Fragmentation energy calculation model of coal crushed by impact load

ABSTRACT

Rock fragmentation is a common physical and mechanical phenomenon that exists in a variety of ranges from the mining and processing. Communication is an important operation in coal processing whereby the coal block coming from coalmines is crushed into fragmentations with reduced size, which accounts for 80% of the electricity consumption of mineral processing circuits. Fragmentation energy, which is related to the coal particle size distribution, is an essential parameter for improving the efficiency of shearer, road-header, and crusher. Coal particles are generally simplified into fine or near spherical shapes for analytical and numerical simulation purposes. This research aims to establish the fragmentation energy calculation model for coal fragmentations with coarse and wide size distribution based on the analysis of size distribution and energy-size relationships of coal particles. It has been demonstrated by the results that the fragmentation energy of impact load crushed coal can be determined based on Rittinger’s theory with fractal or RR model particle size distribution.

KEYWORDS:

• Coal crushing
• fragmentation energy
• digital image processing
• particle size distribution

Introduction

Rock fragmentation is a common physical and mechanical phenomenon that exists in a variety of ranges from the mining and processing (Trechera et al. 2022; Zhu et al. 2023). In underground mining or development face, cutting of coal is the key step of mining process, which consumes 80%-90% power of the entire shearer and road-header (X. H. Liu, Liu, and Tang 2015). Communication is an important operation in coal processing whereby the coal block coming from coalmines is crushed into fragmentations with reduced size, which accounts for 80% of the electricity consumption of mineral processing circuits (Numbi and Xia 2015, 2016). More importantly, the cracks within coal blocks formed by impact and seismic load will lead to the sudden fragmentation of underground structures, which will significantly affect mining safety and efficiency (J. W. Cheng et al. 2023; Yang, Ren, and Tan 2020a). Hence, thorough research has been made by researchers around the energy consumption of rock/coal fragmentation process.

Fragmentation energy, which is related to the coal particle size distribution, is an essential parameter for improving the efficiency of shearer, road-header, and crusher. The relationship between the fragmentation energy and the particle size for single-sized particles has been extensively researched over the last century. Energy-size equations based on theoretical and experimental studies have been put forward by Rittinger, Kick and Bond (Morrell 2008), known as the three theories of comminution. However, these experimental data and theoretical equations mentioned in the literature are mostly limited to rock or other ores, or pulverized coal (Kossovich et al. 2023). Besides, in many researches, coal particles are generally simplified into fine or near spherical shapes for analytical and numerical simulation purposes (Chen et al. 2020; Z. F. Cheng and Zhu 2015). Zhou et al. proposed six different agglomerate polyhedrons to characterize the shape of coal particles and discussed the shape effect on pneumatic conveying process (Zhou, Liu, Du, et al. 2017; Zhou, Liu, Liu, et al. 2017). In these particle size and shape characteristic models, fractal equation is widely used to describe the particle size distribution of coal/rock particles (Qin et al. 2022).

This research aims to establish the fragmentation energy calculation model for coal fragmentations with coarse and wide size distribution based on the analysis of size distribution and energy-size relationships of coal particles. A drop weight impact system was used to crush the coal into particles with designed energy input. The statistical mass-size curves of coal particles crushed by impact load were obtained based on manual sieving and digital image processing technique, which is used to validate the fractal and Rosin-Ramler (RR) model distribution curve of coal particles. The fragmentation energy calculated based on different size distribution model and energy-size relationships were compared with the impact energy input to determine the effectiveness of each method. It has been demonstrated by the results that the fragmentation energy of impact load crushed coal can be determined based on Rittinger’s theory with fractal or RR model PSD distribution.

Analytical method

Particle size distribution

For coal fragmentation and crushing process, the coal fragments satisfy specific size distribution law. Hence, the particle size distribution (PSD) needs to be taken into consideration for the calculation of fragmentation energy. The most widely used mathematical equations mainly used to describe PSD are the Rosin-Ramler (R-R), the Gate-Gaudin-Schuhmann (G-G-S) and the fractal distribution.

The GGS model can be given by the following expression (MacıMacıAs-Garcıa, Cuerda-Correa, and Dıaz-Dıez 2004; Petrakis, Stamboliadis, and Komnitsas 2017):

(1) $\begin{array}{c}\mathit{F}\left(\mathit{d}\right)={\left(\frac{\mathit{d}}{{\mathit{d}}_{\mathit{max}}}\right)}^{\mathit{m}}\end{array}$(1)

Where $\mathit{F}\left(\mathit{d}\right)$ is the cumulative mass fraction of the fragments smaller than size $\mathit{d}$, $d_{\mathit{max}}$ is the maximum size of PSD and $\mathit{m}$ is the adjustable parameter depended on rock properties.

