A monotone interpolation method for estimating cumulative distribution of ore particle size

Abstract

The invention relates to a monotonous interpolation method for estimating cumulative distribution of granularity of ores. The monotonous interpolation method comprises the following steps: (1) carrying out granularity screening measurement on ore samples by using screening nets with n pore diameters and measuring to obtain cumulative distribution data of the granularity of the ores; sequentially marking the pore diameter sizes of the screening nets to x1, x2,...and xn; sequentially marking the cumulative distribution data of the granularity of the ores to y1, y2,...and yn, wherein the y1 is less than or equal to the y2, the y2 is less than or equal to y3,...and y(n-1) is less than or equal to the yn; obtaining n known data points (x1,y1), (x2,y2),...and (xn,yn), wherein n is a natural number; (2) calculating the gradient of a connection line of each two adjacent data points; (3) carrying out log30.5 power mean value Hermite interpolation on the known data points. The monotonous interpolation method adopts a power mean value Hermite interpolation framework and shows that in all methods used under the framework, a log30.5 power mean value method is a method which can guarantee the monotonicity of interpolation and lowest flatness. Meanwhile, the monotonous interpolation method is simple in calculation steps and extra revising steps used in many known methods are not needed, so that the application is very convenient.

Description

technical field [0001] The invention relates to a monotone interpolation method, in particular to a monotone interpolation method for estimating the cumulative distribution of ore particle size. Background technique [0002] The monotonic interpolation problem is to interpolate known data points that satisfy monotonicity, so that the interpolation curve still satisfies the same monotonic interpolation problem. Because many problems in reality, such as the growth of the population, the accumulation of workload, etc., have monotonicity, if you want to interpolate them, the interpolated curve should also satisfy the monotonicity, otherwise it is contrary to the physical meaning. Therefore, the monotone interpolation problem has a large practical application space. [0003] The cumulative distribution of ore particle size is a representation of ore particle size, which is widely used in the mineral processing industry. When beneficiating ore, it is first necessary to crush and...

AI Technical Summary

Problems solved by technology

Since the actual method of measuring ore particle size is the sieving method, and the sieving method can only measure certain specific particle sizes due to the limitation of the sieve aperture.

Involving the integrity of the expression and the matching of the simulation, usually the distribution of only a few specific particle sizes cannot meet the use requirements. Therefore, it is usually desired to obtain the cumulative distribution of any particle size. In order to meet this requirement, interpolation calculations are required

The interpolation problem of the cumulative distribution of ore particle size is a typical monotonic interpolation problem. However, in many existing international well-known mineral processing simulation software, the interpolation of the cumulative distribution of ore particle size is too arbitrary, and no effective monotonic interpolation method is used. The obtained interpolation The effect is not satisfactory, which is a very unfavorable situation for the simulation of ore particle size change that is of great concern to the mineral processing industry

Moreover, the existing main interpolation methods, such as polynomial interpolation, cubic spline interpolation, etc., cannot meet the requirements of monotonicity

However, the existing monotone interpolation methods have their own advantages and disadvantages, and many of them still have room for improvement.

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