The microscopic characteristics of particle matter and image algorithm based on fractal theory

. The effects of ash and sulfur content on the morphology of particulate matter (PM) in diesel particle filter (DPF) were investigated with five different components of lubricants. The aggregate morphology of primary particles in diesel were analyzed using transmission electron microscopy (TEM). The fractal dimensions of carbon particles were calculated by box-counting method (BCM), differential box-counting method (DBC), relative differential box-counting method (RDBC) and MAD-based box counting method (MAD-DBC), and the results were compared. The results showed that the microstructure of PM developed from chain-like structure to agglomerate structure with the increase of sulfur and ash content in lubricating oil. The fractal dimension of carbon particles increased with the increase of sulfur and ash content. The SSE of RDBC fitting results was smaller, and the R-square is larger. MAD-DBC fitting results had stronger anti-noise interference performance.


Introduction
Particulate matter (PM) from diesel engines can cause significant damage to the environment and human health [1] .The European VI emission standard puts forward more stringent indicators for particle quality (PM) and particle quantity (PN) of diesel engines [2] .Diesel particulate emissions (PM) are 30-80 times higher than those of gasoline engines with the same displacement [3] .The morphology is one of the main characteristics of diesel particles, which affects the oxidation of particles and determines the concentration of active sites and activated surface area [4,5] .The particle morphology is affected by the quality of fuel and lubricating oil used in diesel engine [6] .The fractal dimension is an important parameter to characterize the particle morphology [7] .
There have been a lot of studies on the micro morphology of diesel particles, fractal dimension and its algorithm.Liati et al. [8] studied the change from primary particle size to nano size of PM by SEM and TEM.Wang et al. [9] studied the influence of injection pressure on particle size distribution and morphology of diesel engine during combustion.Zhang et al. [4] found that under the same injection strategy, increasing the intake pressure would accelerate the oxidation rate of particles in the combustion process, and then reduced the fractal dimension of particles in diesel engine.
Zhu et al. [10] found that the particle morphology of 1.7L diesel engine mainly presented aggregation chain structure, and its fractal dimension was calculated from 1.46 to 1.70 by using the fractal theory.Soewono et al. [11] used TEM to analyze the fractal dimension of 1.9L diesel engine particles and the results were 1.75-1.80. Lee et al. [12,13] found that the particles are mostly composed of amorphous and graphitized carbon elements.
Li et al. [14] proposed an RGB-based fractal dimension calculation method for color images.Ji et al. [15] proposed a rotating skeleton method to calculate the fractal dimension of twodimensional images, which reduces the influence of rotating structure on the fractal dimension.
At present, the influence of different operating conditions on the particle morphology of diesel engine has been widely studied.The calculation method of fractal dimension and image processing technology are also mature.However, there are few studies on the effects of different lubricants on particle morphology.It is also rare to apply different fractal dimension image processing algorithms to analyze the microstructure of diesel particles.Therefore, this paper explores the influence of different sulfur content and ash content of lubricating oil on the microscopic morphology of particles, and uses different fractal dimension image processing algorithms to characterize them.Finally, the advantages and disadvantages of different image processing algorithms are analyzed and compared.

Experimental method
Figure 1 shows the schematic diagram of the main components of the experimental system used in this study.The system is mainly composed of test diesel engine, dynamometer, engine control system, fuel system, exhaust gas analysis system and particle sampling system for collecting particles.The exhaust gas analysis system directly captureed the exhaust gas by drilling holes in the exhaust pipe.The particle sampling system picked up diesel particles by inserting a probe into a second small hole in the exhaust pipe.At the end of each test, the copper gate was removed from the probe and stored in a gate protection box for subsequent TEM analysis.In this study, five lubricants were tested under four different engine conditions.Considering the actual working performance of the engine, the following conditions were selected: the maximum torque speed was 1600rpm, and the maximum power speed was 2 E3S Web of Conferences 360, 01003 (2022)  https://doi.org/10.1051/e3sconf/202236001003VESEP2022 2400rpm, which means the selection of load was 50% and 100%.In order to eliminate the cross-contamination effect of different lubricants during the test, the previously tested lubricants should be completely discharged before the new experiment begins.

Experimental equipments
A 2.22L four-stroke light diesel engine was used in the test.Specifications for transmission electron microscopes used to analyze particle morphology were listed in Table1.