The RR model is defined by (Bu et al. 2020; Rosin and Rammler 1933):

(2) $\begin{array}{c}\mathit{F}\left(\mathit{d}\right)=1-\mathit{exp}\left[-{\left(\frac{d}{d_0}\right)}^{\mathit{m}}\right]\end{array}$(2)

Where $d_0$ is the characteristic fragment size in mm usually corresponding to 63.2% of the total volume of distribution $\mathit{F}\left(\mathit{d}\right)$.

The Fractal model can be written as (Ullah et al. 2022):

(3) $\begin{array}{c}\mathit{F}\left(\mathit{d}\right)={\left(\frac{\mathit{d}}{{\mathit{d}}_{\mathit{max}}}\right)}^{\left(3-\mathit{n}\right)}\end{array}$(3)

Where $\mathit{n}$ is the fractal dimension of PSD, which is related to rock properties.

It can be seen from the equations that the mathematical expressions of GGS model and fractal model are the same concept. Hence, only fractal and RR models are compared for the calculation of coal fragmentation energy in this study.

Energy-size relationship

The relationships between fragmentation size and specific energy consumption have been thoroughly studied by many researchers. Rittinger believed that the energy consumed by mineral fragmentation is proportional to the new surface area generated as all the energy is dissipated by overcoming the molecular cohesion among new fragments surfaces (Du et al. 2022). Taking the coal fragment as platonic solid or sphere, the volume of fragment is directly proportional to the cubic of fragment size while the surface area is directly proportional to the square of size. The surface area change of coal after fragmentation can be expressed as:

(4) $\begin{array}{c}\mathit{S}=\mathit{a}\ast \mathit{V}\ast \left(\frac{1}{d}-\frac{1}{D}\right)\end{array}$(4)

Where $\mathit{S}$ is the surface area change of coal, $\mathit{V}$ is the total volume of framents, $\mathit{d}$ is the fragment size after failure, $\mathit{D}$ is the equivalent size of total fragments before failure and $\mathit{a}$ is shape factor which is the constant related to fragment shape.

Hence, Rittinger’s theory can be written in the following equation:

(5) $\begin{array}{c}{E}_{\mathit{fragmentation}}=K_R\ast \mathit{a}\ast \mathit{V}\ast \left(\frac{1}{d}-\frac{1}{D}\right)\end{array}$(5)

Where $K_R$ is fragmentation energy consumed by formation of per unit surface area, also called Rittinger constant, which is only related to the mineral properties.

Kick proposed that the energy required for mineral fragmentation with a given size is proportional to the volume of resulting fragments (Locat et al. 2003). Tavares et al. believe that Kick’s theory is suitable for fragmentation energy calculation of relatively large particles based on experimental data (Tavares and King 1998). Kick’s theory can be expressed as:

(6) $\begin{array}{c}{E}_{\mathit{fragmentation}}=K_K\ast \mathit{a}\ast \mathit{V}\ast \left(\mathit{logD}-\mathit{logd}\right)\end{array}$(6)

Where $K_K$ is energy index in Kick’s theory, which depends on mineral properties.

Bond’s theory suggests that deformation happens initially inside the intact rock or ore under applied forces until a threshold is reached at which the crack emerges (J. X. Liu et al. 2016). Hence, the fragmentation energy is proportional to the total length of the new cracks generated during coal fragmentation. The resulting equation based on Bond’s theory is:

(7) $\begin{array}{c}{E}_{\mathit{fragmentation}}=K_B\ast \mathit{a}\ast \mathit{V}\ast \left(\frac{1}{\sqrt{\mathit{d}}}-\frac{1}{\sqrt{\mathit{D}}}\right)\end{array}$(7)

Where $K_B$ is a constant named Bond’s index, which is related to the mineral properties.

However, the above fragmentation energy calculation equations are for single sized particles. To determine the fragmentation energy for wide range of particle sizes, the equation needs to be in differential form by considering the particle size distribution, as listed in Table 1. In Table 1, W is the total weight of coal fragments and $\mathit{\rho }$ is density of coal.

Table 1. Fragmentation energy differential formula.

