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.

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.

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.

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.

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.

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.

Microwave method based on curve fitting method for high-precision collision frequency diagnosis

In this work,the results of plasma microwave transmission diagnosis were analyzed.According to the attenuation and phase shift of the electromagnetic wave propagating in the plasma,the electron density and collision frequency of the plasma can be diagnosed.Since part of the electromagnetic wave is reflected or diffracted when propagating in the plasma,and is not absorbed by the plasma,and this part of the attenuation is still included in the measured attenuation,the attenuation is distorted.Therefore,a curve fitting method is proposed to remove the attenuation caused by the plasma reflection,thereby improving the accuracy of the diagnosis of the collision frequency.The calibration effect of this method on plasmas with different electron densities and collision frequencies is analyzed,and a diagnostic frequency band with good calibration results is given.The curve fitting method is verified by experiment and simulation.After adopting the newly proposed method,the diagnosis accuracy of collision frequency can be increased by 30%.This method can be widely used in various types of plasma diagnosis and provides a new idea for plasma diagnosis.

NON-STATIONARY SIGNAL DENOISING USING TIME-FREQUENCY CURVE SURFACE FITTING

Based on the theory of adaptive time-frequency decomposition and Time-Frequency Dis- tribution Series (TFDS), this paper presents a novel denoising method for non-stationary signal. Ac- cording to the input signal features, an appropriate kind of elementary functions with great concen- tration in the Time-Frequency (TF) plane is selected. Then the input signal is decomposed into a linear combination of these functions. The elementary function parameters are determined by using ele- mentary function TF curve surface to fit the input signal’s TFDS. The process of curved surface fitting corresponds to the signal structure matching process. The input signal’s dominating component whose structure has the resemblance with elementary function is fitted out firstly. Repeating the fitting process, the residue can be regarded as noises, which are greatly different from the function. Selecting the functions fitted out initially for reconstruction, the denoised signal is obtained. The performance of the proposed method is assessed by means of several tests on an emulated signal and a gearbox vi- brating signal.

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.

Arm-Root Curve Fitting Based on Body Surface Feature Points for Young Male

This paper is aiming to obtain an arm-root curve function performing the human arm-root size and shape realistically. A gypsum replica of upper arm for young male was made and scanned for extracting the 3D coordinates of 4 feature points of shoulder point, the anterior/posterior armpit point and the axillary point describing the real arm-root shape under the normalized definitions, and the 5 landmarks were confirmed additionally for improving the fitting precision. Then, the wholly and piecewise fitting of arm-root curve with 9 feature points and mark points in total were generated respectively based on least square polynomial fitting method. Comparing to the wholly fitting, the piecewise fitted function segmented by the line between anterior and posterior axillary points showed a high fitting degree of arm-root morphology with R-square of 1, the length difference between fitted curve and gypsum curve is 0.003 cm within error range. And it provided a basic curve model with standard feature points to simulate arm-root morphology realistically by curve fitting for accurate body measurement extraction.

Predicting of Land Surface Temperature Distribution in Freetown City, Sierra Leone by Using Polynomial Curve Fitting Model

Global warming has attracted much concern about the worldwide organization, civil society groups, researchers, and so forth because the worldwide surface temperature has been expanding. This investigation intends to assess and compare the ability of a combination of land cover indices to predict the future distribution of land surface temperatures in Freetown using the Polynomial model analysis. Landsat satellite images of 1988, 1998, 2000, 2010, and 2018 of the Freetown Metropolitan zone were utilized for analysis. The investigation had adopted two land covers indices, Modification of normalized difference water index and Urban Index (UI) (e.g., MNDWI and UI) and applied a multi regression equation for forecasting the future LST. The stimulation results propose that the development will be accompanied by surface temperature increases, especially in Freetown’s western urban area. The temperature prevailing in the west of the metropolitan area may increase in the city somewhere in the range from 1988 to 2018. Additionally, the results of the LST prediction show that the model is perfect. Our discoveries can be represented as a helpful device for policymakers and community awareness by giving a scientific basis for sustainable urban planning and management.