Fuel and lubricating oil characteristics
Five lubricants were used in this study, and their specifications are shown in Table 2. Sulphur and ash content of base lubricants is low enough to meet ACEA C1 standards.Other oils are made by adding sulfur-containing additives to the base oils of high-sulfur sm-oil and SH-oil, and calcium sulfonate to the high-ash am-oil and AH-oil.In order to minimize the impact of fuel quality, ultra-low sulfur fuels with sulfur content less than 10ppm were used in this study.
The main specifications of the experimental fuel are listed in Table 3.

Fractal theory
In the definition of fractal dimension, Haussdorff, defined Haussdorff dimension from the perspective of measurement.Its definition is as follows: where r is the metric scale.The physical meaning of Haussdorff dimension is that for an object with a definite dimension, a definite value can be obtained when a measure equal to its dimension is used to measure it, and the result is zero when a measure larger than its dimension is used to measure it.Otherwise, the result is infinite.
The most widely used fractal is box dimension, which is defined as follows: Assuming A was any non-empty bounded subset of space, any r which is greater than zero, Nr(A) represents the minimum number of n-dimensional cubes of side length r needed to cover A. If exist a d, when r 0 → , There is the following relationship: The box counting dimension Db is defines as follows: ( )

Image preprocessing
Before calculating the fractal dimension of particles by TEM image, the original image is transformed into grayscale image.The RGB parameters of the image are linearly combined and weighted average.After the gray image is obtained, the gray threshold segmentation method is used to transform the image into binary image.Finally, image boundary is extracted based on binary graph.As shown in Figure 2.

Fig. 2. Image preprocessing rendering.
There are the following methods in the process of image binarization: (1) Fixed threshold method: read the gray value of each pixel of the image and set the threshold.The pixel whose gray value exceeds the threshold is white.Otherwise, the pixel is black.
(2) Double fixed threshold method: on the basis of the fixed threshold method, two thresholds are selected for the same gray scale image.If the gray level of a pixel falls between the two thresholds, it is white pixel; otherwise, it is black pixel.
(3) The respective pixel threshold method: the gray scale map is divided into different regions, and the respective gray scale threshold is set for each region.
Canny operator is mainly used to extract the boundary of the study area when boundary graph is extracted from binary graph.Canny operator has the following three important characteristics: (1) low error rate; (2) High position accuracy; (3) Single response criteria.

Box-counting Fractal Dimension (BCM)
Consider a binary graph as a plane in 2 -dimensional space: z = f(x,y), Where x and y correspond to the position of each pixel of the image respectively, and z corresponds to the gray value of the image pixel.The image size is set as M×N, and the image plane is divided into multiple grids with the size of R × R. The grid coordinates are set as (i,j), ( ) where, (i,j) is the coordinate of grid grid, nr(i,j) is the number of covered boxes of a single grid, and Zmax(i,j) is the maximum gray value of pixels in a single grid.Let Cl = [M/r], rw = [N/r], where [] is rounded up, and the total number of covered boxes is: where Nr is the total number of boxes covering the image.By changing the box scale R, a set of (-lnR, lnNr) sequences can be obtained, and the slope of which is the fractal dimension of the image.The flow chart of BCM algorithm is shown in Figure 3.

Other fractal dimension algorithm
With the research and development of image processing counting, various fractal dimension calculation methods have emerged, such as difference box counting algorithm (DBC), relative difference box counting algorithm (RDBC), MAD difference box counting method (MAD-DBC), RGB fractal dimension algorithm and rotating skeleton method [15] .The block diagrams of DBC, RDBC and MAD-DBC algorithms are shown in Figure 4.

