Comparative Analysis of Equal and Unequal Grounding Grid Configurations by Compression Ratio and Least Square Curve Fitting Techniques

The primary aim of the power system grounding is to safeguard the person and satisfying the performance of the power systemtomaintain reliable operation.With equal conductor spacing grounding grid design,the distribution of the current in the grid is not uniform.Hence,unequal grid conductor span in which grid conductors are concentrated more at the periphery is safer to practice than equal spacing.This paper presents the comparative analysis of two novel techniques that create unequal spacing among the grid conductors:the least-square curve fitting technique and the compression ratio techniquewith equal grid configuration for both square and rectangular grids.Particle Swarm Optimization(PSO)is adopted for finding out one optimal feasible solution among many feasible solutions of equal grid configuration for both square and rectangular grids.Comparative analysis is also carried out between square and rectangular grids using the least square curve fitting technique as it results in only one unequal grid configuration.Simulation results are obtained by theMATLAB software developed.Percentage of improvement in ground potential rise,step voltage,touch voltage,and grid resistancewith variation in compression ratios are plotted.

Curve Fitting and Least Square Analysis to Extrapolate for the Case of COVID-19 Status in Ethiopia

On 30 January 2020 World Health Organization (WHO), declared the novel corona virus as a Public Health Emergency of International Concern (PHEIC), COVID-19 virus as an epidemic transmitted virus. It was on 31 December 2019, the WHO China Country office was informed the cases of pneumonia unknown etiology detected in Wuhan city, Hubei Province of China. Just after WHO’s declaration, Ethiopia has taken different measures to protect from this public health emergency problem. The disease is human to human transmitted virus. It comes from outside of the country, so that it opens check points in different entrance of the country. However, in 13 March 2020 the first positive case was reported from Japanese man. The virus is continuing the transmission in the public progressively more. While this research has been working, within 90 days from the first case, the country reported 2506 positive cases, 35 deaths. The research has done after collecting the first 90 days of data in Ethiopian case. Daily report announced by Ethiopian MoH is based on the test. And hence, the reported data as positive cases with COVID-19 is not actual positive case data in the country. There for, this paper has contribution for planning and taking further measure on the viruses by demonstrating the next 90 days predictive data. I use best curve fitting analysis using python function of the module polyfit algorithm to predict the trend of COVID-19 cases in Ethiopia.

Estimation of mass transfer coefficient in ozone absorption by linear least square fitting and Simplex search methods

For physical ozone absorption without reaction,two parametric estimation methods,i.e.the common linear least square fitting and non-linear Simplex search methods,were applied,respectively,to determine the ozone mass transfer coefficient during absorption and both methods give almost the same mass transfer coefficient.While for chemical absorption with ozone decomposition reaction,the common linear least square fitting method is not applicable for the evaluation of ozone mass transfer coefficient due to the difficulty of model linearization for describing ozone concentration dissolved in water.The nonlinear Simplex method obtains the mass transfer coefficient by minimizing the sum of the differences between the simulated and experimental ozone concentration during the whole absorption process,without the limitation of linear relationship between the dissolved ozone concentration and absorption time during the initial stage of absorption.Comparison of the ozone concentration profiles between the simulation and experimental data demonstrates that Simplex method may determine ozone mass transfer coefficient during absorption in an accurate and high efficiency way with wide applicability.

LEAST-SQUARES METHOD-BASED FEATURE FITTING AND EXTRACTION IN REVERSE ENGINEERING

The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.

Least squares fitting of coordinate parameters model

This paper starts with untime-diversification of the time-diversification deformation model and gives displacement distribution model of untime-diversification and simplifies further the study of deformation model. The paper discusses the problem of least squares fitting of coordinate parameters model—parameters of deformation model. During discussion, the basic means of cubic B splines and two steps of multidimensional disorder datum fitting are adopted which can make fitting function calculated mostly approximate coordinate parameters model and it can make calculation easier.

Calculation of stratum surface principal curvature based on a moving least square method

With the east section of the Changji sag Zhunger Basin as a case study, both a principal curvature method and a moving least square method are elaborated. The moving least square method is introduced, for the first time, to fit a stratum surface. The results show that, using the same-degree base function, compared with a traditional least square method, the moving least square method can produce lower fitting errors, the fitting surface can describe the morphological characteristics of stratum surfaces more accurately and the principal curvature values vary within a wide range and may be more suitable for the prediction of the distribution of structural fractures. The moving least square method could be useful in curved surface fitting and stratum curvature analysis.

