Identification method of fly ash spherical particles

Abstract

The invention provides a fly ash spherical particle identification method, which comprises the following steps: preparing a fly ash sample, and scanning by using a microscope to obtain a sample image; carrying out image preprocessing on the sample image, wherein the image preprocessing comprises image cutting, filtering noise reduction and image enhancement; using the training model to identify particle features of the sample image, and classifying and marking spherical particles and non-spherical particles; respectively calculating the proportions of the spherical particle area and the non-spherical particle area in the total particle area; the identification result of the fly ash spherical particles obtained through the steps is used for identifying the ground fly ash. According to the method, the training model is utilized to learn the characteristics of the fly ash particles with different shapes and sizes, so that the training model has generalization ability, and automatic and accurate identification and classification of spherical particles and non-spherical particles of the fly ash are realized; and judging and identifying the ground fly ash according to the identification result of the fly ash spherical particles, namely the proportion of the spherical particle area in the whole particle area.

Description

Technical Field

[0001] The present invention relates to the field of fly ash identification, and particularly to a method for identifying spherical particles of fly ash. Background Art

[0002] Fly ash is the fine ash particles generated during the combustion process in coal-fired power plants, etc. These particles are very small and mostly spherical. Due to their good physical and chemical properties, fly ash usually has excellent properties such as pozzolanic effect, filling effect, and ball bearing effect after being incorporated into concrete, thereby achieving the effect of improving the performance of concrete and has become one of the widely used admixtures in concrete. When fly ash is used as a mineral admixture, the particle size distribution, morphology, and surface characteristics of fly ash particles will have a great impact on the water consumption and workability of fresh concrete and the performance development of hardened concrete. In GB1596 "Fly Ash Used in Cement and Concrete", the main detection items include water demand ratio, fineness (residue on 45μm square hole sieve), loss on ignition, etc., and no requirements are made for the microscopic morphology of fly ash. As-received fly ash mainly presents as spherical or approximately spherical particles, with different particle sizes. Some smaller spherical particles are unevenly adhered to the surface of larger spherical particles. The spherical particles and smooth surface can improve the fluidity of the concrete mixture, reduce water consumption, and improve the workability of concrete. Grinding is a common method for processing fly ash at present. The as-received fly ash is ground to improve its performance. Through grinding treatment, the fineness of fly ash and its filling effect in concrete can be increased, thereby enhancing some properties of concrete. However, at the same time, there are also fly ashes that are passed off as good ones and over-ground. If fly ash is over-ground, the spherical particles in fly ash will be severely damaged. The particle refinement and structural damage result in a low proportion of spherical particles, many non-spherical particles with different shapes, such as hemispherical or angular particles, which affect its work performance in concrete.

[0003] Chinese patent CN114778585A discloses a method for distinguishing genuine fly ash from fake fly ash disguised as solid waste, and records that the method includes the following steps: a. taking a small amount of dried ash sample to be tested and spreading it evenly on the conductive tape of the sample stage to obtain a single layer of powder material; b. placing the sample stage into the sample chamber of a scanning electron microscope, taking at least 5 fields of view within each field of view, and obtaining a clear image of the ash particles; c. converting the image into a gray image, and binarizing it to measure the particle size, area and roundness of the ash particles in the binary image; d. using data processing software to calculate the total area value of particles with a roundness of more than 0.8 and the total area value of particles with a roundness of more than 0.5, and dividing the two to obtain the judgment criterion SR>0.8 / SR>0.5 value: when it is higher than 5%, it is genuine fly ash; when it is between 2% and 5%, it is inferior fly ash mixed with some fake ash; when it is lower than 2%, it is fake fly ash disguised as solid waste. This patent uses an electron microscope and image analysis software to obtain the required parameters to quantitatively distinguish between real and fake fly ash. However, this method is not suitable for situations where the particles are of various shapes or are agglomerated and not dispersed. It will make image recognition more complicated and result in inaccurate identification of particle roundness to judge the authenticity of fly ash. Summary of the invention

[0004] The main purpose of the present invention is to provide a method for identifying spherical particles of fly ash, so as to solve the problems that it is difficult to accurately identify spherical particles and non-spherical particles, the shape characteristics of spherical particles are not easy to judge, and there are deviations in the judgment of ground fly ash.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for identifying spherical particles of fly ash, the method comprising the following steps:

[0006] S1. Prepare fly ash samples and obtain sample images by scanning with a microscope;

[0007] S2, performing image preprocessing on the sample images, including image cropping, filtering noise reduction and image enhancement;

[0008] S3, using the training model to identify the particle features of the sample image, and classify and mark spherical particles and non-spherical particles;

[0009] S4, respectively calculating the proportion of the spherical particle area and the non-spherical particle area in the total particle area;

[0010] The above steps provide an identification result of spherical fly ash particles, which is used to identify ground fly ash.

