CN111898246A - Method and system for fitting particle size distribution and calculating parameters of debris sediment - Google Patents
Method and system for fitting particle size distribution and calculating parameters of debris sediment Download PDFInfo
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- CN111898246A CN111898246A CN202010611090.3A CN202010611090A CN111898246A CN 111898246 A CN111898246 A CN 111898246A CN 202010611090 A CN202010611090 A CN 202010611090A CN 111898246 A CN111898246 A CN 111898246A
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Abstract
The invention discloses a method and a system for fitting particle size distribution of debris sediment and calculating parameters, and a computer-readable storage medium, belongs to the technical field of particle size distribution of debris sediment, and solves the technical problems of low fitting speed of particle size distribution of debris sediment, low parameter calculation speed and large error in the prior art. A method for fitting particle size distribution and calculating parameters of debris sediments comprises the following steps: acquiring the cumulative frequency of the particle size distribution of the debris sediments, establishing a fitted curve equation of the cumulative frequency of the particle size distribution of the debris sediments, and acquiring parameters of the fitted curve equation; obtaining a frequency fitting value of the particle size distribution of the debris sediment; and according to the fitting curve equation, establishing an inverse function of the fitting curve equation of the accumulated frequency, and determining the median, the mean and the variance of the particle size according to the inverse function of the fitting curve equation of the accumulated frequency and the parameters of the fitting curve equation. The method of the invention improves the fitting speed and the parameter calculation speed, and reduces the calculation error of the distribution parameters.
Description
Technical Field
The invention relates to the technical field of particle size distribution of debris sediments, in particular to a method and a system for fitting particle size distribution of debris sediments and calculating parameters and a computer-readable storage medium.
Background
Particle size analysis of clastic sediments has been a fundamental problem in the field of geoscience research, and is also the most widely used data in sedimentology and geology; the particle size distribution of the sediment is essentially the frequency distribution of different particle diameters, which not only reflects the particle size of the sediment, but also indirectly indicates the sediment carrying mode, the dynamic conditions of the sediment water and the sediment environment, and is also the most common data information for deducing the sediment process. The frequency, cumulative frequency, and common parameters of particle size distribution (median particle size, mean particle size, and variance) are the most common data for sediment particle size distribution.
At present, aiming at the particle size distribution fitting of the debris sediment, a large amount of optimized numerical solution calculation is needed, the process is complicated, and the speed is low; in addition, for the particle size distribution parameter calculation, the most common method is still a graphical method, namely, a cumulative frequency scatter diagram of the particle size distribution is drawn, the particle diameter corresponding to the cumulative frequency is read from the cumulative frequency scatter diagram, and the particle size distribution common parameters are respectively calculated by utilizing a Folk-Ward graphical method formula; the method needs to draw cumulative frequency scatter diagrams one by one, the manual reading value is not accurate, and the calculated parameters have large errors; therefore, for the particle size distribution of massive debris sediments, a method capable of quickly fitting the particle size distribution and calculating distribution parameters is needed to be found so as to improve the timeliness of the application of the particle size distribution.
Disclosure of Invention
In view of the above, the present invention provides a method, a system and a computer readable storage medium for fitting particle size distribution of a debris deposit and calculating parameters, which solve the technical problems of slow fitting speed of particle size distribution of the debris deposit, slow calculation speed of parameters and large error in the prior art.
In one aspect, the invention provides a method for fitting particle size distribution and calculating parameters of a debris deposit, which comprises the following steps:
acquiring the cumulative frequency of the particle size distribution of the debris sediment, establishing a fitted curve equation of the cumulative frequency of the particle size distribution of the debris sediment, and acquiring parameters of the fitted curve equation according to the cumulative frequency of the particle size distribution of the debris sediment and the fitted curve equation;
obtaining a frequency fitting value of the particle size distribution of the debris sediment according to the parameters of the fitting curve equation and the fitting curve equation;
and according to the fitting curve equation, establishing an inverse function of the fitting curve equation of the accumulated frequency, and according to the inverse function of the fitting curve equation of the accumulated frequency and the parameters of the fitting curve equation, determining the median, the mean and the variance of the particle size.
Further, the establishing a fitted curve equation of the cumulative frequency of the particle size distribution of the debris deposit specifically includes establishing a fitted curve equation of the cumulative frequency of the particle size distribution of the debris deposit
Wherein k, b, xcFor the parameters, k and b are growth rate factors of the curves, xcIs the inflection point of the curve, x is the grain size,
the values are fitted to the accumulated frequency.
