Improved absorbing boundary condition based on linear interpolation for ADI-FDTD method

With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.

Numerical Solution of Euler-Bernoulli Beam Equation by Using Barycentric Lagrange Interpolation Collocation Method

Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology. Some authors have put forward many different numerical methods, but the precision is not enough high. In this paper, we will illustrate the high-precision numerical method to solve Euler-Bernoulli beam equation. Three numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by our method indicate new algorithm has the following advantages: small computational work, fast convergence speed and high precision.

Seismic ray-tracing calculation based on parabolic travel-time interpolation

A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method are used to compute seismic travel-time and ray-path in a 2-D grid cell model. Firstly, some basic concepts are introduced. The calculations of travel-time and ray-path are carried out only at cell boundaries. So, the ray-path is always straight in the same cells with uniform velocity. Two steps are applied in PTI and LTI method, step 1 computes travel-time and step 2 traces ray-path. Then, the derivation of LTI formulas is described. Because of the presence of refraction wave in shot cell, the formula aiming at shot cell is also derived. Finally, PTI method is presented. The calculation of PTI method is more complex than that of LTI method, but the error is limited. The results of numerical model show that PTI method can trace ray-path more accurately and efficiently than LTI method does.

C^1 natural element method for strain gradient linear elasticity and its application to microstructures

C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.

On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions

By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.

Optimized Hybrid Block Adams Method for Solving First Order Ordinary Differential Equations

Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency.Hybrid block methods for instance are specifically used in numerical integration of initial value problems.In this paper,an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations(ODEs).In deriving themethod,the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval.Furthermore,the convergence properties along with the region of stability of the method were examined.It was concluded that the newly derived method is convergent,consistent,and zero-stable.The method was also found to be A-stable implying that it covers the whole of the left/negative half plane.From the numerical computations of absolute errors carried out using the newly derived method,it was found that the method performed better than the ones with which we compared our results with.Themethod also showed its superiority over the existing methods in terms of stability and convergence.

三种方法的乡镇减灾能力评估结果比较——以某市区18个乡镇为例

减灾能力是区域防灾减灾、应急救援和恢复重建过程中所具有的综合能力。以某市区“第一次全国自然灾害综合风险普查”基础调查数据为例,分别采用秩和比法(RSR)、非整秩和比法(非整RSR)和TOPSIS法对该区18个乡镇的减灾能力进行定量化评估,从评估模型的实用性、数值大小、等级排名、整体趋势、计算工作量等五方面进行对比分析。结果表明:三种模型均适用于区域减灾能力定量化评估,可根据区域评估目的和需求进行选择。总体上,以秩和比法优劣分档最佳、信息损失最大,TOPSIS法信息损失最小、优劣分档最差。而基于非整秩和比法评估原理,利用线性插值法对各评价指标进行编秩,所编秩次与原指标值间存在更为紧密的线性对应关系,既克服了秩和比法源数据的信息损失,又能对TOPSIS法的优劣分档进行优化。因此,改进后的非整秩和比法的信息损失与优劣分档均比较适中,是三者中的较优选择。对非整秩和比法的研究可为减灾能力定量化评估提供参考。

跨域飞行器惯导装置设计及抗冲击测量方法

跨域飞行器由于工作环境复杂多变,在飞行过程中运动参数受瞬态冲击影响较大,导致导航精度降低且难以稳定控制。针对瞬态冲击导致跨域飞行器难以获取准确运动参数的问题,本文研制了一种基于大小量程加速度计组合的惯性导航装置,并提出了一种大小量程加速度计切换策略,利用巴特沃斯滤波器对采集的数据进行滤波处理,通过预设阈值的累计和控制图算法和自主可变滑动窗口实现对冲击点的检测,并采用分段式线性插值方法保证了数据的同步性,最后通过模拟仿真和跌落台试验对本文所提出的切换策略进行试验验证,试验结果表明,分段式线性插值方法的估计误差不超过0.6 g,并在小量程加速计测量值饱和后,切换至大量程加速计的测量值,满足了实时切换的要求,进一步证明该惯性导航装置及大小量程切换策略可应用于飞行器进行跨域试验。

