文献翻译-基于MATLAB的数据曲线拟合分析

英文翻译系别专业班级学生姓名学号指导教师报告日期Data Curve Fitting Based on MATLABCurve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points,possibly subject to constraints. Curve fitting can involve eitherinterpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables.Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to adegree of uncertaintysince it may reflect the method used to construct the curve as much as it reflects the observed data. Research and Application of a New Method of Curve Fitting.The technique of curve fitting is used proverbially for the image processing, reverse engineering, test data processing, etc. It is inequitable to process physical parameters by some usual methods of curve fitting. Those methods are performed only by minimizing the fitting error of one physical parameter, but do not take other parameters into account. The new method of curve fitting processes each physical parameter equally The simulation also proves that this new curve fitting method is right and effective.In the experiment of sound velocity, the voltammetry to measure the resistance experiment and the volt-ampere characteristic of diode experiment data processing as an example, introduced the experiment data processing based on MATLAB.With the traditional experimental data processing methods, experimental data is processed by using MATLAB can effectively avoid the error caused by manual processing, but also can reduce the computational workload, obtain accurate curve fitting, thereby increasing the accuracy of data processing and fast,rom graphic display results also can be more intuitive to judge the validity of the experiment.Mathematical expressionGiven set of discrete data(x k,y k) (k=1,2,…,m),(1)Where xk is the independent variable x (scalar or vector, i.e., a mono-or polyhydric variable) values; yk of (scalar) corresponding to the value of the dependent variable y. Curve fitting is to seek to solve the problem of (1) to adapt the laws of the analytical expression of the backgroundy=f(x,b),(2)Making best approximation in some sense or fit (1), (x, b) is called fitting model;? Parameters to be determined, when b) only appears when the linear, called a linear model? otherwise non-linear.Amount(k=1,2,…，m)In xk place called residual or remaining fit,The standard measure of goodness of fit is usually或Where ωk> 0 as weight coefficient or weight(Unless otherwise specified, generally taken to be the average weight,w k(k=1,2,…,m),At this time without mention weight).When the parameter b) make T (b)) or Q (b)) to achieve the most hours,Appropriate (2) are referred to (1) the weighted Chebyshev fitting meaning orweighted least squares sense,latter is more simple and most commonly used in the calculation.General linear model to determine the model parameters are parameters b) generalized polynomial coefficients,thatf(x,b)=b0g0(x)+b1g1(x)+…b n g n(x)(3)Wherein g0, g1, ..., gn called basis functions.Gj on various different choices may constitute a variety of typical and commonly used linear model.From the point of view of function approximation, equation (3) can be approximated reflect the nature of many of nonlinear models.In the least squares sense (3) fitting a linear model with a discrete set of points(1),parameter b can be obtained by solving equations=0(i=0,…,n)to determine,that solution on b0,b1,…,bn of linear algebraic equations(i=0,1,…，n),(4)Formula (i,j＝0,1,…，n),Equations (4) commonly referred to as the normal equation or the normal equation, when m> n, generally have a unique solution.As for the case of non-linear model and the principle of least squares, the parameter b) can be determined (see numerical solution of nonlinear equations, optimization) nonlinear equations or calculations about the method optimization.Select the modelFor a given discrete data (1), the need to properly select the general model (2) of the function f (x, b) the type and specific form, which is the basis of fitting results.If known, (1) the actual background of the law, that is the dependent variable ydependence of the empirical formula of the independent variable x has an expression determined directly take appropriate empirical formula is fitting model.On the contrary, through the model (3) of the basis functions g0, g1, ..., gn (number and types) of different choices, each corresponding proposed merger by choosing the good effect.Function g0, g1, ..., gn adaptation plays a role the model for testing, it is also known test function.Another way is: the number and types into a sufficient number of test functions in the model (3), by means of statistical methods in mathematical correlation analysis and test of significance of the test function contains screened individually or sequentially with establish more appropriate model (see regression analysis).Certainly, the above method may fit residuals (as a new discrete data) is performed again to compensate for the lack of the first fitting.In conclusion, when the intrinsic link between the variables in the data is not clear, as the choice to adapt the model to fit generally requires repeated testing and analysis to identify.Procedure（一）Draw a scatter plot, select the appropriate type of curve.Generally based on the nature of the information can be combined with the expertise to determine the type of curve data, not reallytaht can be plotted on graph paper squares scatter plot, according to the distribution of scattered points, choose close, the appropriate curve type.Can be plotted on graph paper squares scatter plot, according to the distribution of scattered points, choose close, the appropriate curve type.（二）Be variable transformationY’=f(Y),X’=g(X)(12.37)The two variables transformed linear relationship.（三）Solving linear equations and variance analysis by the least squares method（四）Convert the linear equations on the original variables X, Y of the function expression基于MATLAB的数据曲线拟合分析曲线拟合是构建的过程曲线，或数学函数，具有最适合于一系列的数据点，可能受到约束。