Further, acquiring parameters of the fitted curve equation according to the cumulative frequency of the particle size distribution of the debris sediment and the fitted curve equation, specifically, establishing an equation set according to the cumulative frequency of the particle size distribution of the debris sediment and the fitted curve equation, and acquiring the parameters of the fitted curve equation according to the equation set.
Further, establishing an equation set according to the accumulated frequency of the particle size distribution of the debris sediment and the fitted curve equation, and acquiring parameters of the fitted curve equation according to the equation set,
according to the accumulated frequency of the particle size distribution of the debris sediment and the fitted curve equation, establishing an equation set, and acquiring parameters k, b and x of the fitted curve equation according to the equation setc，
Wherein the system of equations is
N is the number of granularity intervals in the cumulative frequency, yiIs the cumulative frequency of the ith granularity interval,
fitting values for the cumulative frequency of the ith granularity interval.
And further, obtaining a frequency fitting value of the particle size distribution of the debris sediment according to the parameters of the fitted curve equation and the fitted curve equation, specifically, obtaining a cumulative frequency fitting value of the particle size distribution of the debris sediment according to the parameters of the fitted curve equation and the fitted curve equation, and subtracting the cumulative frequency fitting values of the particle size distribution of the adjacent debris sediment to obtain the frequency fitting value of the particle size distribution of the debris sediment.
Further, establishing an inverse function of a fitted curve equation of the accumulated frequency based on the fitted curve equation specifically includes establishing an inverse function of a fitted curve equation of the accumulated frequency based on the fitted curve equation
Wherein ln is a natural logarithm function, and k is not equal to 0.
Further, determining a median particle size according to an inverse function of the cumulative frequency fitting curve equation and parameters of the fitting curve equation, specifically including determining the median particle size according to formula Md＝f-1(50) Determination of median particle size Md。
Further, determining a mean and a variance of the particle size according to an inverse function of the cumulative frequency fitting curve equation and parameters of the fitting curve equation, specifically including, by a formula
Determination of the mean value of the particle size MzBy the formula
The particle size variance σ is determined.
In another aspect, the present invention further provides a system for fitting a particle size distribution of a debris deposit and calculating parameters, which includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the method for fitting a particle size distribution of a debris deposit and calculating parameters according to any one of the above technical solutions is implemented.
In another aspect, the invention also provides a computer readable storage medium, on which a computer program is stored, which when executed by a processor, implements the method of fitting a particle size distribution of a debris deposit and calculating parameters as described in any one of the above aspects.
Compared with the prior art, the invention has the beneficial effects that: establishing a fitted curve equation of the accumulated frequency of the particle size distribution of the debris sediment by acquiring the accumulated frequency of the particle size distribution of the debris sediment, and acquiring parameters of the fitted curve equation according to the accumulated frequency of the particle size distribution of the debris sediment and the fitted curve equation; obtaining a frequency fitting value of the particle size distribution of the debris sediment according to the parameters of the fitting curve equation and the fitting curve equation; according to the fitting curve equation, establishing an inverse function of the fitting curve equation of the accumulated frequency, and according to the inverse function of the fitting curve equation of the accumulated frequency and parameters of the fitting curve equation, determining a median value, a mean value and a variance of the particle size; the fitting speed and the parameter calculation speed of the particle size distribution of the debris sediment are improved, and the calculation error of the particle size distribution parameters of the debris sediment is reduced.
Drawings
FIG. 1 is a schematic flow chart of a method for fitting particle size distribution and calculating parameters of a crumb sediment according to example 1 of the present invention;
FIG. 2 is a schematic diagram of a cumulative frequency fit curve according to example 1 of the present invention;
FIG. 3 is a graph showing the frequency fit of the particle size distribution according to example 1 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
The invention provides a method for fitting particle size distribution and calculating parameters of a debris deposit, which comprises the following steps of:
s1, acquiring the cumulative frequency of the particle size distribution of the debris sediment, establishing a fitted curve equation of the cumulative frequency of the particle size distribution of the debris sediment, and acquiring parameters of the fitted curve equation according to the cumulative frequency of the particle size distribution of the debris sediment and the fitted curve equation;
s2, obtaining a frequency fitting value of the particle size distribution of the debris sediment according to the parameters of the fitting curve equation and the fitting curve equation;
s3, according to the fitting curve equation, establishing an inverse function of the fitting curve equation of the accumulated frequency, and according to the inverse function of the fitting curve equation of the accumulated frequency and parameters of the fitting curve equation, determining the median, the mean and the variance of the particle size.
