2024 Volume 64 Issue 8 Pages 1279-1290
3D vision technologies have been widely used in metallurgy industry to measure particle size distribution (PSD) of green pellets on conveyor. However, 3D camera only captures the point clouds of surface pellets, and algorithms measure the surface PSD. To what extent the measured surface PSD can reflect whole PSD is a question that hasn’t been answered yet. In the present work, a simulation method is proposed to analyze the PSD measurement error of green pellets. First, the motion process of green pellets on conveyor is simulated by discrete element method to obtain PSD of whole pellets; then, a transformation method is proposed to generate point clouds of simulated surface pellets, and region growing-based method is adopted to measure the PSD of surface pellets; finally, the PSD measuring error can be obtained by comparing surface PSD and whole PSD of pellets. Error analysis of green pellet size distribution measurement on conveyors is conducted, in aspects of camera location, patch number of point clouds, thickness as well as size distribution of pellet bed. Results illustrate that although the PSD measuring error (up to 12.3%) cannot be neglected when camera is installed above conveyor, it can be effectively reduced by increasing the patch number of captured point clouds (reduced by more than 7.4%) or installing camera near discharge of conveyor (reduced to less than 3.1%).
Iron ore green pellets are one of the most important raw materials commonly used in metallurgy industry.1,2) Particle size distribution (PSD) of green pellets is a significant quality metric that affects production efficiency and product quality.3,4,5,6) It should be monitored to ensure that the pellet size is within a desired range (9–18 mm). However, current manual measurement method is tedious, subjective, time-consuming, and disadvantageous for the in-time control of the production process.7)
Machine vision technology has become a hot issue in the quality measurement of products owing to its simple and economical hardware configuration.8) In metallurgy industry, many vision-based methods9,10,11,12) have been proposed to automatically measure the PSD of green pellets, in which 2D or 3D camera is installed above the conveyor or near the discharge to capture surface information of pellets every few seconds, and the algorithm is adopted to measure pellet size. A typical 3D vision-based system for PSD measurement of pellets is shown in Fig. 1. The 3D camera is installed above the conveyor and projects a laser line to capture point clouds of surface pellets. Then, vision-based method is adopted to obtain the PSD measuring results, in which the segmentation algorithms are used to extract each pellet (such as morphological,13) region growing,14) and VCCS algorithm15)), and sphere fitting methods are used to measure the pellet size (such as M-estimation,16) maximum expectation,17) maximum likelihood estimation18)). Compared to the 3D camera, 2D camera is easily affected by environmental light in industry, which may deteriorate the image quality and lead to the failure of pellet size measurement algorithm. Therefore, 3D vision-based methods are more suitable for PSD measurement of green pellets in industry due to their good robustness to varying illumination.
However, 3D vision-based PSD measuring methods have a limitation: camera is only able to capture point clouds of surface pellets on conveyor, so the vision-based methods only measure the PSD of surface pellets. During the motion process of pellets on conveyor, some small pellets are dropped to the bottom (particle segregation) or covered by large particles (particle overlap), which may result in error between surface PSD and whole PSD.19) However, current vision-based PSD measuring methods are mainly aimed at the improvement of point clouds segmentation or sphere fitting algorithm, and little effort has been made to analyze the PSD measuring error caused by particle segregation and overlap. To what extent the PSD measuring results of surface PSD can reflect whole PSD of green pellets, is still a question that has not been solved.
In the past few years, some methods are available to investigate the PSD of whole pellets and surface pellets, which can be divided into two groups, including: (1) Traditional contact method,20) in which the worker collects some pellets from conveyor and then adopts sieving method to measure the pellet size. The PSD of collected pellets is regarded as the PSD of whole pellets, and it is used to compare with the surface PSD measured by vision-based methods. However, such a method cannot continuously collect pellets, and the pellets captured by camera are not exactly those manually collected sample pellets. It is unreasonable to directly compare the surface PSD measured from captured particles with whole PSD of the randomly sampled pellets. (2) Non-contact methods, including nuclear magnetic resonance (NMR)21) and positron emission particle tracking (PEPT).22) NMR is used to measure the structure of the pellet bed, and PEPT can be used to track each pellet. However, they are relatively expensive and need experienced workers to solve complex sample preparation and handling, such as isotope labeling and sample dissolution.
