WEIGHTED LEAST SQUARE METHOD FOR S-N CURVE FITTING

An S-N curve fitting approach is proposed based on the weighted least square method, and the weights are inversely proportional to the length of mean confidence intervals of experimental data sets. The assumption coincides with the physical characteristics of the fatigue life scatter. Two examples demonstrate the method. It is shown that the method has better accuracy and reasonableness compared with the usual least square method.

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.

Penalized total least squares method for dealing with systematic errors in partial EIV model and its precision estimation

When the total least squares(TLS)solution is used to solve the parameters in the errors-in-variables(EIV)model,the obtained parameter estimations will be unreliable in the observations containing systematic errors.To solve this problem,we propose to add the nonparametric part(systematic errors)to the partial EIV model,and build the partial EIV model to weaken the influence of systematic errors.Then,having rewritten the model as a nonlinear model,we derive the formula of parameter estimations based on the penalized total least squares criterion.Furthermore,based on the second-order approximation method of precision estimation,we derive the second-order bias and covariance of parameter estimations and calculate the mean square error(MSE).Aiming at the selection of the smoothing factor,we propose to use the U curve method.The experiments show that the proposed method can mitigate the influence of systematic errors to a certain extent compared with the traditional method and get more reliable parameter estimations and its precision information,which validates the feasibility and effectiveness of the proposed method.

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.

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.

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.

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.

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.

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.

Science Letters:Evaluation of a kinetic uricase method for serum uric acid assay by predicting background absorbance of uricase reaction solution with an integrated method

A patented kinetic uricase method was evaluated for serum uric acid assay. Initial absorbance of the reaction mixture before uricase action （A0） was obtained by correcting the absorbance at 293 nm measured before the addition of uricase solution, and background absorbance （Ab） was predicted by an integrated method. Uric acid concentration in reaction solution was calculated from AA, the difference between A0 and Ab, using the absorptivity preset for uric acid. This kinetic uricase method exhibited CV〈4.3% and recovery of 100%. Lipids, bilirubin, hemoglobin, ascorbic acid, reduced glutathione and xanthine 〈0.32 mmol/L in serum had no significant effects. △A linearly responded to 1.2 to 37.5 μmol/L uric acid in reaction solution containing 15 μl serum. The slope of linear response was consistent with the absorptivity preset for uric acid while the intercept was consistent with that for serum alone. Uric acid concentrations in clinic sera by different uricase methods positively correlated to each other. By Bland-Altman analysis, this kinetic uricase method accorded with that by quantifying the total change of UV absorbance on the completion of uricase reaction. These results demonstrated that this kinetic uricase method is reliable for serum uric acid assay with enhanced resistance to both xanthine and other common errors, wider range of linear response and much lower cost.

Kinetic method for enzymatic analysis by predicting background with uricase reaction as model

Objective：To investigate the reliability for kinetic assay of substance with background predicted by the integrated method using uricase reaction as model. Methods： Absorbance before uricase action （Δ0） was estimated by extrapolation with given lag time of steady-state reaction. With Km fixed at 12.5μmol/L, background absorbance （Δb） was predicted by nonlinearly fitting integrated Michaelis-Menten equation to Candida utilis uricase reaction curve. Uric acid in reaction solution was determined by the difference （ΔA） between Δ0 and Δb. Results .Ab usually showed deviation 〈3% from direct assay with residual substrate done fifth of initial substrate for analysis. ΔA showed CV 〈5% with resistance to common interferences except xanthine, and it linearly responded to uric acid with slope consistent to the absorptivity of uric acid. The lower limit was 2.0 μmol/L and upper limit reached 30 μmol/L in reaction solution with data monitored within 8 min reaction at 0. 015 U/ml uricase. Preliminary application to serum and urine gave better precision than the direct equilibrium method without the removal of proteins before analysis. Conclusion .This kinetic method with background predicted by the integrated method was reliable for enzymatic analysis, and it showed resistance to common interferences and enhanced efficiency at much lower cost.

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.

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.