Curve Fitting in Analyzing the Menstrual Irregularities afterImplantation of Norplant

This paper presents the menstrual disorders produced by implantation of Norplantin women during a course of five-year usage. Total 1000 women were recruited. Themain side thects consisted of changes in bleeding patterns, including: menostaxis, hxpomenorrhoea, spotting,frequent menstruation, lnfrequent menstruation, amenorrhoeaand menorrhagia. Authors of this paper suggested that all the above-mentioned men-strual disorders could be explained by mathematical methods. Except for the incidenceof menorrhagia which revealed a negative linear correlation with the implantation timeinterval (correiation coefficient is - 0. 98), all the other six patterns of the abnormalbleeding changes could be fitted by the hyperbola model, because their incidencesreached a very high value in 3~ 6 months after implantation, then sharply dropped toa lower value at the end of one year, whence in turn were reduced slowly but progres-sively to the the end of the 5 th year. The results of all F tests were statistically signWicant (P< 0.01). The advantages of this curve fitting method are: 1, to show the re-lationships between the mismenstruational rates and time afer implantation of Norplant at a theoretical level; 2, to make a direct image; 3, tosmooth the values of the ob-servation and decrease the sampling variation; 4, to estimate the incidences of mismen-struation at a given time; 5, to tell women the changing rule of mismenstruations anddeveloping prospect before and after the implantation in order to increase their confi-dence and meanwhile to increase the conlinuous using rate.

Weight-based shape modification of NURBS curves by constrained optimization

A new method for shape modification of non-uniform rational B-splines (NURBS) curves was presented, which was based on constrained optimization by means of altering the corresponding weights of their control points. Using this method, the original NURBS curve was modified to satisfy the specified geometric constraints, including single point and multi-point constraints. With the introduction of free parameters, the shapes of modified NURBS curves could be further controlled by users without destroying geometric constraints and seem more naturally. Since explicit formulae were derived to compute new weights of the modified curve, the method was simple and easy to program. Practical examples showed that the method was applicable for computer aided design (CAD) system.

EVALUATION OF SOFTWARE OF FOUR-PARAMETER SINE WAVE CURVE -FIT

Sinusoid curve fit is a very useful method in precise measurement, based on the modeling measurement. There are many valuable uses. But, what′s the specifications of the sinusoid curve fit software, and how to evaluate the uncertainty of it are still unknown yet, because they involve manifold factors and are complicated. Every one using the sinusoid curve fit software wants to know it. In this paper, the basic process and the uses of sinusoid curve fit are described, and some specifications and evaluation methods are introduced. One evaluation example of sinusoid curve fit software is discussed, the results and the specification are good.

Determination of Material Parameters of EVA Foam under Uniaxial Compressive Testing Using Hyperelastic Models

The objective of this research was to determine the mechanical parameter from EVA foam and also investigate its behavior by using Blatz-Ko,Neo-Hookean,Mooney model and experimental test.The physical characteristic of EVA foam was also evaluated by scanning electron microscopy(SEM).The results show that Blatz-Ko and Neo-Hookean model can fit the curve at 5%and 8%strain,respectively.The Mooney model can fit the curve at 50%strain.The modulus of rigidity evaluated from Mooney model is 0.0814±0.0027 MPa.The structure of EVA foam from SEM image shows that EVA structure is a closed cell with homogeneous porous structure.From the result,it is found that Mooney model can adjust the data better than other models.This model can be applied for mechanical response prediction of EVA foam and also for reference value in engineering application.

A frequency domain estimation and compensation method for system synchronization parameters of distributed-HFSWR

To analyze the influence of time synchronization error,phase synchronization error,frequency synchronization error,internal delay of the transceiver system,and range error and angle error between the unit radars on the target detection performance,firstly,a spatial detection model of distributed high-frequency surface wave radar(distributed-HFSWR)is established in this paper.In this model,a method for accurate extraction of direct wave spectrum based on curve fitting is proposed to obtain accurate system internal delay and frequency synchronization error under complex electromagnetic environment background and low signal to noise ratio(SNR),and to compensate for the shift of range and Doppler frequency caused by time-frequency synchronization error.The direct wave component is extracted from the spectrum,the range estimation error and Doppler estimation error are reduced by the method of curve fitting,and the fitting accuracy of the parameters is improved.Then,the influence of frequency synchronization error on target range and radial Doppler velocity is quantitatively analyzed.The relationship between frequency synchronization error and radial Doppler velocity shift and range shift is given.Finally,the system synchronization parameters of the trial distributed-HFSWR are obtained by the proposed spectrum extraction method based on curve fitting,the experimental data is compensated to correct the shift of the target,and finally the correct target parameter information is obtained.Simulations and experimental results demonstrate the superiority and correctness of the proposed method,theoretical derivation and detection model proposed in this paper.