Preferably, the establishing a fitted curve equation of the cumulative frequency of the particle size distribution of the debris deposit specifically comprises establishing a fitted curve equation of the cumulative frequency of the particle size distribution of the debris deposit
Wherein k, b, xcFor the parameters, k and b are growth rate factors of the curves, xcIs the inflection point of the curve, x is the grain size,
the values are fitted to the accumulated frequency.
In one embodiment, a fitted curve equation of the cumulative frequency of the particle size distribution of the debris deposit is established based on the cumulative frequency characteristic of the particle size distribution of the debris deposit, i.e. a fitted sigmoid curve Gompertz equation
In the above formula, k, b and xcFor the parameter to be solved, k and b are growth rate factors of the S-shaped curve, xcIs the inflection point of the S-shaped curve, x is the granularity,
the cumulative frequency fitting value is obtained; according to the limit theorem have
Obviously meet the data characteristic of the cumulative frequency of granularity;
preferably, the parameters of the fitted curve equation are obtained according to the accumulated frequency of the particle size distribution of the debris sediment and the fitted curve equation, specifically, the method includes establishing an equation set according to the accumulated frequency of the particle size distribution of the debris sediment and the fitted curve equation, and obtaining the parameters of the fitted curve equation according to the equation set;
preferably, an equation set is established according to the cumulative frequency of the particle size distribution of the debris sediment and the fitted curve equation, and parameters of the fitted curve equation are obtained according to the equation set, which specifically comprises,
according to the accumulated frequency of the particle size distribution of the debris sediment and the fitted curve equation, establishing an equation set, and acquiring parameters k, b and x of the fitted curve equation according to the equation setc，
Wherein the system of equations is
N is the number of granularity intervals in the cumulative frequency, yiIs the cumulative frequency of the ith granularity interval,
fitting a value for the cumulative frequency of the ith granularity interval; i is 0,1,2, …, N;
in one embodiment, the parameters k, b and x of the particle size distribution cumulative frequency S-shaped curve Gompertz equation are solved by using an equation system according to the cumulative frequency of the particle size distributioncThe parameters k, b and xcSubstituting the formula (1) to obtain an S-shaped curve Gompertz equation expression fitting the cumulative frequency of the particle size distribution; a schematic diagram of a cumulative frequency fitting curve obtained by an expression of an S-shaped curve Gompertz equation fitted with a particle size distribution cumulative frequency is shown in FIG. 2For the cumulative frequency of the particle size distribution in fig. 2, the parameters of the cumulative frequency S-shaped curve Gompertz equation calculated are k-0.9139, b-1.1176, and x, respectivelyc1.3090; calculating the accumulated frequency value under each granularity in the granularity interval of the granularity distribution according to a known accumulated frequency S-shaped curve Gompertz equation expression;
because the expression of the solved accumulated frequency S-shaped curve Gompertz equation is a continuous function, the accumulated frequency of any particle size can be calculated, and an accumulated frequency fitting curve (the curve in figure 2) can be obtained; in order to facilitate comparison with the cumulative frequency, the cumulative frequency corresponding to the original particle size needs to be obtained, and a cumulative frequency fitting value (a hollow circle in fig. 2) can be obtained;
preferably, the frequency fitting value of the particle size distribution of the debris sediment is obtained according to the parameters of the fitted curve equation and the fitted curve equation, and the method specifically comprises the steps of obtaining a cumulative frequency fitting value of the particle size distribution of the debris sediment according to the parameters of the fitted curve equation and the fitted curve equation, and obtaining the frequency fitting value of the particle size distribution of the debris sediment by subtracting the cumulative frequency fitting values of the particle size distribution of the adjacent debris sediment.
