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Limited distribution integral inversion algorithm for grain diameter measurement

A technology of finite distribution and inversion algorithm, applied in the field of finite distribution integral inversion algorithm, it can solve the problems of amplifying noise, error, ill-posedness, etc., and achieve the effect of reducing principle error and vibration reduction.

Active Publication Date: 2011-07-27
安徽欧泰祺智慧水务科技有限公司
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0005] Since the measured value I(θ) is inevitably noisy, the numerical differentiation of the noise-containing data by formula (1) will not only amplify the noise, but also be an ill-posed problem, which will cause a large error

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  • Limited distribution integral inversion algorithm for grain diameter measurement
  • Limited distribution integral inversion algorithm for grain diameter measurement
  • Limited distribution integral inversion algorithm for grain diameter measurement

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Embodiment Construction

[0026] The present invention, that is, a finite distribution integral inversion algorithm for particle size measurement, comprises the following steps:

[0027] Step 1: Firstly, the parameter distribution of particle size is obtained by measurement as f a b The particle group diffraction light intensity distribution I(θ) of the particle group in (x) on the finite particle size interval [a, b];

[0028] I ( θ ) = λ 2 4 π 2 F 2 θ 2 I 0 ∫ a b x 2 J 1 2 ( xθ ) f a b ( ...

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Abstract

The invention relates to a limited distribution integral inversion algorithm for grain diameter measurement. The invention is characterized in that the algorithm comprises the following steps: (1) obtaining the light distribution I (theta) of diffraction light of a grain group the grain size parameter distribution of which is fab (x) in the limited grain size interval [a,b] by measuring; (2) obtaining an inversion expression by Hankel conversion and the analytic solution of a Scholmilch equation; (3) carrying out discretization treatment on the equation obtained in step (2) by utilizing the Gaussian interpolation method; and (4) substituting Gaussian interpolation coefficients and interpolation nodes into the formula after by discretization treatment in step (3), thereby obtaining the grain diameter distribution fab (x). Since the integral inversion algorithm with a limited grain diameter distribution range is adopted, the invention is suitable for the condition that in actual measurement, the grain diameters are distributed in a limited interval. In the formula (2) of the claims, spline function derivative is directly adopted instead of difference, thereby decreasing theoretical errors. The algorithm only contains a Bessel function, thereby remarkably decreasing inversion result oscillation.

Description

【Technical field】 [0001] The invention relates to a finite distribution integral inversion algorithm for particle size measurement, which belongs to the field of particle size measurement. 【Background technique】 [0002] At present, the integral inversion algorithm for measuring particle size distribution by laser diffraction method generally adopts the Chin-Shifrin integral transformation method. Let f(x) be the mass distribution probability density function of the particle group, then [0003] xf ( x ) = - 8 π 3 F 2 λ 2 ∫ 0 ∞ J 1 ( θx ) Y 1 ( θx ) θ ...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G01N15/02G06F19/00
Inventor 曹章徐立军丁洁
Owner 安徽欧泰祺智慧水务科技有限公司