[0011] In a preferred embodiment, step S1 comprises the following steps:

[0012] S11, randomly sampling from the fly ash to be identified, and sieving to obtain a fly ash sample;

[0013] S12. Add pure water and a surfactant to the mixed fly ash sample, and add gelatin and mix evenly to obtain a gel-like fly ash sample;

[0014] S13. The gel-like fly ash sample is dried and prepared into a fly ash sample piece, which is fixed on a conductive tape.

[0015] In a preferred embodiment, in step S12, a fluorescent agent for showing the particle characteristic profile of fly ash is also added.

[0016] In a preferred embodiment, in step S13, a conductive film for increasing conductivity is provided on the surface of the fly ash sample piece.

[0017] In a preferred embodiment, step S2 includes the following steps:

[0018] S21. Initially observe the sample piece image, remove the edge blank area of the sample piece image, and crop the sample piece image to the same size;

[0019] S22. Perform filtering and noise reduction on the cropped sample piece image, and remove the noise in the sample piece image by using the spatial domain and gray value range of the sample piece image;

[0020] S23. Divide the noise-reduced sample piece image into several sub-regions for histogram equalization, and interpolate and merge the equalization results of each sub-region.

[0021] In a preferred embodiment, step S3 includes the following steps:

[0022] S31. Collect fly ash images including spherical particles and non-spherical particles as training data;

[0023] S32. Through a pre-trained model for feature extraction, use the region proposal network, classifier and regressor for joint training to obtain a training model;

[0024] S33. Use the training model to perform model inference on the sample piece image, and identify the spherical particles and non-spherical particles in the sample piece image.

[0025] In a preferred embodiment, data augmentation is performed on the training data, including rotation, scaling, translation and flipping, so that the training data includes particle characteristics of different sizes and different shapes.

[0026] In a preferred embodiment, the method further includes the following step: S5. Calculate the bluntness of the spherical particles according to the spherical particles in the sample piece image to verify the identified spherical particles.

[0027] In a preferred embodiment, the bluntness is the ratio of the sum of the diameters of the inscribed circles at the protruding parts of the particle contour to the diameter of the largest inscribed circle, which is used to accurately reflect the particle shape characteristics of the particles.

[0028] The present invention provides a method for identifying spherical particles of fly ash, which comprises the following steps: preparing a fly ash sample slice, and obtaining a sample slice image by microscopic scanning; performing image preprocessing on the sample slice image, including image cropping, filtering and noise reduction, and image enhancement; using a trained model to identify the particle features of the sample slice image, and classifying and labeling spherical particles and non-spherical particles; respectively calculating the proportions of the areas of spherical particles and non-spherical particles in the total particle area; obtaining the identification result of spherical particles of fly ash through the above steps to identify ground fly ash. This method uses a trained model to learn the particle features of fly ash with different shapes and sizes, enabling the trained model to have generalization ability, and realizing automatic and accurate identification and classification of spherical particles and non-spherical particles of fly ash; according to the identification result of spherical particles of fly ash, that is, the proportion of the area of spherical particles in the total particle area, ground fly ash is determined and identified. Preferably, if the proportion of the area of spherical particles in the fly ash sample slice image is greater than 60%, it is identified as high-quality fly ash; if the proportion of the area of spherical particles in the fly ash sample slice image is less than 20%, it is identified as ground fly ash. Description of the Drawings

[0029] The present invention will be further described below in conjunction with the drawings and embodiments:

[0030] Figure 1 is the flowchart of the method of the present invention;

[0031] Figure 2 is the original fly ash sample slice image of Embodiment 3 of the present invention;

[0032] Figure 3 is the sample slice image of spherical particles and non-spherical particles after the original fly ash in Embodiment 3 is ball milled and ground for 0.5 h;