In specific implementation, on the basis of the cumulative frequency fitting value of the particle size distribution, the frequency fitting values of the particle size distribution can be obtained by subtracting the adjacent cumulative frequency fitting values, and the frequency fitting value schematic diagram of the particle size distribution is shown in fig. 3, wherein the hollow circle in fig. 3 is the frequency fitting value of the particle size distribution; to this end, a quick fit of the crumb sediment particle size distribution, including a cumulative frequency and frequency fit, has been accomplished; therefore, the rapid fitting of the particle size distribution provided by the embodiment of the invention is simpler, and the optimal numerical solution of the probability density function is avoided;
preferably, the step of establishing an inverse function of a fitted curve equation of the accumulated frequency according to the fitted curve equation specifically comprises establishing an inverse function of a fitted curve equation of the accumulated frequency according to the fitted curve equation
Wherein ln is a natural logarithm function, and k is not equal to 0;
preferably, determining the median particle size according to the inverse function of the cumulative frequency fitting curve equation and the parameters of the fitting curve equation specifically comprises determining the median particle size according to the formula Md＝f-1(50) Determination of median particle size Md；
Preferably, the determining the mean and variance of the particle size according to the inverse function of the cumulative frequency fitting curve equation and the parameters of the fitting curve equation comprises using a formula
Determination of the mean value of the particle size MzBy the formula
Determining a granularity variance sigma;
during specific implementation, an inverse function of a fitting curve equation of the accumulated frequency is established, namely an inverse function of an accumulated frequency S-shaped curve Gompertz equation is established;
calculating the inverse function values of the Gompertz equation of the cumulative frequency S-shaped curve corresponding to the cumulative frequencies of 5%, 16%, 50%, 84% and 95% respectively; according to the above formula (3), respectively
16. 50, 84 and 95, respectively, calculating f-1(5)、f-1(16)、f-1(50)、f-1(84) And f-1(95) (ii) a For example, for the cumulative frequency of the particle size distribution in fig. 2, k-0.9139, b-1.1176, and xcSubstitution of 1.3090 into each of the above formulas (3) yields f-1(5)＝0.2301、f-1(16)＝0.7678、f-1(50)＝1.8317、f-1(84) 3.3419 and f-1(95)＝4.6807；
Calculating an inverse function value of a Gompertz equation of the accumulated frequency S-shaped curve, and calculating a median value, a mean value and a variance of the granularity; for the particle size distributions of fig. 2 and 3, the median particle size was calculated to be 1.8317 phi (phi ═ log)2D, D is the particle sizeDiameter in centimeters), the mean particle size is 1.9805 phi, and the variance of the particle size is 1.3178; by now, rapid calculations of crumb sediment particle size distribution parameters, including median particle size, mean particle size and variance, have been accomplished.
Example 2
The embodiment of the invention provides a system for fitting particle size distribution and calculating parameters of a debris deposit, which comprises a processor and a memory, wherein the memory is stored with a computer program, and when the computer program is executed by the processor, the method for fitting particle size distribution and calculating parameters of the debris deposit is realized as in the embodiment 1.
Example 3
Embodiments of the present invention provide a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a method of fitting a particle size distribution of a debris deposit and calculating parameters as described in embodiment 1 above.
The invention discloses a method, a system and a computer-readable storage medium for fitting particle size distribution and calculating parameters of a clastic sediment; establishing a fitted curve equation of the accumulated frequency of the particle size distribution of the debris sediment by acquiring the accumulated frequency of the particle size distribution of the debris sediment, and acquiring parameters of the fitted curve equation according to the accumulated frequency of the particle size distribution of the debris sediment and the fitted curve equation; obtaining a frequency fitting value of the particle size distribution of the debris sediment according to the parameters of the fitting curve equation and the fitting curve equation; according to the fitting curve equation, establishing an inverse function of the fitting curve equation of the accumulated frequency, and according to the inverse function of the fitting curve equation of the accumulated frequency and parameters of the fitting curve equation, determining a median value, a mean value and a variance of the particle size; the method avoids errors caused by manual drawing and reading of the cumulative frequency of the particle size distribution one by one, avoids the optimal numerical solution of the probability density function, improves the fitting speed and the parameter calculation speed of the particle size distribution of the debris sediments, and reduces the calculation errors of the particle size distribution parameters of the debris sediments; the method can be used for batch processing of mass particle size distribution.
