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.

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.

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 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.

Detection of Broad Bean Diseases by Fourier Transform Infrared Spectroscopy Combined with Curve Fitting

Fourier transform infrared （FTIR） spectroscopy was used to study diseased leaves in broad bean. Results showed that the infrared spectra of different broad bean diseased leaves were similar, which were mainly made up of the vibrational absorption bands of protein,lipid and polysaccharide.There were minor differences in-cluding the spectral peak position, peak shape and the absorption intensity in the range of 1 800-1 300 cm-1. There were obvious differences among their second derivative spectra in the range of 1 800-1 300 cm-1. After the procedure of the Fourier self-deconvolution and curve fitting of health bean leaves and broad bean diseased leaves in the range of 1 700-1 500 cm-1, three sub-peaks were obtained at 1 550 cm-1 （protein amide Ⅱ band）, 1 605 cm-1 （lignin） and 1 650 cm-1 （protein amide I band）.The ratios of relative areas of the bands of amide Ⅱ, lignin, and amide I were 38.86%, 28.68% and 32.47% in the spectra of healthy leaves, respec-tively. It was distinguished from the diseased leaves （chocolate spot leaf： 15.42%, 42.98% and 41.61%, ring spot leaf：32.39%, 35.63% and 31.98%, rust leaf： 13.97%, 46.40% and 39.65%, yel owing leaf curl disease leaf： 24.01%,36.55% and 39.44%）. For sub-peak area ratios （A1 563/A1 605, A1 650/A1 605 and A1 563/A1 654）, those of four kinds of diseased leaves were smal er than that of healthy leaves, and there were also differences among four kinds of diseased leaves. The results proved that FTIR combining with curve fitting might be a potential y useful tool for detecting different kinds of broad bean diseases.

Study on Growth and Development Rules and Growth Curve Fitting of Minghua Black Minks

Growth curves of Minghua black minks at 0-180 days old were fitted and analyzed by using two growth models Logistic and Gompertz. The results showed that the growth curves of Minghua black minks could be fitted very well by Logistic model and Gompertz model （the degree of fitting FF≥0.99）, but Gompertz model was better at fitting and predicting their weight.

基于Curve Fitting Toolbox的普朗克常数测定

介绍了使用MATLAB曲线拟合工具箱(Curve Fitting Toolbox)对光电效应实验数据进行曲线拟合,并利用曲线拟合的结果计算得到了普朗克常数.结果显示,利用曲线拟合工具箱能方便、直观的对实验数据进行拟合,使得实验的数据处理过程方便、准确.

Study on curved surface fitting model using GPS and leveling in local area

The height anomaly surface is fitt and the quasi-geoid can be obtained when the height anomaly is determined with the geometric analytic method. Therefore, some mathematical models to fit height anomaly surface using GPS, leveling and terrain data in a local area, including the polynomial fitting model, the multi-surface function fitting model, the motion surface fitting model and the fitting model of little flexibility deformation of thin board, are given. Then the digital characteristics are analyzed with the curved surface theory. The General curvature and the mean curvature of surface are concluded. The advantage, disadvantage and application of the above models are discussed. The effect of terrain undulation on height anomaly is considered in the surface fitting models. The practical case indicates that these models are of validity and practicability. It is concluded that the above models can give the good fitting results at the centimeter level. But the polynomial fitting model is worse than the other models.

A new ellipse fitting method of the minimum differential-mode noise in the atom interference gravimeter

Ellipse fitting is a useful tool to obtain the differential signal of two atom interference gravimeters. The quality standard of ellipse fitting should be the deviation between the true phase and the fitting phase of the interference fringe. In this paper, we present a new algorithm to fit the ellipse. The algorithm is to minimize the differential noise of two interference gravimeters and obtain a more accurate value of the gravity gradient. We have theoretically derived the expression of the differential-mode noise and implemented the ellipse fitting in the program. This new algorithm is also compared with the classical methods.

Evaluating instrumented Charpy impact strain signals using curve fitting equations

An effective and simple way to develop equations from impact strain signals was proposed.Little research has been performed in this area,but this equation is very important for evaluating input signals in finite element analysis impact tests and for obtaining additional information on material deformation and fracture processes under impact loading.For this purpose,dynamic impact responses were examined through signals obtained from a strain gauge installed on an impact striker connected to a data acquisition system.Aluminium 6061-T6 was used to extract strain responses on the striker during Charpy impact testing.Statistical analysis was performed using the I-kaz method,and curve fitting equations based on the equation for vibration response under a non-periodic force were used to evaluate the Charpy impact signals.The I-kaz coefficients and curve fitting equations were then compared and discussed with related parameters,such as velocities and thicknesses.Velocity and thickness were found to be related to the strain signal patterns,curve fitting equations and I-kaz coefficients.The equations developed using this method had R2 values greater than 97.7%.Finally,the constructed equations were determined to be suitable for evaluating Charpy impact strain signal patterns and obtaining additional information on fracture processes under impact loading.

The Research of Ellipse Parameter Fitting Algorithm of Ultrasonic Imaging Logging in the Casing Hole

In order to estimate intensity and direction of pressure acted on oil well in horizontal, this paper proposes an algorithm of ellipse fitting based on least square method for sections of oil well with ultrasonic imaging logging data. Five parameters about ellipse corresponding to the sections of oil well are extracted and their geometry deformations and direction are estimated. The tested results show that the fitting algorithm is robust and the estimating error of parameter is small, which have very important practical significance on processing the well logging.

