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Least square method-based curve fitting method

A technology of least squares and curve fitting, applied in complex mathematical operations, etc., can solve problems such as inability to guarantee, and achieve the effect of simple method, avoiding minimal changes, and strong logic.

Inactive Publication Date: 2017-10-20
BEIJING INST OF AEROSPACE CONTROL DEVICES
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Problems solved by technology

[0023] Analyzing the reasons, the main reason is that the least square method can only guarantee minimum, but not guaranteed the smallest

Method used

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  • Least square method-based curve fitting method
  • Least square method-based curve fitting method
  • Least square method-based curve fitting method

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Experimental program
Comparison scheme
Effect test

Embodiment 1

[0091] Taking Table 1 in the reference ("Assessment of accelerometer storage life under temperature stress", "Journal of Armored Forces Engineering College", Vol.28 No.3, 2014, P28) as an example, the inertial instrument—accelerometer is set at The failure data of the natural storage environment test under the condition of 25°C (the sample size of each test is 100), the test result is

[0092] Table 1 Statistical situation of test failure data

[0093]

[0094]

[0095] Using the Weibull distribution , solve ln(-ln(1-F))=m ln(T)-m ln(η) by least squares method and provide the solution of step (3) with parameters m and η: m=1.7618596, η=49.748074 . Fitting curves such as figure 2 As shown, the "*" point in the figure is the experimental data in Table 1, and the "o" point is the fitted value. It can be seen that there is still a large gap between the two. at this time,

[0096] Adopt the curve fitting method based on least square method of the present invention, p...

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Abstract

The present invention relates to a curve fitting method based on the least squares method. The method establishes a linear model on the basis of a nonlinear fitting curve, uses an iterative calculation method to provide coefficients in the function of the fitting curve, and substitutes the coefficients into The theoretical value obtained after fitting the function has the characteristics of the minimum sum of squares of errors, and the method can accurately provide the coefficients of the fitting function by means of precise iterative calculation, so that the sum of squares of errors of fitting is minimized; the present invention avoids The minimization problem existing in the least square method in the linear transformation process is solved, and the curve fitting method provided by the invention has high fitting precision, strong logic, easy programming, simple method and easy realization.

Description

technical field [0001] The invention relates to a curve fitting method based on the least square method, which belongs to the technical field of numerical analysis and reliability. Background technique [0002] There are many functions in scientific experiments and engineering applications, whose analytical expressions are not known. For example, with the prolongation of storage time, the performance and parameters of inertial devices will change, but this change process can only be measured by a series of nodes x i value on f i . The problem now is to seek the approximation function y(x) of the test point sequence, or in geometric language, to seek a curve y(x) to fit (smooth) these n points. [0003] The traditional curve fitting method is the method of least squares, which requires [0004] [0005] in, [0006] [0007] [0008] Then call y(x) as f(x) about the weight coefficient {ω i}'s least squares approximation, and the method for finding the approxima...

Claims

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Application Information

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IPC IPC(8): G06F17/15
CPCG06F17/15
Inventor 魏宗康何远清
Owner BEIJING INST OF AEROSPACE CONTROL DEVICES
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