Recently, Discrete Element Method (DEM) is becoming a powerful tool for particle simulation due to the rapid development of computing technology.23,24) It provides visualizations of the trajectory and property of each pellets.25) Several researchers adopted DEM to simulate the motion process of particles in various industrial processes, such as the coke particles in throat region of a blast furnace,26) the green pellets in deck roller screen,27) spherical nickel pellets in the surface flow of a packed bed.28) Such a method provides theoretical and technical support for simulating the motion process of green pellets on conveyor, which facilitates to obtaining the whole PSD of pellets.
Up to now, little effort has been made to study the PSD measuring error of green pellets on conveyors. Although DEM simulation provides whole PSD of green pellets, it cannot directly provide the 3D point clouds of surface pellets and the surface PSD measured by vision-based method. The questions are: (1) To what extent can the measured surface PSD reflect the wholes PSD of green pellets? (2) How to reduce the PSD measuring error caused by particle segregation and overlap? To answer the question, a simulation method is proposed to measure the PSD measuring error, using DEM and a point cloud transformation method. Quantitative analyses are conducted to compare the PSD measuring errors, in the aspects of thickness as well as size distribution of pellet bed, camera location, and patch number of point clouds. Physical experiments on PSD measurement of green pellets are performed to verify the effectiveness of the proposed simulation results. The main contributions of the present work include:
(1) A simulation method is proposed to analyze the PSD measuring error of green pellets on conveyor, in which DEM is adopted to simulate the motion process of green pellets on conveyor to obtain whole PSD, and a transformation method is proposed to transform the simulated pellets in regions of interest into point clouds, so that the surface PSD can be obtained by vision-based method.
(2) Experiments are conducted to analyze the PSD measuring error of green pellets. For pellet beds with different thicknesses, errors gradually increased from 5.2% to 12.3% as thickness increased from 3 to 11 cm. For pellet beds with different size distributions, the highest error (6.6%) occurred when the number of small pellets (size ≤12 mm) accounted for the largest percentage.
(3) PSD measuring error can be effectively reduced by installing 3D camera near the discharge of conveyor (reduced to less than 3.1%) or increasing the number of captured point clouds (reduced by more than 7.4%), which was verified in physical experiments of PSD measurement of green pellets.
The rest of this paper is organized as follows: In Section 2, the proposed method for analyzing the PSD measuring error of pellets on conveyors is described. In Section 3, comparative analyses are conducted to investigate the PSD measuring error of pellets with different parameters. In Section 4, the testing experiments are performed to verify the effectiveness of the proposed method. In Section 5, the main works are concluded.
The procedures of the proposed PSD error analysis method are shown in Fig. 2. First, the motion process of green pellets on conveyor is simulated by discrete element method (DEM), so that the information of each pellet (coordinate and size) can be obtained, and the PSD of whole particles can be accurately measured. Then, point clouds of simulated pellets are generated by the proposed transformation method, and the surface PSD of pellets is measured using region growing-based method. Finally, the PSD measuring errors of particles on conveyor can be compared and analyzed.