Formula No	Energy-size Relationships	PSD Models	Equations	Note
1	Rittinger Theory	Fractal	$E_{\mathit{fragmentation}}={\int }_0^{{\mathit{d}}_{\mathit{max}}}{K}_R\ast \mathit{a}\ast \frac{W}{\rho }\ast {\left(\frac{\mathit{d}}{{\mathit{d}}_{\mathit{max}}}\right)}^{\mathit{m}}\ast \left[\frac{1}{d}-\frac{1}{\sqrt[3]{\frac{\mathit{W}}{\mathit{a}\ast \mathit{\rho }}\ast {\left(\frac{\mathit{d}}{{\mathit{d}}_{\mathit{max}}}\right)}^{\mathit{m}}}}\right]$	The value of m of fractal model for coal given by Peng et al is 0.91 Peng et al. (2015).
2	Kick Theory	Fractal	$E_{\mathit{fragmentation}}={\int }_0^{{\mathit{d}}_{\mathit{max}}}{K}_K\ast \mathit{a}\ast \frac{W}{\rho }\ast {\left(\frac{\mathit{d}}{{\mathit{d}}_{\mathit{max}}}\right)}^{\mathit{m}}\ast \left[\mathit{log}\left(\sqrt[3]{\frac{\mathit{W}}{\mathit{a}\ast \mathit{\rho }}\ast {\left(\frac{\mathit{d}}{{\mathit{d}}_{\mathit{max}}}\right)}^{\mathit{m}}}\right)-\mathit{logd}\right]$
3	Bond Theory	Fractal	$E_{\mathit{fragmentation}}={\int }_0^{{\mathit{d}}_{\mathit{max}}}{K}_B\ast \mathit{a}\ast \frac{W}{\rho }\ast {\left(\frac{\mathit{d}}{{\mathit{d}}_{\mathit{max}}}\right)}^{\mathit{m}}\ast \left[\frac{1}{\sqrt{\mathit{d}}}-\frac{1}{\sqrt[6]{\frac{\mathit{W}}{\mathit{a}\ast \mathit{\rho }}\ast {\left(\frac{\mathit{d}}{{\mathit{d}}_{\mathit{max}}}\right)}^{\mathit{m}}}}\right]$
4	Rittinger Theory	RR	$E_{\mathit{fragmentation}}={\int }_0^{{\mathit{d}}_{\mathit{max}}}{K}_R\ast \mathit{a}\ast \frac{W-W\ast exp\left[-{\left(\frac{d}{d_0}\right)}^{\mathit{m}}\right]}{\mathit{\rho }}\ast \left\{\frac{1}{d}-\frac{1}{\sqrt[3]{\frac{W-W\ast exp\left[-{\left(\frac{d}{d_0}\right)}^{\mathit{m}}\right]}{\mathit{a}\ast \mathit{\rho }}}}\right\}$	The value of m of RR model is 1.32 for coal in this paper.
5	Kick Theory	RR	$E_{\mathit{fragmentation}}={\int }_0^{{\mathit{d}}_{\mathit{max}}}{K}_K\ast \mathit{a}\ast \frac{W-W\ast exp\left[-{\left(\frac{d}{d_0}\right)}^{\mathit{m}}\right]}{\mathit{\rho }}\ast \left\{\mathit{log}\left[\sqrt[3]{\frac{W-W\ast exp\left[-{\left(\frac{d}{d_0}\right)}^{\mathit{m}}\right]}{\mathit{a}\ast \mathit{\rho }}}\right]-\mathit{logd}\right\}$
6	Bond Theory	RR	$E_{\mathit{fragmentation}}={\int }_0^{{\mathit{d}}_{\mathit{max}}}{K}_B\ast \mathit{a}\ast \frac{W-W\ast exp\left[-{\left(\frac{d}{d_0}\right)}^{\mathit{m}}\right]}{\mathit{\rho }}\ast \left\{\frac{1}{\sqrt{\mathit{d}}}-\frac{1}{\sqrt[6]{\frac{W-W\ast exp\left[-{\left(\frac{d}{d_0}\right)}^{\mathit{m}}\right]}{\mathit{a}\ast \mathit{\rho }}}}\right\}$