A CONCISE M-METRIC LEAST SQUARE FORMULA FOR POLYNOMIAL ANALOGY

An M-metric least square method for polynomial analogy is presented. The relative normal eqUation is of diagonal form, such that the concise solution formula is explicit, and it is suitable to Parallel computation. On the other hand, by error analysis of a typical example, we can see that the presented method is reliable.

Design of Ballistic Consistency Based on Least Squares Support Vector Machine and Particle Swarm Optimization

In order to improve the firing efficiency of projectiles,it is required to use the universal firing table for gun weapon system equipped with a variety of projectiles.Moreover,the foundation of sharing the universal firing table is the ballistic matching for two types of projectiles.Therefore,a method is proposed in the process of designing new type of projectile.The least squares support vector machine is utilized to build the ballistic trajectory model of the original projectile,thus it is viable to compare the two trajectories.Then the particle swarm optimization is applied to find the combination of trajectory parameters which meet the criterion of ballistic matching best.Finally,examples show the proposed method is valid and feasible.

Perturbation Analysis of Structured Least Squares Problems and Its Application in Calibration of Interest Rate Term Structure

A structured perturbation analysis of the least squares problem is considered in this paper.The new error bound proves to be sharper than that for general perturbations. We apply the new error bound to study sensitivity of changing the knots for curve fitting of interest rate term structure by cubic spline.Numerical experiments are given to illustrate the sharpness of this bound.

Weighted Least-Squares for a Nearly Perfect Min-Max Fit

In this note, we experimentally demonstrate, on a variety of analytic and nonanalytic functions, the novel observation that if the least squares polynomial approximation is repeated as weight in a second, now weighted, least squares approximation, then this new, second, approximation is nearly perfect in the uniform sense, barely needing any further, say, Remez correction.

基于幂加权最小二乘拟合的红外相机辐射定标方法

分析了现有线性度计算方法的不足,提出基于偏差/测量值的新线性度评价方式,通过该方式最小二乘拟合的低端温度偏差比高端大一个数量级,并采用加权拟合提高系统响应线性度。在分析不同光谱的温度和辐亮度拟合函数基础上,提出一种基于辐亮度倒数幂加权最小二乘线性拟合的地面和星上辐射定标方法,确认最佳权重幂次,建立了幂次n=1的加权最小二乘拟合外黑体线性定标方程、内黑体线性定标方程、内外黑体辐亮度转换模型。针对星上内黑体高精度两点定标建立了基于加权最小二乘拟合内外黑体辐亮度转换模型;针对星上黑体发射率退化提出了基于恒星定标的红外相机星上内黑体辐亮度定标修正方法,建立了外黑体辐亮度、内黑体辐亮度和恒星辐亮度转换模型。采用加权线性拟合后,积分时间10 ms的低温端外黑体反演偏差由1.63 K下降到0.52 K,内黑体偏差反演温度偏差由0.83 K下降到0.39 K,系统响应线性度明显提升。

曲线曲面局部最小二乘渐进迭代逼近

作为一种有效的大数据拟合方法,曲线曲面最小二乘渐进迭代逼近方法(LSPIA)吸引了众多研究者的关注,并获得了广泛的应用。针对LSPIA算法拟合局部数据点效果较差的问题,提出了一种局部的LSPIA算法,称为LOCAL-LSPIA。首先,给定初始曲线(曲面)并从给定的数据点中选择部分数据点;然后在初始曲线(曲面)上选择需要调整的控制点;最后,LOCAL-LSPIA通过迭代调整这一部分控制点来生成一系列局部变化的拟合曲线(曲面),并且保证生成的曲线(曲面)的极限是在仅调整这部分控制点的情况下拟合部分数据点的最小二乘结果。在多个曲线曲面拟合上的实验结果表明,为达到相同的拟合精度,LOCAL-LSPIA算法比LSPIA算法需要的步骤和运算时间更少。因此,LOCAL-LSPIA是有效的,而且在拟合局部数据的情况下比LSPIA算法的收敛速度更快。