Quantitative Assessment of Right Ventricular Systolic Function by the Analysis of Right Ventricular Contrast Time-intensity Curve

Summary: To study reliability and reliable indices of quantitative assessment of right ventricular systolic function by time-intensity curve (TIC) with right ventricular contrast, 5 % sonicated human albumin was injected intravenously at a does of 0.08 ml/kg into 10 dogs at baseline status and cardiac insufficiency. Apical four-chamber view was observed for washin and washout of contrast agent from right ventricle. The parameters of TIC were obtained by curve fitting. The differences of parameters were analyzed in different states of cardiac functions. Among the parameters derived from TIC, the time constant (k) was decreased significantly with decline of cardiac function (P<0.001). But half-time of decent of peak intensity (HT) and mean-transit-time (MTT) of washout were increased significantly (P<0.001). The k was strongly related to cardiac output of right ventricle (CO) and ejection fraction (EF) of left ventricle and fractional shortening (FS) of left ventricle. Right ventricular systolic function could be assessed reliably by the parameters derived from TIC with right ventricular contrast echocardiography. The k, HT and MTT are reliable indices for quantitative assessment of right ventricular systolic function.

Edge detection and mathematic fitting for corneal surface with Matlab software

AIM：To select the optimal edge detection methods to identify the corneal surface,and compare three fitting curve equations with Matlab software. METHODS：Fifteen subjects were recruited. The corneal images from optical coherence tomography（OCT）were imported into Matlab software. Five edge detection methods（Canny,Log,Prewitt,Roberts,Sobel）were used to identify the corneal surface. Then two manual identifying methods（ginput and getpts）were applied to identify the edge coordinates respectively. The differences among these methods were compared. Binomial curve（y=Ax2＋Bx＋C）,Polynomial curve [p（x）=p1xn＋p2x（n-1）＋....＋pnx＋pn＋1] and Conic section（Ax2＋Bxy＋Cy2＋Dx＋Ey＋F=0）were used for curve fitting the corneal surface respectively. The relative merits among three fitting curves were analyzed. Finally,the eccentricity（e）obtained by corneal topography and conic section were compared with paired t-test. RESULTS：Five edge detection algorithms all had continuous coordinates which indicated the edge of the corneal surface. The ordinates of manual identifying were close to the inside of the actual edges. Binomial curve was greatly affected by tilt angle. Polynomial curve was lack of geometrical properties and unstable. Conic section could calculate the tilted symmetry axis,eccentricity,circle center,etc. There were no significant differences between ＇e＇ values by corneal topography and conic section（t=0.9143,P=0.3760 〉0.05）.CONCLUSION：It is feasible to simulate the corneal surface with mathematical curve with Matlab software. Edge detection has better repeatability and higher efficiency. The manual identifying approach is an indispensable complement for detection. Polynomial and conic section are both the alternative methods for corneal curve fitting. Conic curve was the optimal choice based on the specific geometrical properties.

A NURBS Fitting Optimization Method for High⁃Speed Five⁃Axis NC Machining Path Based on Curvature Smoothing Preset Point Constraint

Existing curve fitting algorithms of NC machining path mainly focus on the control of fitting error,but ignore the problem that the original discrete cutter position points are not enough in the high curvature area of the tool path.It may cause a sudden change in the drive force of the feed axis,resulting in a large fluctuation in the feed speed.This paper proposes a new non-uniform rational B-spline(NURBS)curve fitting optimization method based on curvature smoothing preset point constraints.First,the short line segments generated by the CAM software are optimally divided into different segment regions,and then the curvature of the short line segments in each region is adjusted to make it smoother.Secondly,a set of characteristic points reflecting the change of the curvature of the fitted curve is constructed as the control apex of the fitted curve,and the curve is fitted using the NURBS curve fitting optimization method based on the curvature smoothing preset point constraint.Finally,the curve fitting error and curve volatility are analyzed with an example,which verifies that the method can significantly improve the curvature smoothness of the high-curvature tool path,reduce the fitting error,and improve the feed speed.

Analysis-Aware Modelling of Spacial Curve for Isogeometric Analysis of Timoshenko Beam

Geometric fitting based on discrete points to establish curve structures is an important problem in numerical modeling.The purpose of this paper is to investigate the geometric fitting method for curved beam structure from points,and to get high-quality parametric model for isogeometric analysis.ATimoshenko beam element is established for an initially curved spacial beam with arbitrary curvature.The approximation and interpolation methods to get parametric models of curves from given points are examined,and three strategies of parameterization,meaning the equally spaced method,the chord length method and the centripetal method are considered.The influences of the different geometric approximation algorithms on the precision of isogeometric analysis are examined.The static analysis and the modal analysis with the established parametric models are carried out.Three examples with different complexities,the quarter arc curved beam,the Tschirnhausen beam and the Archimedes spiral beam are examined.The results show that for the geometric approximation the interpolation method performs good and maintains high precision.The fitting algorithms are able to provide parametric models for isogeometric analysis of spacial beam with Timoshenko model.The equally spaced method and centripetal method perform better than the chord length method for the algorithm to carry out the parameterization for the sampling points.