Experimental

Impact crushing tests

The impact crushing test of coal was conducted in laboratory to get the crushed coal particles. The impact load was achieved by a drop weight system as shown in Figure 2. The drop weight with 73.35 kg was released from a height of 2.5 m, which can accelerate the drop weight maximum to 7 m/s. It has been verified by previous application this test system that the energy loss due to the internal frictions of drop hammer system can be negligible (Yang et al. 2021). To guide the direction of impact load, an additional test set consists of transmission bar, bolt and base was placed right under the drop weight. The transmitted and reflected energy of transmission bar subject to different impact velocity have been thoroughly studied (Feng et al. 2018). Based on energy conservation, the energy dissipation can be defined using equation (8)(8) $\begin{array}{c}{E}_f+E_k=E_i-E_r-E_t\end{array}$(8) :

(8) $\begin{array}{c}{E}_f+E_k=E_i-E_r-E_t\end{array}$(8)

where $E_f$ is the fragmentation energy, $E_k$ is the kinetic energy driving the coal particle movement, $E_i$ is the total impact energy, $E_r$ is the reflected energy of reflected wave $E_t$ is the transmitted energy of transmitted wave.

The sum of fragmentation and kinetic energy also called dissipated energy as this is the energy dissipated by rock fracture and projectile subject to dynamic loads.

Coal sample was placed between the transmission bar and the base. Coal sample used in this test was 50 mm *50 mm *100 mm cuboid coal blocks as shown in Figure 1. Coal samples were sourced from local Australian coal mines with 7-10MPa uniaxial compression strength. The crushed coal particles were collected after particle size distribution analysis once the impact test was done.

Figure 1. Drop weight system for impact crushing test of coal Sample.

Digital image processing

Generally, the size distribution of coal particles can be measured by manual sieving, which is time-consuming and low-efficiency (Hou et al. 2015). Besides, further damage to coal particles may be caused by vibration during sieving process, which will affect the accuracy of measurement results. Especially for larger coal particles with natural weaknesses or bedding, manual sieving will break coal particles into smaller size. Digital image processing method, developed based on the application of digital image acquisition equipment, process software package and mathematical analysis algorithm, enables the fast and accurate measurement of size distribution of solid particles (Wu and Yu 2012). Previous research has demonstrated the application feasibility of digital image processing method for size distribution measurement of coal particles ranging from 2.5 to 80 mm (Yang, Ren, and Tan 2020b).

To determine the particle distribution curve for fractal and RR models, the cumulative distribution curve of coal particles was measured by combined manual and digital sieving. Manual sieving was used to determine the cumulative mass at three sizes including 2.5, 5 and 10 mm. All other particles larger than 10 mm were measured by digital image processing. As shown in Figure 2, digital image processing includes two main steps: image acquisition and image analysis. The acquisition of high-resolution image is achieved by a fixed Nikon D60 camera remotely controlled by mobile phone through wireless connection. The wireless control of the camera can ensure the image quality by avoiding the shadow caused by the camera shakiness. The image analysis is conducted by Image Processing Toolbar of MATLAB R2020a software. More detailed introduction of digital image processing procedure can be found in the literature (Yang, Ren, and Tan 2020b). The image analysis code is attached as Appendix A at the end of this paper.

Figure 2. Procedure of Digital Image Processing (after (Yang, Ren, and Tan 2020b)).

The data acquired by digital image analysis includes maximum axis length, minor axis length and area of each particle. The particle area, which is the two-dimensional pixel area forming each particle on the image, will be used to calculation the shape parameter for example equivalent diameter of each particle. All the data are originally in pixels and then transformed into millimeter through scale calibration.

Results

According to equation (1)(1) $\begin{array}{c}\mathit{F}\left(\mathit{d}\right)={\left(\frac{\mathit{d}}{{\mathit{d}}_{\mathit{max}}}\right)}^{\mathit{m}}\end{array}$(1) , the particle size distribution determined by manual and digital sieving is plotted in Figure 3. The measured data was used to calibrate the fractal and RR particle distribution model. To get the best fitting results to the measured data, the fractal and RR model can be evaluated by the root mean square error (RMSE) and coefficient of determination (R²) from the following equations (Bu et al. 2019):

(9) $\begin{array}{c}\mathit{RMSE}=\sqrt{\frac{1}{n}\sum _{\mathit{i}=1}^n{\left(X_i-Y_i\right)}^2}\end{array}$(9)

(10) $\begin{array}{c}{R}^2=1-\frac{{\sum }_{i=1}^n{\left(X_i-Y_i\right)}^2}{{\sum }_{i=1}^n{\left(X_i-Z_i\right)}^2}\end{array}$(10)

Figure 3. RMSE for particle size distribution models.

where $X_i$ is the cumulative mass fraction measured by manual or digital sieving, $Y_i$ is the cumulative mass fraction estimated by fractal distribution or RR model, $Z_i$ is the mean value of all experimental data, and $\mathit{n}$ is the number of data points.