堆取料机取料过程中防坍塌预警及路径规划研究

在运煤轮船船舱进行取料作业时,由于路径规划可能引发煤堆坍塌的危险,提出一种基于分层点云边缘信息提取的防止煤堆坍塌的模拟堆取料机取料路径规划方法。首先利用搭载二维激光扫描试验装置采集原始三维点云数据,通过坐标转换,采用直通滤波算法去噪滤波,随机采样法简化算法精简点云数据,基于切片法计算煤堆体积和质量,实现对来煤精准盘点;然后提取每层煤料堆表面的边缘信息,将不同层次的煤料堆边缘信息组合起来,构建出整个煤料堆表面的边缘模型,实时计算待取料煤堆边缘安息角,实现煤堆坍塌预警信息;最后基于直线插补方法进行取料路径规划,给出防止煤堆坍塌的模拟堆取料机执行机构作业路径。

甘肃省泾河流域流量监测站网布局优化设计

鉴于河流流量监测站网是收集流域内径流相关水文信息的重要网格系统,立足于甘肃省泾河流域流量监测站网现状,采用径流递变率法和线性内插精度法确定大河控制站数目的上下限,采用欧氏贴近度法确定区域代表性站点,进而提出站网布局的优化方案。布局优化后的甘肃省泾河流域流量监测站总数由21站增加至27站,包括增设大河控制站1站、区域代表站5站,迁移区域代表站1站;站网密度由原来的1 476 km^(2)/站优化至1 148 km^(2)/站。研究成果实现了对甘肃省泾河流域水资源在时间和空间分布变化上的控制,提高了站网的社会效益和经济效益。

超高压容器开孔处裂纹最深点处应力强度因子的计算方法

由于超高压容器开孔处的应力梯度变化很大,通常由最小二乘法拟合的三次多项式往往与实际的应力分布之间存在较大偏差。针对这一问题,提出了一种分段插值求解的计算方法。首先,基于应力强度因子及通用权函数的理论,推导出了常数插值、线性插值、二次插值求解的计算公式;其次,结合工程实例,基于无裂纹体的弹性应力分析,对比分析了常规最小二乘法与常数插值、线性插值、二次插值的应力分布表征精度及应力强度因子计算结果,确定了线性插值和二次插值方法的可靠性;然后,分析了数据采集量对线性插值和二次插值计算结果的影响,确定了线性插值方法的实用性;最后,对线性插值与有限元分析的计算结果进行了分析验证。研究结果表明:应力分布表征精度为“最小二乘法<常数插值<线性插值<二次插值”,计算结果相对误差约为15%;随着采集数据量的增加,采用线性插值方法的计算结果能较快收敛,更适合于工程计算;线性插值与有限元法的计算结果高度一致,证明了线性插值计算的可靠性。

规章政策变化下的延程运行飞行计划仿真

随着民航局相关规章的持续更新及国产C919即将商业运行,建立能适应规章变化且关键技术自主可控的国产飞行计划系统具有重要意义。首先,梳理了延程运行(ETOPS)核心概念及其飞行计划制作流程;然后,采用迭代法求解无风等时点、线性插值法计算特定时空点风温,进而求得实际等时点、改航燃油、改航距离以及燃油关键点等ETOPS飞行计划的关键信息。最后,以厦门至伦敦某航班进行实例验证。研究结果表明,所构建的ETOPS飞行计划制作流程与求解算法具有较高的精度,使用Python软件编写的飞行计划制作程序具有可行性,可为国产飞行计划系统的研发提供参考。

Optimization Methods for Box-Constrained Nonlinear Programming Problems Based on Linear Transformation and Lagrange Interpolating Polynomials

In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optimization methods are developed.The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker(KKT)points in general.Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method.Some numerical examples are reported to show the effectiveness of the proposed methods.