DEM is usually adopted to simulate the motion process of green pellets at different working conditions.29,30,31) It tracks the trajectory of every individual particle in the simulation domain by continuously updating pellet position, velocity, acceleration, angular velocity, etc. based on Newton’s second law of motion. Green pellets are complex agglomerates with sticky behavior, and the contact force between green pellets can be represented by Hertz-Mindlin with Johnson-Kendall-Roberts (JKR) cohesion model.27)
The contact forces between green pellets include normal contact force fJKR, tangential contact force
| (1) |
| (2) |
where t represent the tangential components, δ is pellet overlap, and S is stiffness,
| (3) |
| (4) |
where n represent the normal components, vrel is relative velocity, R* is equivalent radius and m* is equivalent mass. In Eqs. (3), (4), the coefficient β, normal Sn and tangential stiffness St are given as follows:
| (5) |
| (6) |
| (7) |
where e is the coefficient of restitution, and G* is the equivalent shear modulus. By calculating the contact force of each particle and updating the particle location, the motion process of green pellets on conveyor can be simulated.
2.1.2. DEM Simulation SettingThe schematics of the simulated green pellets and conveyor using DEM simulation are shown in Fig. 3. The qualified size of green pellet is 9–18 mm, therefore, green pellets with five different sizes ranging from 10 mm to 18 mm are simulated. Pellets with different sizes are represented by different colors to facilitate visual observation (red: 10 mm, blue: 12 mm, yellow: 14 mm, green: 16 mm, white: 18 mm). The conveyor system includes a feeding port, a conveyor belt, and two baffles. The velocity of conveyor belt is set along the direction of the x-axis. In Table 1, the parameters of the simulated conveyor and pellets are shown, including the properties of pellets and conveyor, and contact force between each material. The parameters of pellet properties and contact force are obtained from literature,27) which have been proven to be effective in the DEM simulation of green pellets.
| Particle properties27) | Pellet size (mm) | 10, 12, 14, 16, 18 |
| Poisson’s ratio | 0.25 | |
| Density (kg/m3) | 3150 | |
| Shear modulus (MPa) | 1.8 | |
| Conveyor properties | Conveyor length (m) | 3 |
| Conveyor width (m) | 0.50 | |
| Conveyor speed (m/s) | 1.0 | |
| Inclination angle (°) | 10 | |
| Particle size (mm) | 0.25 | |
| Poisson’s ratio | 860 | |
| Density (kg/m3) | 7.1 | |
| Contact force27) | Coefficient of static friction (−) | Pellet-pellet: 0.30; Pellet-conveyor: 0.71 |
| Coefficient of rolling friction (−) | Pellet-pellet: 0.10; Pellet-conveyor: 0.05 | |
| Coefficient of restitution (−) | Pellet-pellet: 0.05; Pellet-conveyor: 0.05 | |
| JKR surface energy (γJKR) (J/m) | Pellet-pellet: 1.50; Pellet-conveyor: 0.50 |
In order to study the difference between the surface PSD and whole PSD of pellets with different parameters, a total of 8 experiments of DEM simulation are conducted to simulate the motion process of green pellets on conveyor. The simulation parameters of each group are shown in Table 2, including the pellet number of each size, the thickness as well as size distribution of pellet bed. The size distribution S of pellet bed in each experiment is defined as
| (8) |
where N10, N12, N14, N16, N18 are the number of pellets with sizes of 10 mm, 12 mm, 14 mm, 16 mm, 18 mm, respectively. In Exp. #1–#5, the total number of pellets is gradually increased, and the thicknesses of pellet bed are ranging from 3 cm to 11 cm. In Exp. #6–#8, the size distributions of pellet beds are different, and the thicknesses are controlled to 8 cm to ensure the single variable. The simulation time t of each group is set to 80 s.