具有多MO喷嘴垂直MOCVD反应腔外延层厚度均匀性的优化理论及应用

金属有机物化学气相淀积(metal organic chemical vapor deposition,MOCVD)作为异质结半导体材料外延的关键手段,其外延层厚度均匀性会直接影响产品的良率.本文将理论与实验相结合,针对3个MO源喷嘴的垂直反应腔MOCVD,将各MO源喷嘴等效为蒸发面源,并引入一等效高度来涵盖MOCVD的相关外延参数,建立外延层厚度与各MO源喷嘴流量间的定量关系,设计并利用EMCORE D125 MOCVD系统外延生长了AlGaAs谐振腔结构,根据实验测得的外延层厚度分布结果,利用最小二乘法对模型参数进行了拟合提取,基于提取的模型参数,给出了优化外延层厚度均匀性的方法.4 in(1 in=2.54 cm)外延片mapping反射谱的统计结果为,腔模的平均波长为651.89 nm,标准偏差为1.03 nm,厚度均匀性达到0.16%.同时外延生长了GaInP量子阱结构,4 in外延片mapping荧光光谱的统计结果为,峰值波长平均值为653.3 nm,标准偏差仅为0.46 nm,厚度均匀性达到0.07%.本文提出的调整外延层厚度均匀性的方法具有简单、有效、快捷的特点,且可以进一步推广至具有4个MO喷嘴以上的垂直反应腔MOCVD系统.

广场舞和健步走锻炼对绝经后女性体成分影响的研究

为探讨长期广场舞与健步走锻炼在改善绝经后女性体成分方面的优劣以及锻炼年限与体成分之间的相关关系,本研究招募长期分别以广场舞与健步走锻炼为主的绝经后女性各40人(广场舞组和健步走组),长期为非体育人口的绝经后女性40人(对照组),测量其体成分。结果显示:除了骨骼肌外,广场舞组各指标值与对照组之间均具有统计学差异(P<0.05);健步走组体脂肪、体脂率和健康评估指标值与对照组之间均具有统计学差异(P<0.05);广场舞组体脂率指标值显著低于健步走组(P<0.05)。在相关性方面,广场舞组绝经后女性锻炼年限均分别与体脂肪、体脂率、骨肌比和健康评估指标值间存在高度负相关关系(P<0.01);健步走组绝经后女性的锻炼年限与体脂率指标值之间呈高度负相关关系,而与体脂肪、骨肌比和健康评估指标值之间呈中度正相关关系(P<0.01)。结果表明:长期广场舞与健步走锻炼均能改善绝经后女性的体成分,主要表现为降低体脂,提高健康水平,且广场舞的改善效果优于健步走。广场舞与健步走的锻炼年限与绝经后女性的体脂肪、体脂率、骨肌比和健康评估均呈高度相关关系,但广场舞锻炼的相关程度大于健步走锻炼,这可能与广场舞锻炼的运动强度高于健步走有关。

融入几何先验的圆柱表面三维应变场双目视觉测量方法

针对现有基于双目视觉的圆柱表面三维应变场测量方法从位移场计算应变场效率低下的问题,将圆柱结构几何先验信息融入子域投影法理论,利用圆柱标准坐标变换替代大量冗余的局部切平面最小二乘拟合求解,提出了一种融合圆柱拟合和子域投影的表面三维应变场计算方法;然后采用数值模拟方式,在不同应变区域和位移场噪声条件下,将所提方法与一般曲面子域投影法进行对比分析;最后开展圆柱拉伸实验,分别从单点和全场两个角度将所提方法的应变计算结果与应变片测量结果进行了对比。研究结果表明:在保证计算精度和位移场噪声鲁棒性的同时,所提方法将计算效率提高了约20%,且与应变片实验测量结果吻合较好,验证了该方法能够实现圆柱结构表面三维应变场的高效测量,也为规则结构表面三维应变场的计算提供了新思路。

基于拟合椭圆的等震线长短轴测量方法

提出了一种改进的拟合椭圆算法用于测量等震线长短轴,即将等震线测量的模式和直接测量算法的概念以约束的形式加入拟合椭圆算法,并使用最小二乘法求解椭圆系数,在与传统等震线测量方法保持一致的基础上,减少了直接测量方法的主观不确定性。在此基础上讨论了拟合椭圆算法的适用性和鲁棒性,将等震线长短轴的测量结果与前人的结果进行了对比。结果表明:拟合椭圆算法的适用性较好,可用于等震线的拟合;拟合椭圆算法的鲁棒性较好,计算结果较为稳定;对于未闭合且形状复杂的等震线,计算结果相对离散,要单独验证结果是否合理;利用拟合椭圆算法得到的等震线长短轴结果与前人的结果较为一致,可用于建立烈度衰减关系。