[0033] Figure 4 is the sample slice image of spherical particles and non-spherical particles after the original fly ash in Embodiment 3 is ball milled and ground for 2.0 h;

[0034] Figure 5 is the partial frame selection diagram of the identification of spherical particles and non-spherical particles of the original fly ash in Embodiment 3;

[0035] Figure 6 is the partial frame selection diagram of the identification of spherical particles and non-spherical particles after ball milling and grinding for 0.5 h in Embodiment 3;

[0036] Figure 7 is the partial frame selection diagram of the identification of spherical particles and non-spherical particles after ball milling and grinding for 2.0 h in Embodiment 3. Detailed Embodiments

[0037] Embodiment 1:

[0038] As Figure 1As shown in the figure, a method for identifying spherical particles of fly ash includes the following steps: S1. Prepare a fly ash sample slice, place the sample slice on the objective stage of a microscope, ensure that the objective stage is adapted to the vacuum environment inside the microscope, start the microscope and adjust the working parameters, and use the microscope to scan to obtain a sample slice image;

[0039] S2. Perform image preprocessing on the obtained sample slice image, including image cropping, filtering and noise reduction, and image enhancement, to improve the quality of the sample slice image and help improve the subsequent analysis and recognition effect;

[0040] S3. Classify and identify the particle characteristics of the sample slice image through a trained model, and mark spherical particles and non-spherical particles respectively;

[0041] S4. Calculate the proportions of the areas of spherical particles and non-spherical particles in the total particle area respectively, that is, obtain the content proportion of spherical particles of fly ash; through the above steps, the identification result of spherical particles of fly ash is obtained, which is used to identify ground fly ash.

[0042] According to this solution, a microscope is used to observe and scan a fly ash sample slice to obtain a high-resolution sample slice image. After image preprocessing, a trained model is used to learn the particle characteristics of fly ash with different shapes and sizes, so that the trained model has generalization ability, realizing automatic and accurate identification and classification of spherical particles and non-spherical particles of fly ash; according to the identification result of spherical particles of fly ash, that is, the proportion of the area of spherical particles in the total particle area, ground fly ash is judged and identified. Preferably, if the proportion of the area of spherical particles in the fly ash sample slice image is greater than 60%, it is identified as high-quality fly ash; if the proportion of the area of spherical particles in the fly ash sample slice image is less than 20%, it is identified as ground fly ash.

[0043] In the preferred solution, step S1 includes the following steps:

[0044] S11. Randomly sample from the fly ash to be identified, and obtain a fly ash sample through screening with a 45um sieve to avoid too large differences in the particle sizes of fly ash and facilitate subsequent analysis and identification of particle characteristics;

[0045] S12. Add pure water and a surfactant to mix the fly ash sample, and add gelatin and mix evenly to obtain a gel-like fly ash sample; preferably, add pure water with a volume 5-10 times that of the fly ash sample for dilution, and add a surfactant with a volume of 0.1%-1% of the fly ash sample for mixing;

[0046] S13. After the gel-like fly ash sample is dried at 85°C, it is prepared into a fly ash sample slice and fixed on a conductive tape. According to this solution, it can ensure that the particles of the fly ash sample slice are evenly dispersed, avoid particle agglomeration, and make the fly ash particles observed by the microscope in a dispersed or single-layer state, which is convenient for identifying spherical particles.

[0047] In the preferred solution, in step S12, a fluorescent agent for displaying the particle characteristic contour of fly ash is further added. With this solution, the contour characteristics of the particles can be better displayed, further ensuring the correctness of the spherical particle recognition result. Preferably, a fluorescent agent with a volume of 0.05 - 0.2% of the fly ash sample is added.

[0048] In the preferred solution, in step S13, a conductive film for increasing conductivity is provided on the surface of the fly ash sample piece. With this solution, the surface of the fly ash sample piece is evenly sprayed with a spraying device to ensure that the surface of the fly ash sample piece is completely covered with the conductive film, further enhancing the conductivity of the fly ash sample piece and improving the quality of the sample piece image scanned by the microscope. Preferably, the thickness of the conductive film is 10 - 30 nm.