基于机载无人机三维激光扫描技术的不动产测绘研究

由于数据采集阶段位姿状态的变化,导致对目标的测绘结果往往存在较大误差。为此,提出基于机载无人机三维激光扫描技术的不动产测绘研究。选用型号为飞越X6的六旋翼无人机机架作为搭载装置,基于棱镜技术的Livox Mid40激光扫描仪作为采集装置,在全覆盖的轨迹下采集目标不动产点云数据,基于匀速运动假设和线性插值的方法进行不动产点云数据的对齐校正处理后,引入了ICP算法匹配不同位姿的不动产点云数据,将匹配后的点云数据按照坐标定位到对应的三维坐标系,构建完整的不动产模型,并使用最小二乘法对提取的边缘点进行直线拟合,完成测绘。在测试结果中,对应的误差始终在0.01m以内。

五孔探针实验数据处理的线性插值法

在使用五孔探针校准数据时通常采用样条插值或最小二乘法拟合,相同的探针校准曲线用这两种方法分别插值得到的结果有较大的差异。本文通过对两种方法理论上分析,提出了一种实用性更强的线性插值法。对于特性良好的探针,该方法的精度接近样条插值;对于特性较差的探针,能够在不改变探针特性曲线的基础上保证插值精度。相对于样条插值和最小二乘法拟合,该方法有着更为广泛的适应性。

水文资料插值计算方法探讨

本文利用5种常用的插值计算方法,对海洋实测资料序列中的某些固定节点进行插值计算,然后根据均方误差和图形拟合相结合的方法,探讨插值计算方法的适用性及应用条件并得出结论:阿基玛插值和三点拉格朗日插值效果拟合性最好,具有普遍应用性,多点拉格朗日和线性插值较为中性,在插值步长不大的条件下,插值效果较好,而牛顿插值不稳定,应用条件相对苛刻。

滑坡初始涌浪高度计算方法的改进及其应用

在阐述了使用潘家铮算法对滑坡水平运动模式和垂直运动模式下初始涌浪高度进行求解的基础上,基于线性插值原理,提出了滑坡斜向运动模式下的初始涌浪高度的计算公式。以长江的新滩滑坡为例,根据修正后的算法对其初始涌浪高度进行了计算,并利用计算结果采用潘家铮方法对涌浪的传播及爬坡高度进行了分析计算。结果表明计算的初始涌浪高度值及经传播后的爬坡高度与实际调查值比较吻合。

基于扫描激光雷达的列车速度测量系统

针对传统列车速度测量装置存在量程小、调试复杂等问题,基于扫描激光雷达技术,设计了一套适用于高速列车动态限界测量的列车速度测量系统。将扫描激光雷达固定在距列车10m左右的位置上,根据激光脉冲飞行时间测距原理,沿列车行驶方向对进入扫描范围内的列车车身逐点扫描,获得由测量点组成的车身轮廓信息;通过最小二乘拟合车厢测量点,得到列车行驶轨迹,确定列车行驶方向;采用分段线性差值确定相邻两次测量周期内列车行驶的距离,完成列车速度的测量。结果表明:该测速系统操作方便,量程可达600km/h,测速误差控制在±1.2%以内,可以满足高速列车速度测量需求。

工业CT图像的三维重建

工业CT图像三维重建是近年来工业CT技术研究的热点之一,将二维断层图像数据直接堆垒起来,结合阈值分割、线性内插等方法,获得了直观性较好的三维工业CT图像。通过对重建图像进行旋转、截取等操作,获得了不同方向、不同部位的三维图形。这种简单、快速的重建方法对更复杂的工业CT图像三维重建具有重要的指导意义。

高频大地电磁法有限元数值模拟

由于中深度工程地球物理勘探的迫切需要,以美国EH-4电导率成像系统为代表的高频率大地电磁法,在我国地球物理勘探行业的应用越来越广泛。其勘探深度在地下1 000 m以内,频率范围在10 Hz^100 kHz。这里研究了高频率大地电磁法有限元高精度,快速数值模拟。首先利用广义变分原理推导出电磁场的有限元方程,编制了双线性和双二次插值有限元程序,并进行了层状模型的验证性计算,然后对典型地堑模型的数值模拟结果进行了分析,得出了一些有意义的结论。