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.

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.

采用改进遗传算法优化LS-SVM逆系统的外转子无铁心无轴承永磁同步发电机解耦控制

为了实现外转子无铁心无轴承永磁同步发电机(outer rotor coreless bearingless permanent magnet synchronous generator,ORC-BPMSG)的精确控制,提出一种基于改进遗传算法(improved genetic algorithm,IGA)优化最小二乘支持向量机(least square support vector machine,LS-SVM)逆系统的解耦控制策略。首先,基于ORC-BPMSG的结构及工作原理,推导其数学模型,并分析其可逆性。其次,建立LS-SVM回归方程,并采用IGA优化LS-SVM的性能参数,从而训练得到逆系统。然后,将逆系统与原系统串接,形成伪线性系统,实现了ORC-BPMSG的线性化和解耦。最后,将提出的控制方法与传统LS-SVM逆系统控制方法进行对比仿真和实验。仿真和实验结果表明:所提出的控制策略可以较好地实现ORC-BPMSG输出电压和悬浮力、以及悬浮力之间的解耦控制。

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.

多项式与LS-SVM自适应融合的GPS高程拟合方法

针对多项式模型在线状GPS拟合工程存在精度较低问题,本文构建二次曲面拟合与最小二乘支持向量机自适应融合GPS高程异常拟合方法。首先,分别利用多项式与最小二乘支持向量机进行线状工程GPS高程拟合;然后,利用最优加权组合方法将两种拟合模型自适应融合生成新的高程异常值。结果表明:该方法拟合精度明显优于多项式拟合方法及最小二乘支持向量机拟合方法。

APPLICATION OF LEAST MEDIAN OF SQUARED ORTHOGONAL DISTANCE (LMD) AND LMD BASED REWEIGHTED LEAST SQUARES (RLS) METHODS ON THE STOCK RECRUITMENT RELATIONSHIP

Analysis of stock recruitment (SR) data is most often done by fitting various SR relationship curves to the data. Fish population dynamics data often have stochastic variations and measurement errors, which usually result in a biased regression analysis. This paper presents a robust regression method, least median of squared orthogonal distance (LMD), which is insensitive to abnormal values in the dependent and independent variables in a regression analysis. Outliers that have significantly different variance from the rest of the data can be identified in a residual analysis. Then, the least squares (LS) method is applied to the SR data with defined outliers being down weighted. The application of LMD and LMD based Reweighted Least Squares (RLS) method to simulated and real fisheries SR data is explored.

MLTS-LS算法在矿浆细度检测中的应用

针对传统矿浆细度检测的离线筛分法效率低且不能及时反馈至上层磨矿系统的问题,为开发出细度自动检测技术,提出一种曲面拟合算法,即:基于最小二乘法改进的移动最小截平方法(MLTS-LS,Moving Least Trimmed Square-Least Square)对矿浆细度数据进行曲面拟合,以达到快速检测矿浆细度的目的。首先,通过细度检测试验采集矿浆细度三维离散数据;其次,计算分析“Nearest”、“Linear”、“Cubic”、“V4”和传统的最小二乘法的曲面拟合评价指标,提出一种改进的插值算法;最后,将“MLTS-LS”算法应用于矿浆细度三维离散数据的拟合。结果显示,“MLTS-LS”算法的和方差值与均方差值明显小于其他算法,且其确定系数值与校正决定系数值均接近于1,表明“MLTS-LS”算法对矿浆细度三维离散数据的拟合效果较好。

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.

用于损伤状态识别的极值延拓EMD和LS-SVM算法

针对机电系统损伤状态识别问题,提出一种基于极值延拓经验模态分解(EMD)和最小二乘支持向量机(LS-SVM)算法。首先,分析EMD算法的基本原理,针对端点效应利用多项式拟合极值延拓的算法改进设计方案,并利用标准化处理的特征向量设计程式;其次,考虑到机电系统损伤状态数据归属小样本特征,利用LS-SVM算法给出了状态识别的设计程式;最后,开展仿真验证实验。实验结果表明,采用所提算法的损伤状态识别方案,可以确保损伤状态识别的正确率超过96%,满足机电系统工程应用要求。

Properties of the total least squares estimation

Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given.

