文献翻译-基于MATLAB的数据曲线拟合分析

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Data Curve Fitting Based on MATLAB

Curve 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 expression

Given 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 background

y=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 or