的区域综合能源系统动态最优能流计算

区域综合能源系统(regional integrated energy system,RIES)的最优能流计算是求解RIES的设备配置、优化调度、故障分析等问题的基础。考虑供冷/热和供气管道传输能量的动态特性,建立RIES动态最优能流计算模型,其中基于特征线法获得了供冷/热管道和供气管道动态偏微分方程的代数解析解。针对基于供冷/热系统质–量调节模式下管道能量传输时滞变量造成RIES的动态能流计算模型难以求解的问题,提出采用分段插值法获得供冷/热管道两端节点温度之间关系的近似表达式并加入动态最优能流计算模型中。此外,针对优化模型中供冷/热系统的流量与温度相乘的双线性项,提出一种能够缩紧松弛间隙的分段凸包络松弛方法将原混合整数非线性优化模型转化为混合整数二次约束规划模型,能够在保证计算精度的同时实现高效求解。最后以某个RIES算例进行分析,验证了所提方法的计算准确性和高效性,并与常用的质调节模式相比,表明在供冷/热系统质–量调节模式下能找到经济性更优的RIES运行点。