基于LS-SVM的宽带接收前端非线性补偿算法

针对目前常用的基于参数化非线性模型(Parameterized Nonlinear Model,PNM)的补偿算法存在易陷入局部最小值,导致补偿性能不稳的问题,该文提出了基于最小二乘支持向量机(Least Squares Support Vector Machine,LS-SVM)的宽带接收前端非线性补偿算法.该算法基于减谱-时频变换法(Spectrum Reduction Algorithm based on Time-Frequency Conversion,SRA-TFC)盲分离接收前端输出信号中的大功率基波信号和其他小功率信号,并以此作为LS-SVM逆模型的训练输入-输出样本对.引入最小二乘支持向量回归(Least Squares Support Vector Regression,LS-SVR)算法高精度拟合接收前端非线性逆模型.通过以宽带接收前端的输出信号为测试样本消除其非线性失真分量.仿真与实测结果表明:该算法可使宽带接收前端的无杂散失真动态范围(Spurs-Free-Dynamic-Range,SFDR)提高约20 dB,较基于PNM的补偿算法提高了约5 dB.

Improved adaptive pruning algorithm for least squares support vector regression

As the solutions of the least squares support vector regression machine （LS-SVRM） are not sparse, it leads to slow prediction speed and limits its applications. The defects of the ex- isting adaptive pruning algorithm for LS-SVRM are that the training speed is slow, and the generalization performance is not satis- factory, especially for large scale problems. Hence an improved algorithm is proposed. In order to accelerate the training speed, the pruned data point and fast leave-one-out error are employed to validate the temporary model obtained after decremental learning. The novel objective function in the termination condition which in- volves the whole constraints generated by all training data points and three pruning strategies are employed to improve the generali- zation performance. The effectiveness of the proposed algorithm is tested on six benchmark datasets. The sparse LS-SVRM model has a faster training speed and better generalization performance.

Fault diagnosis of power-shift steering transmission based on multiple outputs least squares support vector regression

A method of multiple outputs least squares support vector regression （LS-SVR） was developed and described in detail, with the radial basis function （RBF） as the kernel function. The method was applied to predict the future state of the power-shift steering transmission （PSST）. A prediction model of PSST was gotten with multiple outputs LS-SVR. The model performance was greatly influenced by the penalty parameter γ and kernel parameter σ2 which were optimized using cross validation method. The training and prediction of the model were done with spectrometric oil analysis data. The predictive and actual values were compared and a fault in the second PSST was found. The research proved that this method had good accuracy in PSST fault prediction, and any possible problem in PSST could be found through a comparative analysis.

Large Scattered Data Fitting Based on Radial Basis Functions

Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.

Iterative circle fitting based on circular attracting factor

An intuitive method for circle fitting is proposed. Assuming an approximate circle(CA,n) for the fitting of some scattered points, it can be imagined that every point would apply a force to CA,n, which all together form an overall effect that "draws" CA,n towards best fitting to the group of points. The basic element of the force is called circular attracting factor(CAF) which is defined as a real scalar in a radial direction of CA,n. An iterative algorithm based on this idea is proposed, and the convergence and accuracy are analyzed. The algorithm converges uniformly which is proved by the analysis of Lyapunov function, and the accuracy of the algorithm is in accord with that of geometric least squares of circle fitting. The algorithm is adopted to circle detection in grayscale images, in which the transferring to binary images is not required, and thus the algorithm is less sensitive to lightening and background noise. The main point for the adaption is the calculation of CAF which is extended in radial directions of CA,n for the whole image. All pixels would apply forces to CA,n, and the overall effect of forces would be equivalent to a force from the centroid of pixels to CA,n. The forces from would-be edge pixels would overweigh that from noisy pixels, so the following approximate circle would be of better fitting. To reduce the amount of calculation, pixels are only used in an annular area including the boundary of CA,n just in between for the calculation of CAF. Examples are given, showing the process of circle fitting of scattered points around a circle from an initial assuming circle, comparing the fitting results for scattered points from some related literature, applying the method proposed for circular edge detection in grayscale images with noise, and/or with only partial arc of a circle, and for circle detection in BGA inspection.

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.

A SPACE THEORY BASIS FOR CURVE FITTING PROBLEMS

itherto, a precision Concept for curve fitting problems has not been set. By using the theory of functional analysis, the author of this paper established a space theory basis for curve fitting problems. Also given in the paper is the precision concept of the curve fitting problems and the method for constructing the fitting of a curve satisfying given precision requirements.