According to the reference value of distribution parameter for each model in Table 1, the RMSE is calculated for both fractal and RR distribution models with a distribution parameter range from 0 to 3, as shown in Figure 3. The lowest RMSE to achieve best fitting results of each model can be identified from the Figure 3. The RMSE of fractal model is more sensitive to the distribution parameter with a minimum error can be achieved with fractal dimension equals to 2.45, while distribution parameter for RR model is 1.17 for the minimum error. Besides, the minimum error of RR model is slightly lower than fractal model, which means RR model can get a better fitting curve of particle size distribution than fractal model. The determined distribution parameter for RR model is very close to the reference value 1.32 from literature, while the fractal dimension of fractal model is much higher than the reference value 0.91 from literature.

The particle size distribution curve for each model is plotted in Figure 4 based on the manual and digital sieving data points. Most of the coal particles crushed by impact load are smaller 10 mm size as the mass of particles below 10 mm is over 60% of the total weight. It can be seen from Figure 4 that both fractal and RR model can well describe the particle size distribution while the curve of RR model demonstrate a better fitting result than that of fractal model.

Figure 4. Particle size distribution of coal determined by different methods.

As the distribution parameter has been determined based on particle size distribution, the other parameters for the calculation of crushing energy are W, $\mathit{\rho }$, a, K_R, K_K and K_B. The average weight of sample is 338 grams. The density of coal samples is 1.37 g/cm². Considering all particles as sphere shape (Cai and Xiong 2005), the shape factor a is 1.5. The value of crushing energy constant, for each calculation model e.g., K_R, K_K and K_B, for coal and rock has been determined by previous researcher, which is shown in Table 2.

Table 2. Value of K_R, K_K and K_B in literatures.

Constant	Material	Value	Reference
KR	Coal	100.7–288.0	Cai and Xiong (2005)
KK	Taconite	53.30–294.10	Zambrano (2002)
KB	Coal	110.00–138.00	Sahoo, De, and Meikap (2011)
KB	Coke	90.50	Deniz (2013)
	Bituminous Coal	174.00
	Lignite	193.90

Hence, according to the formula listed in Table 1, the fragmentation energy determined by each formula is calculated as listed in Table 3. It can be seen from the determined value that the selected energy-size relationship and particle size distribution model can significantly affect the calculated value of fragmentation energy. For formula 1 and 4 based on Rittinger theory, the fragmentation energy values are in similar range for fractal and RR distribution models. For Kick and Bond theory, the fragmentation energy tends to be underestimated with fractal model while it tends to be overestimated with RR model.

Table 3. Fragmentation energy determined by different formulas.

Formula	Energy-size relationships	PSD models	Fragmentation energy/J	Fragmentation energy rate/J·m^3
1	Rittinger Theory	Fractal	0.06–0.16	243.38–655.07
2	Kick Theory	Fractal	0.00–0.0002	0.00–0.79
3	Bond Theory	Fractal	0.00–0.01	11.20–23.99
4	Rittinger Theory	RR	0.05–0.15	217.58–585.63
5	Kick Theory	RR	0.00–0.24	0.00–963.96
6	Bond Theory	RR	2.89–3.13	11554.04–12532.18

The tested results can be compared with the previous research as well. As shown in Figure 5, the coal samples have been tested by Split Hopkinson Bar (SHPB) system (Z. Y. Liu et al. 2022) with different impact velocity and energy. Most of these tests were using the small disc sample to determine the tensile strength, fracture toughness or elastic modulus of coal samples subject to dynamic loads. Due to the different test nature such as sample size, impact velocity and test aims, some of the tests is not comparable to this research. The dissipated energy is also in a wide range in different literatures as illustrated in Figure 5. The tests done by Gong et al. (2021). have determined the dissipated energy rate per unit volume of coal samples with different angles between loading direction and bedding planes. The unit dissipated energy rate based on the tests results is plotted in Figure 6, which suggested that the dissipated energy rate for coal is averagely around 511 J/m³. The fragmentation energy rate was also calculated based on the tests results of this study, as listed in Table 3. Although the angle between impact loading direction and bedding plane can change the determined dissipated energy rate (Li et al. 2022), it can be seen from the Table 3 and Figure 6 that formula 1 and 4 are within the reasonable range of fragmentation calculation. It can be concluded that Rittinger Theory is more suitable for the fragmentation energy calculation for coal crushed by impact loads.