The above-described embodiments of the present invention should not be construed as limiting the scope of the present invention. Any other corresponding changes and modifications made according to the technical idea of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. A method for fitting particle size distribution and calculating parameters of debris sediments is characterized by comprising the following steps:
acquiring the cumulative frequency of the particle size distribution of the debris sediment, establishing a fitted curve equation of the cumulative frequency of the particle size distribution of the debris sediment, and acquiring parameters of the fitted curve equation according to the cumulative frequency of the particle size distribution of the debris sediment and the fitted curve equation;
obtaining a frequency fitting value of the particle size distribution of the debris sediment according to the parameters of the fitting curve equation and the fitting curve equation;
and according to the fitting curve equation, establishing an inverse function of the fitting curve equation of the accumulated frequency, and according to the inverse function of the fitting curve equation of the accumulated frequency and the parameters of the fitting curve equation, determining the median, the mean and the variance of the particle size.
2. The method of claim 1, wherein establishing a fitted curve equation of cumulative frequency of particle size distribution of debris sediment comprises establishing a fitted curve equation of cumulative frequency of particle size distribution of debris sediment
Wherein k, b, xcFor the parameters, k and b are growth rate factors of the curves, xcIs the inflection point of the curve, x is the grain size,
the values are fitted to the accumulated frequency.
3. The method of claim 2, wherein obtaining the parameters of the fitted curve equation based on the cumulative frequency of the particle size distribution of the debris deposit and the fitted curve equation comprises establishing a system of equations based on the cumulative frequency of the particle size distribution of the debris deposit and the fitted curve equation, and obtaining the parameters of the fitted curve equation based on the system of equations.
4. The method of claim 3, wherein a set of equations is created based on the cumulative frequency of the particle size distribution of the debris deposit and the fitted curve equation, and parameters of the fitted curve equation are obtained from the set of equations, specifically comprising,
establishing an equation set according to the accumulated frequency of the particle size distribution of the debris sediment and the fitted curve equation, and acquiring parameters k, b and x of the fitted curve equation according to the equation setc，
Wherein the system of equations is
N is the number of granularity intervals in the cumulative frequency, yiIs the cumulative frequency of the ith granularity interval,
fitting values for the cumulative frequency of the ith granularity interval.
5. The method according to claim 1, wherein the step of obtaining the frequency fitting value of the particle size distribution of the debris deposit is performed according to the parameters of the fitted curve equation and the fitted curve equation, and specifically comprises the steps of obtaining the cumulative frequency fitting value of the particle size distribution of the debris deposit according to the parameters of the fitted curve equation and the fitted curve equation, and obtaining the frequency fitting value of the particle size distribution of the debris deposit by subtracting the cumulative frequency fitting values of the particle size distributions of the adjacent debris deposits.
6. The method of claim 2, wherein establishing an inverse of a fitted curve equation of cumulative frequency based on the fitted curve equation, specifically comprising establishing an inverse of a fitted curve equation of cumulative frequency based on the fitted curve equation
Wherein ln is a natural logarithm function, and k is not equal to 0.
7. The method of claim 6, wherein determining the median particle size from the inverse of the cumulative frequency fit curve equation and the parameters of the fit curve equation comprises determining the median particle size using the formula Md＝f-1(50) Determination of median particle size Md。
8. The method of claim 6, wherein determining the mean and variance of particle size from the inverse of the cumulative frequency fit curve equation and the parameters of the fit curve equation comprises using a formula
Determination of the mean value of the particle size MzBy the formula
The particle size variance σ is determined.
9. A debris deposit particle size distribution fitting and parameter calculating system comprising a processor and a memory, the memory having stored thereon a computer program which, when executed by the processor, carries out the debris deposit particle size distribution fitting and parameter calculating method of any of claims 1 to 8.
10. A computer readable storage medium having stored thereon a computer program, wherein the computer program, when executed by a processor, implements the method of debris deposit particle size distribution fitting and parameter calculation according to any of claims 1-8.
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| CN108872032A (en) * | 2018-05-02 | 2018-11-23 | 国家海洋信息中心 | Grain size of sediment data processing method and device |
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| CN108872032A (en) * | 2018-05-02 | 2018-11-23 | 国家海洋信息中心 | Grain size of sediment data processing method and device |
| WO2020100952A1 (en) * | 2018-11-13 | 2020-05-22 | 日鉄ケミカル＆マテリアル株式会社 | Silica spherical particles for semiconductor sealing material |
| CN110146420A (en) * | 2019-04-12 | 2019-08-20 | 中国石油大学(北京) | A kind of glutenite granularity intelligent analysis system and method |
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