# US 11,907,331 B1 · Method and system for evaluating fractal dimension of particle matter in dispersing system

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- Number: US 11,907,331 B1
- Document ID: US11907331B1
- Status: Granted
- Kind: B1
- Application number: 18/483,054
- Filed: 2023-10-09
- Granted: 2024-02-20
- Earliest claimed: 2023-03-27
- Assignees: Huazhong University of Science and Technology
- Applicants: Huazhong University of Science and Technology
- Inventors: Mingliang Xie; Yixiong Yang; Zhihao Jiang
- Web page: https://patentgrep.com/patent/US11907331B1

## CPC

- G06F 17/18: for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)}
- G06T 5/20: using local operators
- G06T 5/70: Denoising; Smoothing
- G06T 7/62: of area, perimeter, diameter or volume
- G06T 2207/10056: Microscopic image
- G06T 2207/20032: Median filtering
- G06T 2207/20112: Image segmentation details
- G06T 2207/30242: Counting objects in image
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL

## Abstract

Disclosed in the present invention are a method and system for evaluating a fractal dimension of particle matter in a dispersing system. The method includes: setting that distribution of a particle radius r of particle matter in a dispersing system obeys logarithmic normal distribution lnr˜N(μ, σ2) with an expectation μ and a standard deviation σ, and determining the value of the standard deviation σ; and evaluating a fractal dimension Dƒ of the dispersing system on the basis of the standard deviation σ, an evaluation formula being: Dƒ=1/σ. The present invention provides the formula for evaluating the fractal dimension of particle distribution in a dispersing system. When the formula is used to calculate a fractal dimension, only particle radius distribution of particle matter needs to be measured, and no geometrical morphology feature parameter of the particle matter needs to be measured. Factors such as particle morphology and the like do not affect the fractal dimension. Therefore, the measurement method of the present invention can reduce an error resulting from experimental measurements, can acquire a fractal dimension of particle matter quickly and efficiently, and is especially adapted to data analysis of a dispersion system and a particle swarm.

## Claims

### Claim 1

A method for evaluating a fractal dimension of particle matter in a dispersing system, the method comprising:
setting that distribution of a particle radius r of particle matter in a dispersing system obeys logarithmic normal distribution lnr˜N(μ, σ2) with an expectation μ and a standard deviation σ, acquiring a standard deviation σ of a particle radius r of the particle matter in the dispersing system in logarithmic normal distribution; and
evaluating the fractal dimension Dƒ of the dispersing system on the basis of the standard deviation σ, an evaluation formula being:
D
f
=
1
σ
.

### Claim 2 (depends on 1)

The method for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 1, wherein the acquiring a standard deviation σ of a particle radius r of the particle matter in the dispersing system in logarithmic normal distribution comprises:
particle radius distribution determination: determining the particle radius ri of the particle matter in the dispersing system and a particle content pi of the particle matter having the particle radius ri; and
fitting: fitting particle radius distribution of the particle matter in the dispersing system by using a standard logarithmic normal distribution function, so as to determine an expectation μ and a standard deviation σ in the logarithmic normal distribution function, the form of the logarithmic normal distribution function being:
f
⁡
(
r
)
=
1
r
⁢
2
⁢
π
⁢
σ
⁢
e
-
(
l
⁢
n
⁢
r
-
ln
⁢
μ
)
2
2
⁢
σ
2
wherein, ƒ(r) is a distribution probability density function of the particle radius r.

### Claim 3 (depends on 2)

The method for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 2, wherein the particle radius distribution determination is implemented by using a laser particle sizer.

### Claim 4 (depends on 2)

The method for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 2, wherein the particle radius distribution determination is implemented on the basis of computer image recognition, comprising:
step S110, acquiring a microscopic image by means of a microscopic image capture card;
step S120, removing background or environmental noise by means of median filtering;
step S130, reprocessing the image by means of 0-1 integer optimization;
step S140, marking a connected domain of a particle and the position of a central point thereof according to a seed fill algorithm in the graph theory; and
step S150, calculating the particle radius of the marked particle on the basis of the equivalence principle, and storing the same in a data structure, wherein the equivalence principle refers to using the area of the marked connected domain as the area of a circle, and calculating the radius as an equivalent radius of the corresponding particle, and the particle radius ri of the particle matter and the particle content pi of the particle matter having the particle radius ri are acquired according to stored data of the data structure.