Differential box counting (DBC)
The basic idea of differential box counting (DBC) method is to determine fractal dimension by calculating the number of boxes required to cover the gray scale surface of an image.For an image with an area of M×M, if it is divided into grids of size s×s, then R = S /M.The pixel of the grayscale image is regarded as a coordinate (x,y,z), where (x,y) is the position of the pixel point and z is the grayscale value.It can be considered that a series of boxes with volume of S × S × H are stacked on the image, and the box height H can be calculated by the total gray level of the image G: [G/h] = [M/s].If the minimum gray value and the maximum gray value in the (i,j) grid of the image fall in the l and U small box respectively, the number of boxes required to cover the (i,j) region nr(i,j) is: The total number of boxes of statistical images Nr is:

Relative differential box counting (RDBC)
The relative difference box dimension method (RDBC) uses the gray scale standard deviation of pixels in the grid to replace the difference between the maximum and minimum gray scale to calculate the number of boxes occupied by the gray scale surface of the image in the grid.
Specifically, if the scale scaling ratio is given as r and the standard deviation of gray scale of pixels in the (i,j) grid of the image is set as σr(i, j), the number of boxes nr(I,j) can be calculated by the following formula:

MAD differential box counting (MAD-RDBC)
Since the median deviation (MAD) is robust to salt and pepper noise, the median absolute deviation (MAD) of grey order is used to replace the grey order standard deviation σr(i, j) in the grid.In general, the median absolute deviation (MAD) is calculated using the following formula: where med(ui,j) represents the median value of image pixel value in grid (i,j).If the scale scaling ratio r is given and the median absolute deviation of gray order pixels in the (i,j) grid of the image is ρr(i,j), then the number of boxes nr(i,j)can be calculated by the following formula:

Image processing algorithm evaluation indicators
Different algorithms get different results for the calculation of fractal dimension, so the results need to be evaluated to get the relatively optimal algorithm.
In essence, the acquisition of fractal dimension is to fit some data points.In this study, the evaluation parameters of linear fitting of data points are used as evaluation indexes to measure the merits of the algorithm.The selected indexes are sum variance (SSE) and determination coefficient (R-square).SSE (sum of squares of variance and error): This statistical parameter calculates that the squares and SSE of the errors of the corresponding points of the fitted data and the original data are closer to 0, indicating that the model selection and fitting are better and the data prediction is more successful.The normal value range of the determined coefficient is [0,1], and the closer it is to 1, the stronger the explanatory ability of the variable is.
And R-square (determining coefficient) is defined as follows: SSR R-square SST = (14)   SSR formula is as follows: As can be seen from Figure 5, the particle is composed of dozens of spherical primary particles, which are bonded into a chain structure due to electrostatic interaction.With the increase of sulfur content and ash content, the microstructure of particles shows a trend of transformation from chain structure to more complex and disordered agglomeration structure [6] .Sulfuric acid formed by sulfur leads to agglomeration in which inorganic elements can attach to the original particles [17] , increasing the possibility of overlap and collision between the host particles.Ash content can also enhance the agglomeration and agglomeration of these particles, resulting in the difference of particle morphology.
High sulfur content in lubricating oil will reduce the oxidation activity of diesel PM.Sulfur promotes the formation of SO3, which in turn promotes the formation of complexes with other elements.Sulfate can occupy active sites on the surface of particles, but cannot be oxidized, occupying available particle micropores [18] .
Ash in lubricating oil will increase the content of inorganic salt in diesel engine exhaust.Unlike soot, this salt is not easily oxidized and can be attached to the outer shell of the original particle.The higher the ash content in the lubricating oil, the oxidation of particles will also be promoted, which to a certain extent leads to the reduction of particle size, and then leads to more complex particle structure [19] .

Particle morphology analysis based on fractal dimension
For different lubricating oils, the analysis results based on BCM calculation theory are shown in FIG. 6.In this study, the values of the fractal dimension of particles ranged from 1.522 to 1.646.The high fractal dimension indicates that the particle structure is dense, which reduces the transfer of oxygen to the main particle gap and results in a significant decrease in the oxidation activity of particles.The absolute value of fractal dimension is affected by many conditions in the calculation process, including image resolution, size, filling degree of key images in the picture, image noise and algorithm selection.Therefore, the absolute value of fractal dimension obtained by different algorithms for images with different resolutions and different regions is not of great comparative significance.But its relative value and variation trend have certain reference significance.
For different lubricating oils, fractal dimension analysis results based on DBC, RDBC and MAD-DBC calculation theory are shown in Figure 7~9.It can be found that when calculating the fractal dimension of particles with different image processing algorithms, although there is a slight difference in the absolute value of the fractal dimension, the relative value of the fractal dimension keeps the same trend when representing the influence of  It can be seen from the fractal dimension values of the generated particles of four lubricating oils with different sulfur content and ash content that when sulfur content increases from 0.182% to 0.583%, the fractal dimension of particles increases by 1.2%~4.6%.When the sulfur content increases to 1.060%, the fractal dimension of particles increases by 3.4%-8.6%.When ash content increased from 0.48% to 1.21%, the fractal dimension of particles increased by 1.0%~3.6%,and when ash content increased to 1.99%, the fractal dimension of particles increased by 2.9%~6.4%.The oil with high sulfur content and high ash content increases the fractal dimension.
Higher sulfur and ash content can lead to higher concentrations of volatile substances.The lubricating oil with higher sulfur and ash content allows the increase of primary particles on the shell forming amorphous materials, which increases the probability of adhesion between primary particles, leading to greater overlap and point aggregation of compactness, resulting in an increase in fractal dimension of particles.