一种平面静电离子阱非正弦镜像电荷/电流信号的定量转换新算法

傅里叶变换质谱(FTMS)的质量分辨率取决于镜像电荷/电流的采集时间。为了在较短的时间内获得较高的分辨率,除增加分析器场强外,还可以利用镜像电荷信号中的高次谐波。平面静电离子阱获得的镜像电荷信号具有非正弦波形,其中包含许多高次谐波成分,增加了频谱分析的复杂程度,例如,难以辨认1个谱峰的谐波次数,以及当不同次的谐波发生重叠时出现定量困难。为了将多质荷比离子的镜像电荷信号转换成质谱,本文开发了一种新的定量算法,包含谱峰评分分类(SC)和最小二乘法拟合(LSF)。通过评分可以确定每个峰属于哪一次谐波,从而确定其对应的基频。打分算法列出所有候选离子的基频,并使用确定的基频构建所有基信号,然后用其对原频谱进行LSF,以确定每种质荷比离子的数量。使用48种不同质荷比离子的仿真镜像电荷信号对SCLSF算法进行测试。结果表明,该方法允许较宽的质量范围,即使在高噪声条件下,通过SC-LSF算法也能准确得到各种不同质荷比离子的数量。因为频谱中通常存在大量的空白频点,可以选择1个频点子集进行LSF,这相对于时域中的LSF,能够大大减少计算量,提高效率和准确度。此外,只有使用复数频谱数据进行LSF时才能获得良好的定量效果,而使用幅值数据则会对质荷比接近的离子定量造成较大的误差,这是因为质荷比接近的离子信号的低次谐波峰未能彻底分解,而复数的幅值不具有可加性,从而造成拟合的错误。

基于最小二乘的椭圆拟合及其FPGA实现

针对现有的基于FPGA平台实现的最小二乘椭圆拟合算法中线性方程求解输出时延较大的问题,采用Cholesky分解法解线性方程,并对Cholesky分解中的平方根求解,运用单向旋转、合并迭代、迭代次数可调等手段,提出了一种基于CORDIC算法的迭代自适应的平方根求解结构。实验结果表明,改进的平方根求解算法对缩短Cholesky分解输出时延有良好的效果,Cholesky分解在FPGA平台相较于现有的LDLT分解法实现63.26%的速度提升;椭圆拟合算法在保证输出绝对误差小于0.1 pixel的情况下,FPGA平台相对于计算机软件实现了1000倍以上的速度提升,适合实时性要求较高的应用场合。

中老年女性广场舞者健康体适能和HRQoL间关系研究

目的:评定自发锻炼广场舞者健康体适能和健康相关生活质量(HRQoL)水平,并分析两者间关系。方法:采用便利抽样法,选择2020年6月-9月杭州市中老年女性广场舞者199名为研究对象。采用自制问卷和SF-36量表调查广场舞者基本信息和HRQoL水平,并对血压、肺活量和握力等7个健康体适能指标进行测评。结果:①健康体适能各单项情况如下,肺活量合格率为54.7%,握力合格率为64.3%,坐位体前屈合格率为71.3%,动态平衡合格率为51.3%,血压正常率为31.1%,BMI指数正常率为48.2%,骨量正常率为49.2%;HRQoL总分为(83.63±11.79)分(满分100分,低于60分不合格),不合格占5.5%,合格占8.0%,良好占16.1%,优秀占70.4%。②以年龄和参与锻炼情况为协变量,对健康体适能和HRQoL进行偏相关分析,健康体适能部分指标(肺活量、握力、坐位体前屈和动态平衡)和HRQoL间存在显著性正向相关(P<0.05),但相关系数均不高。③二元Logistic回归分析结果显示,参与其他运动情况、骨质健康和坐位体前屈成绩是HRQoL达到优秀水平的良性影响因素(P<0.05)。结论:长期参与广场舞练习对锻炼者健康水平具有积极影响,在HRQoL各维度得分较高,生活质量呈现较高水平,但健康体适能部分指标结果仍不理想,仍需进一步提高。健康体适能与HRQoL两者测评结果间存在一定差异,但两者间仍呈正向相关,其中骨质健康、柔韧适能(坐位体前屈成绩)和参与其他运动情况是达到HRQoL优秀水平的主要因素。

一种适用于北斗三号星间扩展用户的定轨算法

针对北斗卫星导航系统星间链路网络扩展服务航天器的精密轨道确定及时间同步需求,提出了基于多项式轨道拟合方法的轨道确定与时间同步算法,克服了传统算法中使用北斗星间链路双向测量数据必须具备初始轨道和钟差等先验信息的约束,可有效拓宽北斗星间链路使用场景。该算法以多项式表达航天器一段时间的轨道和钟差,并使用星间双向测量数据基于最小二乘算法迭代估计多项式系数,从而完成航天器轨道和钟差解算。利用北斗三号星间链路在轨实测数据的试验表明定轨和时间同步精度均在0.12 m以内,有效验证了该算法的正确性。