[0049] In the preferred solution, step S2 includes the following steps:

[0050] S21. Initially observe the sample piece image, remove the edge blank area of the sample piece image, and crop the sample piece image to the same size. By cropping the image, the redundant edge blank parts are removed, the area with more particle distribution is retained, and a unified image size is set, facilitating subsequent analysis and image processing.

[0051] S22. Perform filtering and noise reduction on the cropped sample piece image, and remove the noise in the sample piece image by using the spatial domain and gray value domain of the sample piece image. Bilateral filtering is used for filtering and noise reduction. Combining the spatial domain and gray value domain can not only remove the noise in the sample piece image but also retain the detailed information of the particle contour edges in the sample piece image. For each pixel of the cropped sample piece image, use bilateral filtering to define a filtering window with the current pixel as the center; for each pixel in the filtering window, calculate its spatial domain weight and gray value domain weight, and multiply them to obtain the total weight; multiply the gray values of all pixels in the filtering window by their corresponding total weights, sum them up, and divide by the sum of all total weights to obtain the filtered pixel value, thereby obtaining the sample piece image after filtering and noise reduction.

[0052] S23. Divide the noise-reduced sample piece image into several sub-regions for histogram equalization, and interpolate and merge the equalization results of each sub-region to obtain the sample piece image after image enhancement. By calculating the gray histogram of each sub-region, calculating the cumulative distribution function according to the histogram, and mapping the original gray value to a new gray value, histogram equalization is realized. The interpolation and merging adopt bilinear interpolation or cubic spline interpolation, that is, interpolate the equalization results of adjacent sub-regions to make the transition between different sub-regions smoother, so as to enhance the contrast between the background and particle characteristics of the sample piece image.

[0053] With this solution, preprocessing of fly ash sample images, including cropping, noise reduction, and contrast enhancement, can effectively remove noise in the sample images, enhance the contrast of the sample images, and provide a better basis for subsequent particle recognition and analysis.

[0054] In the preferred solution, step S3 includes the following steps:

[0055] S31. Collect fly ash images including spherical particles and non-spherical particles as training data. Among the collected fly ash images, there are fly ashes of different types and batches to make the training data diverse and ensure the generalization ability of the training model; the particles in the fly ash images are clearly visible, and each particle has been classified and marked as spherical or non-spherical characteristics; the fly ash images are used as training data to train the model to learn the characteristics of fly ash particles.

[0056] S32. Through a pre-trained model for feature extraction, use the region proposal network, classifier, and regressor for joint training to obtain a training model. The Faster R-CNN model is adopted. Faster R-CNN is a two-stage object detection model. First, it generates candidate regions, and then classifies and performs bounding box regression on the candidate regions. Through the convolutional neural network CNN feature extractor, extract the feature map in the training data; the input image is I, and after passing through the CNN, the feature map F is obtained, expressed as F = CNN(I). Use the region proposal network RPN to slide a window on the feature map F, and each window corresponds to generating a candidate region; at the position of each window, a plurality of bounding boxes of different sizes and aspect ratios are preset, and the classifier is used to judge whether each bounding box contains particle features, aiming to distinguish particle features from the background; use the regressor to adjust the position and size of the bounding box to predict the bounding box of the candidate region. Perform region of interest pooling on each candidate region to map candidate regions R of different sizes to a fixed-size feature map F RoI = RoIPooling(F, R). Map the feature map F RoI to the convolutional layer and fully connected layer of the Faster R-CNN model for particle feature classification and bounding box regression; use the classifier to distinguish spherical particle features from non-spherical particle features, and use the regressor to precisely adjust the border position of the particle features to accurately locate the particle features.

[0057] Jointly train the region proposal network RPN, classifier, and regressor. The total loss function is L = L cls + λL reg ; where L cls is the classification loss, and the cross-entropy loss function is adopted; L reg is the regression loss, and the smooth L1 loss function is adopted; λ is the weight coefficient. Use the stochastic gradient descent optimizer to update the model parameters to minimize the loss function and obtain the optimized training model.

[0058] S33. Use the trained model to perform model inference on the sample image to identify the spherical particles and non-spherical particles in the sample image. Input the sample image into the trained model, that is, use the optimized trained model parameters to identify the actual sample image, and obtain the classification results of the spherical particles and non-spherical particles in the sample image, so as to achieve the purpose of efficient and accurate automatic identification.