Comparative Study on Analysis and Fitting of Pudong Chicken Growth Curve

The objective of this paper was to study the growth and development laws of Pudong chicken. The growth curve of Pudong chicken （cock and hen） from 0 to 20 weeks was analyzed and fitted with three models（Gompertz, Logistic and Bertalanffy）. It was concluded that the growth curves were appropriately fitted with three models, and fitness degree （R2）in growth data of Pudong chicken were all above 0.992. The Bertalanffy model was the most effective with the highest R2 for cock （R^2=0.995） and hen （R^2=0.999）, respectively. With further analysis of fitted parameters for Logis- tic model of cock, 0-3 weeks＇ fitted values were significantly greater than measured values and 4-8 weeks＇ fitted values were lower than measured values. Compared with Logistic model, the values calculated by Gompertz model and Bertalanffy model were more coincident with the practical measuring values. For hens, 0-3 weeks＇ fitted values of Logistic model were significantly greater than measured values and 0-2 weeks＇ fitted values of Gompertz model were slightly greater than measured values, while the values calculated by Bertalanffy model best matched the observed values from actual measure. The results showed that Bertalanffy model used to estimate the growth weight of Pudong chicken was the best while Logistic model was the worst. So the fitness and analysis of growth curves of Pudong chicken are valid, which may be adopted to predict growth and development laws of Pudong chicken and provide reliable data for precise feeding and breeding.

Measuring Carbon Dioxide Sink of Betung Bamboo （Dendrocallamus asper （Schult f.） Backer ex Heyne） by Sinusoidal Curves Fitting on Its Daily Photosynthesis Light Response

Planting plant such as Betung bamboo （Dendrocalamus asper （Schult f.） Backer ex Heyne） is one of the best ways for reducing global warming effect. Betung bamboo is giant grass （Poaceae） which has been traditionally used by Indonesian people for construction material since a long time ago. Poaceae family commonly has better carbon sink ability than trees because of its Ca photosynthesis mechanisms, but bamboo sub-family （Bambusoideae） lacks the Ca photosynthetic pathway and anatomy. In the absence of this feature the maximum possible productivity of bamboos is unlikely to greatly exceed that of other bioenergy crops with C3 photosynthesis such as fast growing tree species. This research proposed a sinusoidal equation as a basic equation for plant＇s daily photosynthesis light response curve fitting. The sinusoidal equation was success for Betung bamboo＇s daily photosynthesis light response curve fitting （R2 〉 60%）. It had similar result in estimating carbon sink （82.35 kg/clump/year） compared to those which calculated by annual increment （69.01-107.82 kg/clump/year）. It is better to choose sinusoidal equation than quadratic or cubic Betung bamboo is a good choice to be planted in order to resist the global warming effect because it has superior carbon sink capability （82.35 kg/clump/year） than slow growing tree, and equal to fast growing tree species, besides many other advantages.

Energy-Minimizing Curve Fitting for High-Order Surface Mesh Generation

We investigate different techniques for fitting Bézier curves to surfaces in context of high-order curvilinear mesh generation. Starting from distance-based least-squares fitting we develop an incremental algorithm, which incorporates approximations of stretch and bending energy. In the process, the algorithm reduces the energy weight in favor of accuracy, leading to an optimized set of sampling points. This energy-minimizing fitting strategy is applied to analytically defined as well as triangulated surfaces. The results confirm that the proposed method straightens and shortens the curves efficiently. Moreover the method preserves the accuracy and convergence behavior of distance-based fitting. Preliminary application to surface mesh generation shows a remarkable improvement of patch quality in high curvature regions.

FTIR Study of White and Green Broad Beans Based on Curve-fitting

Fourier transform infrared(FTIR)spectroscopy was used to study two kinds of broad beans with white and green cotyledons respectively.The results show that the infrared spectra of the two kinds of broad beans are similar and mainly made up of the absorption bands of protein,and polysaccharides.The second derivative infrared spectra amplified the differences and revealed that there were some obvious differences in the range of 1 800-700 cm-1and 1 200-700 cm-1.Hierarchical cluster analysis(HCA)were used for the discrimination of the two kinds broad beans based on the second derivative spectral data in the region of 1 611-1 100 cm-1,and yielded 88.9%accuracy.The spectra in the range from 1 700 to 1 600 cm-1were used to perform Fourier self-deconvolution and curve fitting,which obtained nine peaks.The ratios of relative areas of the bands atα-helix,β-sheet,β-turn and the unordered structure of protein in white beans were 67.71%,35.6%,35.6%and 21.09%respectively,while the ratios in green beans were 8.02%,31.59%,37.12%and 23.27%respectively.The results indicate that the secondary structure of protein was different in the two kinds of broad beans.

A NEW APPROACH TO THE CURVE FITTING OF IN VITRO RADIOASSAYS BASED ON THE MASS ACTION LOW

A new curve fitting method with its mathematical models derived from the mass action law is presented which is applicable to several in vitro radioassays including RIA and RBA. Experiments revealed that the robustness of this method is better than the conventional methods like Woolf plot in RBA and 4- parameter logistic plot in RIA. However, the robustness of this method is only relative: in some cases of RIA and RBA, the bias of the results may still be too large to be acceptable. Further improvement is expected to be studied.

Linearly optimum seeking K-value in the fitting of exponential and geometric curves

Based on logarithmic transformation of exponential and geometric curves, the paper proposes a method of choosing k-value to improve the goodness of fit. Functions between the sum of squares of regression(SSR) and k-value are built up; and the maximum of SSR value can be solved by derivation in which an iterative algorithm is used. A computer program has been developed for application. The result shows that the method is simple, and the goodness of fit is not inferior to other optimum methods of curve fitting.

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.