Study on Coal Consumption Curve Fitting of the Thermal Power Based on Genetic Algorithm

Coal consumption curve of the thermal power plant can reflect the function relationship between the coal consumption of unit and load, which plays a key role for research on unit economic operation and load optimal dispatch. Now get coal consumption curve is generally obtained by least square method, but which are static curve and these curves remain unchanged for a long time, and make them are incompatible with the actual operation situation of the unit. Furthermore, coal consumption has the characteristics of typical nonlinear and time varying, sometimes the least square method does not work for nonlinear complex problems. For these problems, a method of coal consumption curve fitting of the thermal power plant units based on genetic algorithm is proposed. The residual analysis method is used for data detection;quadratic function is employed to the objective function;appropriate parameters such as initial population size, crossover rate and mutation rate are set;the unit’s actual coal consumption curves are fitted, and comparing the proposed method with least squares method, the results indicate that fitting effect of the former is better than the latter, and further indicate that the proposed method to do curve fitting can best approximate known data in a certain significance, and they can real-timely reflect the interdependence between power output and coal consumption.

Research on the Model of Linear Data Fitting Method

By using the method of least square linear fitting to analyze data do not exist errors under certain conditions, in order to make the linear data fitting method that can more accurately solve the relationship expression between the volume and quantity in scientific experiments and engineering practice, this article analyzed data error by commonly linear data fitting method, and proposed improved process of the least distance squ^re method based on least squares method. Finally, the paper discussed the advantages and disadvantages through the example analysis of two kinds of linear data fitting method, and given reasonable control conditions for its application.

Soller slits automatic focusing method for multi-element fluorescence detector

In X-ray absorption fine structure(XAFS) experiments,Soller slits are widely used as filter devices in order to improve the signal to noise ratio.Performing high accuracy manual focusing operations is a time-consuming process;therefore,this work introduces an automatic focusing method for Soller slits in multi-element fluorescence detectors.This method establishes a relation model between the fluorescence intensity distribution and the coordinates of the fluorescence excitation point.According to this relation model,the actual coordinates of the fluorescence excitation point can be deduced from the detected fluorescence intensity distribution and used in focusing operations.This method has proven to be feasible in an XAFS experiment at the BL14W1 beamline of the Shanghai Synchrotron Radiation Facility.

四参数正弦曲线拟合的快速算法

对四参数正弦拟合软件运行时间进行了研究,提出一种软件拟合时间的定量评价方法,对序列长度、序列所含信号周波数、正弦波形幅度、相位、直流分量,以及A/D位数等不同因素条件,给四参数正弦曲线拟合所用时间的影响进行了定量评价,获得了拟合时间随各个因素而变化的规律。针对影响软件运行时间的主要因素,提出了以减少拟合序列长度为手段,进而降低拟合所用时间的快速拟合方法。它们是直接序列截取法和二次抽样法。并在一组实验上验证了所述方法的有效性与可行性,获得了二次抽样法优于直接截取法的明确结论。所述方法可用于四参数正弦拟合的快速运算。

RPC应力-应变曲线系数与塑性损伤因子无量纲化计算模型研究

为了方便活性粉末混凝土(Reactive Powder Concrete,RPC)等效矩形应力图系数与塑性损伤因子的计算与取值,对RPC应力-应变曲线系数与塑性损伤因子的计算模型进行了理论研究。通过对现有的计算方法进行无量纲化转化,推导了决定计算模型的四个原函数条件;对一个实际的应力-应变关系进行了计算,将得到的结果进行了分析;并对受弯矩形梁非极限状态下截面内力和力矩的推定计算进行了演示。针对应力-应变关系式含有非整次有理分式的情况提出了曲线拟合方法;研究了拟合次数、拟合区间和拟合函数类型对拟合精度与稳定性的影响。比较了4种典型的RPC本构模型在同种材料下的应力-应变曲线系数与损伤因子取值模型曲线,结果显示:拟合曲线得到的取值模型与其他原始曲线得到的取值模型在曲线上具有较高的相似度,证明了曲线拟合方法的准确可靠性;最后给出了一种RPC受压应力-应变曲线系数与塑性损伤因子无量纲化取值模型。