[0059] With this solution, by collecting diverse training data, using Faster R-CNN for fly ash particle classification and recognition, and using pre-trained models for transfer learning and joint training, a model for identifying spherical particles and non-spherical particles in fly ash images is obtained, improving the accuracy and efficiency of identifying spherical particles, and providing a basis for subsequent analysis and applications.

[0060] In the preferred solution, data augmentation is performed on the training data, including rotation, scaling, translation, and flipping, so that the training data includes particle features of different sizes and shapes. With this solution, data augmentation can increase the diversity of the training data and further improve the generalization ability of the trained model.

[0061] Example 2:

[0062] Further illustrated in combination with Example 1, as Figure 1 shown, in the preferred solution, the method further includes the following steps: S5. Calculate the bluntness of the spherical particles based on the spherical particles in the sample image to verify the identified spherical particles. With this solution, according to the spherical particles in the sample image identified in step S3, calculate the bluntness of each spherical particle. If the bluntness of the spherical particle approaches 1, that is, the spherical particle is both round and smooth, it is verified as a spherical particle again; if the bluntness of the spherical particle is much less than 1, that is, the spherical particle is sharp and uneven, the spherical particle is verified as a non-spherical particle. According to the bluntness of each spherical particle, calculate the average bluntness of all the spherical particles in the sample image. If the average bluntness of the spherical particles is greater than 70%, the recognition result of the fly ash spherical particles is accurate, thus verifying that the recognition result of the fly ash is accurate; if the average bluntness of the spherical particles is less than 70%, the recognition result of the fly ash spherical particles is inaccurate, and step S3 is performed again to re-identify and classify the spherical particles.

[0063] In the preferred solution, the bluntness is the ratio of the sum of the diameters of the inscribed circles at the protruding parts of the particle contour to the diameter of the largest inscribed circle, which is used to accurately reflect the particle shape characteristics. With this solution, the bluntness is d i is the diameter of the inscribed circle at each protruding part, D n is the diameter of the largest inscribed circle of the particle, and N is the number of protruding parts. If the bluntness is 1, it is a spherical particle with a regular round shape.

[0064] Example 3:

[0065] Further illustrated in combination with Examples 1 and 2, as Figures 2 - 7 shown, the original fly ash is collected in this example, and the original fly ash is ground by a ball mill to obtain fly ash ground for 0.5 h and fly ash ground for 2.0 h by ball milling. As Figures 2 - 4 shown, the above-mentioned step S1 is respectively performed on the collected original fly ash, fly ash ground for 0.5 h by ball milling, and fly ash ground for 2.0 h by ball milling, and the sample images are obtained by scanning with a microscope respectively.

[0066] Using image processing software, image preprocessing is performed on the obtained sample images, spherical particles and non-spherical particles in each sample image are identified through a training model, and the spherical particles and non-spherical particles are framed and marked. As Figures 5 - 7 shown, some of the spherical particles are white frames and some of the non-spherical particles are black frames. The proportion of the area of spherical particles and non-spherical particles in the total particle area is calculated respectively. If the proportion of the area of spherical particles is greater than 60%, then this fly ash is identified as high-quality fly ash; if the proportion of the area of spherical particles is less than 20%, then this fly ash is identified as ground fly ash.

[0067] According to the identified spherical particles, the bluntness of each spherical particle is calculated to verify whether the identification of the spherical particles is accurate. If the average bluntness of all spherical particles is less than 70%, then the identification of spherical particles in step S3 is inaccurate, and step S3 is performed again to identify and classify and mark the spherical particles; if the average bluntness of all spherical particles is greater than 70%, then the identification of spherical particles in step S3 is accurate. The data of the area proportion, average bluntness and water demand ratio of spherical particles of the original fly ash, fly ash ground for 0.5 h by ball milling, and fly ash ground for 2.0 h by ball milling are calculated respectively, as shown in Table 1.