### Claim 5 (depends on 2)

The method for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 2, wherein the fitting comprises:
dividing the particle radii into several ranges, counting the number of particles in each range, drawing a particle size distribution diagram, and performing polynomial fitting and optimization on a particle size distribution curve by using a least square method, to acquire the logarithmic normal distribution function of the particle radius distribution.

### Claim 6 (depends on 1)

The method for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 1, wherein the acquiring a standard deviation σ of a particle radius r of the particle matter in the dispersing system in logarithmic normal distribution comprises:
particle radius distribution determination: determining the particle radius ri of the particle matter in the dispersing system and a particle content pi of the particle matter having the particle radius ri;
first calculation: calculating an expectation E(r) and a variance D(r) of particle radius distribution of the particle matter in the dispersing system, calculation formulas being:
E
⁡
(
r
)
=
∑
i
=
1
n
r
i
⁢
p
i
D
⁡
(
r
)
=
∑
i
=
1
n
[
r
i
-
E
⁡
(
r
)
]
2
⁢
p
i
and second calculation: calculating the standard deviation σ of the particle radius distribution of the particle matter on the basis of the calculated expectation E(r) and variance D(r), a calculation formula being:
σ
=
ln
[
1
+
D
⁡
(
r
)
E
⁡
(
r
)
2
]
wherein, n is the number of particle radii of the particle matter.

### Claim 7

A system for evaluating a fractal dimension of particle matter in a dispersing system, characterized by comprising:
a distribution parameter calculation module, for acquiring a standard deviation σ of a particle radius r of the particle matter in the dispersing system in logarithmic normal distribution, setting that distribution of a particle radius r of particle matter in a dispersing system obeys logarithmic normal distribution lnr˜N(μ, σ2) with an expectation μ and a standard deviation σ; and
a fractal dimension calculation module, for evaluating the fractal dimension Dƒ of the dispersing system on the basis of the standard deviation σ, an evaluation formula being:
D
f
=
1
σ
.

### Claim 8 (depends on 7)

The system for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 7, wherein the distribution parameter calculation module comprises:
a particle radius distribution determination unit, for determining the particle radius ri of the particle matter in the dispersing system and a particle content pi of the particle matter having the particle radius ri; and
a fitting unit, for fitting particle radius distribution of the particle matter in the dispersing system by using a standard logarithmic normal distribution function, so as to determine an expectation μ and a standard deviation σ in the logarithmic normal distribution function, the form of the logarithmic normal distribution function being:
f
⁡
(
r
)
=
1
r
⁢
2
⁢
π
⁢
σ
⁢
e
-
(
l
⁢
n
⁢
r
-
ln
⁢
μ
)
2
2
⁢
σ
2
wherein, ƒ(r) is a distribution probability density function of the particle radius r.

### Claim 9 (depends on 8)

The system for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 8, wherein the particle radius distribution determination unit comprises:
a filtering subunit, for performing median filtering on a microscopic image acquired by means of a microscopic image capture card, so as to remove background or environmental noise;
an integer optimization subunit, for reprocessing the filtered image by means of 0-1 integer optimization;
a marking subunit, for marking a connected domain of a particle and the position of a central point thereof according to a seed fill algorithm in the graph theory; and
an equivalent radius calculation subunit, for calculating the particle radius of the marked particle on the basis of the equivalence principle, and storing the same in a data structure, wherein the equivalence principle refers to using the area of the marked connected domain as the area of a circle, and calculating the radius as an equivalent radius of the corresponding particle.

### Claim 10 (depends on 7)

The system for evaluating the fractal dimension of the particle matter in the dispersing system according to claim 7, wherein the distribution parameter calculation module comprises:
a particle radius distribution determination unit, for determining the particle radius ri of the particle matter in the dispersing system and a particle content pi of the particle matter having the particle radius ri;
a first calculation unit, for calculating an expectation E(r) and a variance D(r) of particle radius distribution of the particle matter in the dispersing system, calculation formulas being:
E
⁡
(
r
)
=
∑
i
=
1
n
r
i
⁢
p
i
D
⁡
(
r
)
=
∑
i
=
1
n
[
r
i
-
E
⁡
(
r
)
]
2
⁢
p
i
and a second calculation unit, for calculating the standard deviation σ of the particle radius distribution of the particle matter on the basis of the calculated expectation E(r) and variance D(r), a calculation formula being:
σ
=
ln
[
1
+
D
⁡
(
r
)
E
⁡
(
r
)
2
]
wherein, n is the number of particle radii of the particle matter.