| Experiments | Pellet number of each size | Size distribution of pellet bed | Thickness of pellet bed | ||||
|---|---|---|---|---|---|---|---|
| 10 mm | 12 mm | 14 mm | 16 mm | 18 mm | |||
| #1 | 1500 | 1500 | 1500 | 1500 | 1500 | S=1:1:1:1:1 | 3 cm |
| #2 | 3000 | 3000 | 3000 | 3000 | 3000 | S=1:1:1:1:1 | 5 cm |
| #3 | 6000 | 6000 | 6000 | 6000 | 6000 | S=1:1:1:1:1 | 7 cm |
| #4 | 7500 | 7500 | 7500 | 7500 | 7500 | S=1:1:1:1:1 | 9 cm |
| #5 | 4500 | 4500 | 4500 | 4500 | 4500 | S=1:1:1:1:1 | 11 cm |
| #6 | 1730 | 3460 | 5190 | 3460 | 1730 | S=1:3:5:3:1 | 5 cm |
| #7 | 1530 | 6120 | 4590 | 3060 | 1530 | S=1:5:4:3:1 | 5 cm |
| #8 | 1320 | 2640 | 3960 | 5280 | 1320 | S=1:3:4:5:1 | 5 cm |
In Fig. 4, the motion process of green pellets on conveyor by DEM is shown, using pellet bed in Exp. #4 as an example. It is shown that green pellets with different sizes are generated from feeding port and dropped to conveyor, and then the pellet bed is formed. After all pellets drop from discharge, the simulation experiment is completed. According to the simulation results, information of each particle at every simulation time can be obtained, including pellet size and the coordinates x, y, z of pellet center. And the whole PSD can be obtained by counting the number of pellets with different sizes in region of interest.
Although DEM simulation results provide information (size, spatial coordinate) of pellets, they can’t be used to directly reflect the PSD of surface pellets. To obtain the PSD of surface pellets, a transformation method is proposed to generate the point clouds of simulated pellets, which facilitates the subsequent acquisition of PSD measurement of surface pellets. In Fig. 5, the procedures of the transformation method are shown.
Firstly, information of simulated pellets from different regions of interest (ROIs) is extracted. In metallurgy industry, cameras are mostly installed above the conveyor to capture point clouds of particles in ROI for obtaining surface PSD,34) while some researchers installed camera near the discharge to obtain PSD of dropping pellets.11) It motivates us to investigate the influence of camera location on PSD measurement results. As shown in Fig. 6, three cameras are installed in different locations, including location #1 (above the particles on conveyor), location #2 (in front of the dropping pellets), and location #3 (behind the dropping pellets). Based on simulation results, the information (spatial coordinate of pellet center, pellet size) of pellets in three different camera acquisition areas (ROI #1–#3) is extracted.
According to the extracted pellet information in DEM simulation results, 3D models of simulated pellets in ROIs are established using visualization toolkit35) on Visual Studio 2019 platform, which can be used to obtain more pellet information such as morphology, arrangement, and spatial distribution. Then, point clouds of simulated pellets in ROIs are generated using Blender Sensor Simulator (Blensor),36) which is a widely used open-source simulation package based on Blender software used to simulate depth camera to capture point clouds from target objects. In Blender software, 3D camera with the type of time-of-flight (TOF) and the resolution of 2000×2000 is simulated. The 3D camera emits rays of light in the form of a light pulse which travel along straight lines to the pellet surface, and then a fraction of light gets reflected back to the camera, so that the point clouds of pellets can be obtained. In Fig. 7, the point clouds of surface pellets using the proposed transformation method are shown. It can be seen that the generated point clouds are in good agreement with simulated pellets, which shows the effectiveness of the transformation method.
After generating point clouds of surface particles, their PSD can be measured by vision-based method. The flowchart of vision-based PSD measuring method is as follows (see Fig. 8). Firstly, the point clouds of each particle are segmented by region growing method, and the size of each particle is calculated by M-estimation fitting method. Then, PSD of surface particles can be obtained after counting the size of detected particles.
Region growing method is widely used in PSD measurement because it is easily implemented and has good robustness.37,38) Therefore, it is adopted in present work to measure the PSD of pellets. For the point clouds of pellets, define the set of points that have not yet been assigned to any cluster as Pr, and set point that has the minimum curvature value as current seed p0. The normal of current seed and its neighboring points are calculated. For a point cloud, its normal is obtained by principal component analysis (PCA):
| (9) |
where C is the covariance matrix, pi (i=1, 2…k) is the k nearest neighbors of seed point p0 identified by the k-dimensional tree space partitioning method.