The results of different fractal dimension algorithms are compared
In this study, the sum variance (SSE) and determination coefficient (R-square) are used to characterize the advantages and disadvantages of different fractal dimension algorithms.The result is shown in Figure 10.In terms of SSE, RDBC < MAD-DBC < DBC < BCM.And in terms of R-square, RDBC > MAD-DBC > DBC > BCM.RDBC and MAD-DBC algorithms have great advantages both in the error of fitting points and in the interpretation of data variation trends.
The influence of sulfur content on the calculation results is shown in Figure 11.With the increase of sulfur content in lubricating oil, BCM, DBC and RDBC algorithms all have the trend of SSE rising and R-Square decreasing.This shows that these three algorithms have poor anti-interference to the noise that affects the standard deviation of the gray order.At the same time, MAD-DBC SSE and R-Square are more stable, less sensitive to Gaussian noise, has good noise resistance.The influence of ash content on the calculation results is shown in Figure 12.With the increase of the ash content of lubricating oil, the results of each algorithm have no significant change rule.The reason is that there is a great difference in microscopic characteristics between sulfate ash and particles caused by sulfur content in lubricating oil, which makes the complexity and noise content of the image increase significantly.As a result, the quality of the calculation results of each algorithm has declined.However, the micro characteristics of ash have a high similarity with the particles, which does not increase the noise content of the image.In conclusion, RDBC algorithm has the highest quality when calculating fractal dimension for more regular images.However, the quality of mad-DBC algorithm is more stable when calculating composite component graphs.

Conclusion
(1) The sulfur in the lubricating oil forms sulfuric acid in the waste gas, which leads to the inorganic elements attached to the original particles and agglomeration, resulting in a more disorderly microstructure of the particles.
(2) The increase of ash content can also enhance the agglomeration and agglomeration of particles, which makes the particles develop from chain to agglomeration structure.
(3) For the research prototype in this paper, when the sulfur content increases from 0.182% to 0.583%, the fractal dimension of particles increases by 1.2%~4.6%;When the sulfur content increases to 1.060%, the fractal dimension of particles increases by 3.4%~8.6%.
(4) For the research prototype in this paper, when the ash content increases from 0.48% to 1.21%, the fractal dimension of particles increases by 1.0%~3.6%;when the ash content increases to 1.99%, the fractal dimension of particles increases by 2.9%~6.4%.
(5) When the fractal dimension of the image with low noise is calculated, the RDBC algorithm has the best fitting result.However, the fitting results of mad-DBC algorithm have stronger anti-interference performance when processing noisy graphics.
: Determination coefficient represents the quality of a fit through changes in data.

1 Fig. 5 .
Figure5shows TEM micrographs of particles extracted from diesel engine exhaust when lubricating the engine with base oil, sm-oil, sh-oil, am-oil and ah-oil and running at 1600rpm and 100% load.In particular, the low-resolution TEM microscopic images of particle agglomerations obtained by magnification of 40,000 times.

Fig. 10 .
Fig. 10.Comparison of the average value of fractal dimension calculation results of each algorithm.

Fig. 11 .
Fig. 11.Comparison of fractal dimension calculation results of different sulfur content in different algorithms.

Fig. 12 .
Fig. 12.Comparison of fractal dimension calculation results of different ash content in different algorithms.

Table 1 .
Technical indexes of TEM.

Table 2 .
Specifications of lubricating oil.

Table 3 .
Specifications of fuel.