[0068] Table 1 Area proportion, average bluntness and water demand ratio of spherical particles of fly ash

[0069] Category As - received fly ash Ball - milled and ground for 0.5 h Ball - milled and ground for 2.0 h Area proportion (%) 61.2 20.1 8.9 Average bluntness (%) 89.7 77.5 72.3 Water demand ratio (%) 92.5 96.2 104.1

[0070] As can be seen from Table 1, the spherical particle content of the original fly ash identified by the present invention is 61.2%. After the original fly ash is ground for 0.5 h by ball milling, the spherical particle content is 20.1%. After ball milling for 2.0 h, the spherical particle content is only 8.9%, and the number of its spherical particles decreases significantly. Calculate the average bluntness of all the identified spherical particles. The average bluntness of the spherical particles of the original fly ash is 89.7%. After the original fly ash is ground for 0.5 h by ball milling, the average bluntness of the spherical particles is 77.5%. After ball milling for 2.0 h, the average bluntness of the spherical particles is 72.3%. The average bluntness of its spherical particles is greater than 70%, verifying that the identification of the spherical particles is correct. At the same time, the water demand ratio of the fly ash in the examples is detected according to "Fly Ash Used in Cement and Concrete" (GB / T 1596-2005). The water demand ratio of the original fly ash is detected to be 92.5%. After the original fly ash is ground for 0.5 h by ball milling, the water demand ratio is 96.2%. After ball milling for 2.0 h, the water demand ratio is 104.1%, indicating that with the destruction of spherical particles, the water demand ratio of fly ash increases significantly, thus affecting its workability in concrete.

[0071] The above embodiments are only the preferred technical solutions of the present invention and should not be regarded as limitations on the present invention. The protection scope of the present invention should be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, the equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A method for identifying spherical fly ash particles, characterized in that: The method comprises the following steps: S1. Prepare fly ash samples and obtain sample images by scanning with a microscope; S2, performing image preprocessing on the sample images, including image cropping, filtering noise reduction and image enhancement; S3, using the training model to identify the particle features of the sample image, and classify and mark spherical particles and non-spherical particles; S4, respectively calculating the proportion of the spherical particle area and the non-spherical particle area in the total particle area; The above steps provide an identification result of spherical fly ash particles, which is used to identify ground fly ash.

2. The method for identifying spherical fly ash particles according to claim 1, characterized in that: Step S1 includes the following steps: S11, randomly sampling from the fly ash to be identified, and sieving to obtain a fly ash sample; S12, adding purified water and a surfactant to mix the fly ash sample, and adding gelatin to evenly mix to obtain a gel-like fly ash sample; S13. The gel-like fly ash sample is dried and prepared into a fly ash sample sheet, which is fixed on a conductive tape.

3. The method for identifying spherical fly ash particles according to claim 2, characterized in that: In step S12, a fluorescent agent is added to display the characteristic particle outline of the fly ash.

4. The method for identifying spherical fly ash particles according to claim 2, characterized in that: In step S13, a conductive film is provided on the surface of the fly ash sample to increase conductivity.

5. The method for identifying spherical fly ash particles according to claim 1, characterized in that: Step S2 includes the following steps: S21, preliminarily observing the sample images, removing the blank areas at the edges of the sample images, and cropping the sample images to the same size; S22, filtering and denoising the cropped sample image, using the spatial domain and grayscale value domain of the sample image to remove noise in the sample image; S23, dividing the sample image after noise reduction into several sub-regions for histogram equalization, and interpolating and merging the equalization results of each sub-region.

6. The method for identifying spherical fly ash particles according to claim 1, characterized in that: Step S3 includes the following steps: S31, collecting fly ash images including spherical particles and non-spherical particles as training data; S32, using the pre-trained model for feature extraction, and jointly training the region proposal network, the classifier, and the regressor to obtain a training model; S33. Perform model inference on the sample image using the training model to identify spherical particles and non-spherical particles in the sample image.

7. A method for identifying spherical fly ash particles according to claim 6, characterized in that: The training data is augmented by rotation, scaling, translation, and flipping, so that the training data includes particle features of different sizes and shapes.

8. The method for identifying spherical fly ash particles according to claim 1, characterized in that: The method further comprises the following steps: S5, calculating the bluntness of the spherical particles according to the spherical particles in the sample image, so as to verify the identified spherical particles.

9. A method for identifying spherical fly ash particles according to claim 8, characterized in that: The bluntness is the ratio of the sum of the inscribed circle diameters of the protruding parts of the particle contour to the maximum inscribed circle diameter, and is used to accurately reflect the particle shape characteristics of the particles.

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