Figure 5. Impact tests of coal in literatures.

Figure 6. Unit dissipated energy rate of coal samples with different angles.

Conclusions

Although the relationship between the fragmentation energy and the particle size for single sized particles has been extensively researched over the last century. The fragmentation energy calculation model for coal fragmentations with coarse and wide size distribution has not been well established. In this research, the differential form of energy-size formula is proposed based on the analysis of size distribution and energy-size relationships of coal particles. The drop weight tests were conducted to validate the effectiveness of each formula. The following conclusions can be summarized based on the research:

The statistical mass-size curves of coal particles crushed by impact load were obtained based on manual sieving and digital image processing technique, which is used to validate the fractal and Rosin-Ramler (RR) model distribution curve of coal particles. It can be seen from Figure 4 that both fractal and RR model can well describe the particle size distribution while the curve of RR model demonstrate a better fitting result than that of fractal model. The fitting error of fractal model is very sensitive to fractal dimension while that of RR model is much less sensitive to distribution parameters. Besides, the optimal value of distribution parameters of RR model is very close to the reference value in literature.

The selected energy-size relationship and particle size distribution model can significantly affect the calculated value of fragmentation energy. The fragmentation energy rate per unit volume of coal is within a reasonable range compared with the impact tests of coal done by Split Hopkinson Bar (SHPB) system. For formula 1 and 4 based on Rittinger theory, the fragmentation energy values are in similar range for fractal and RR distribution models. For Kick and Bond theory, the fragmentation energy tends to be underestimated with fractal model while it tends to be overestimated with RR model. It can further support the communication assumption that crushing work is positively related to the area of generated new fracture surface.

It is worth to do more research of the impact crushing tests of coal samples with different sizes depends on the size requirement of coal crushing. Besides, it has been noted by SHPB tests that the impact velocity will affect fragmentation energy per unit volume as well, which can be further investigated.

Highlights

• Particle size distribution curve of impact crushed coal determined by manual and digital sieving.

• Fragmentation energy calculation model for coal fragmentations with coarse and wide size distribution.

• Impact crushing test of coal with designed impact energy input achieved by a drop weight system.

Acknowledgements

This research is supported by financial grants from Hunan Provincial Department of Public Education (23B0442).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the Hunan Provincial Department of Public Education [23B0442].

Appendix A

“Code for the digital image processing

clc

clear

rgb = imread(‘file name’);

I = rgb2gray(rgb);

gmag = imgradient(I);

L = watershed(gmag);

Lrgb = label2rgb(L);

se = strel(‘disk’,20);

Io = imopen(I,se);

Ie = imerode(I,se);

Iobr = imreconstruct(Ie,I);

Ioc = imclose(Io,se);

Iobrd = imdilate(Iobr,se);

Iobrcbr = imreconstruct(imcomplement(Iobrd),imcomplement(Iobr));

Iobrcbr = imcomplement(Iobrcbr);

fgm = imregionalmax(Iobrcbr);

I2 = labeloverlay(I,fgm);

se2 = strel(ones(5,5));

fgm2 = imclose(fgm,se2);

fgm3 = imerode(fgm2,se2);

fgm4 = bwareaopen(fgm3,20);

I3 = labeloverlay(I,fgm4);

bw = imbinarize(Iobrcbr);

A = 1-bw

Conn = 8;

[s1,s2]=size(A);

A=~bwmorph(A,‘majority’,10);

D=-bwdist(A,‘cityblock’);

Pr=zeros(s1,s2);

for I = 1:s1

for J = 1:s2

if A(I,J)= = 0 && D(I,J)~ = 0

Pr(I,J) = 1;

end

end

end

Pr=bwareaopen(Pr,9,Conn);

[Pr_L,Pr_n]=bwlabel(Pr,Conn);

s = regionprops(Pr_L, ‘Orientation’, ‘MajorAxisLength’, …

‘MinorAxisLength’, ‘Eccentricity’, ‘Centroid’, ‘Area’);

RGB=label2rgb(Pr_L,‘jet’, ‘w’, ‘shuffle’);

writetable(struct2table(s),‘test.xlsx’)