In Fig. 9, the segmented results of pellet point clouds using region growing method are shown. It can be seen that the pellets in ROI#1 are in dense contact, while pellets in ROI #2–#3 are relatively sparse. Both dense pellets and sparse pellets can be well segmented (point clouds with different colors represent different particles), which illustrates the effectiveness of the region growing method.
By using the above-mentioned method, the surface PSD and whole PSD of particles in different camera acquisition areas on conveyor can be compared and analyzed. Then, the PSD measuring error39) σ can be calculated by:
| (10) |
where mk and rk represent the proportions of size k-th particle size fraction of surface pellets and whole pellets, respectively. N is the number of pellet size ranges. Higher metric value represents larger difference between measured surface PSD and whole PSD of particles.
For each simulation experiment, the average PSD errors can be measured as follows: green pellets are generated by DEM and moved by conveyor, then the 3D camera starts to generate point clouds with a time interval of 2 simulation seconds when pellets pass through the ROIs. The surface PSD of pellets from all patches of point clouds is obtained using region-growing methods, whereas the whole PSD can be obtained from the DEM simulation results. Finally, the average PSD measuring error can be obtained using Eq. (10).
Based on the proposed simulation method, the PSD measuring error of pellets on conveyor can be measured. In this section, we will evaluate the PSD measuring pellets in aspects of thickness as well as size distribution of pellet bed, camera locations, and patch number of point clouds.
3.1. Comparison of Vision Measured PSD and Manual Measured PSDIn addition to particles segregation and overlap, the vision-based measuring algorithm may influence the PSD measurement results. To verify the effectiveness of the region-growing method described in Section 2.3, we directly compare the vision-measured surface PSD and the manually measured surface PSD, using pellets in different ROIs from Exp. #3. The patch number of point clouds in each ROI (#1–#3) is 10. The PSD of testing pellets is measured by region growing method, and the corresponding references PSD is measured manually based on DEM simulation results.
In Fig. 10, comparisons between the vision-measured surface PSD and manually measured surface PSD of pellets are shown. For pellets captured in three different ROIs (#1–#3), the cumulative percentage curves of surface PSD by vision-measured method are highly agreed with manually measured PSD, indicating that the vision-based method can effectively measure the surface PSD. Therefore, we ignored the measuring errors caused by vision-based measuring algorithm, and only focused on the differences between the surface PSD and whole PSD caused by pellet segregation and overlap in the subsequent experimental analysis.
The PSD measuring error of green pellets in Exp. #1–#5 are measured and analyzed, in which the thicknesses of pellet bed range from 3 cm to 11 cm, and the size distributions are the same (S=1:1:1:1:1). In each experiment, point clouds of pellets in ROI #1 are generated with a time interval of 2 simulation seconds, and the patch number of point cloud is 16.
In Fig. 11, comparisons between surface PSD and whole PSD of pellets in Exp. #1–#5 are shown. It can be seen that the cumulative percentage of whole PSD is mostly larger than surface PSD at different size segments, and the difference between surface PSD and whole PSD increases as the thickness gradually increases, indicating that the surface PSD by vision-based method is difficult to reflect the whole PSD of pellets on conveyor when the thickness of pellet bed is high. The main reason is that more small pellets are being covered by large pellets or sliding to the bottom layer as the pellet bed gets thicker. The average PSD measuring error σ in five experiments gradually increased from 5.2% to 12.3% when the thickness of pellet bed increased from 3 cm to 11 cm, which indicates that the difference between surface PSD and whole PSD cannot be neglected when using the vision-based method to measure PSD of green pellets on the conveyor.
The above study analyzed the PSD measuring error using pellet beds with the same size distribution, which motivated us to study the error of pellet beds with different size distributions. Pellet bed with different size distributions while the same thickness (h=5 cm) in Exp. #6–#8 are adopted. The patch number of point clouds in each experiment is 16. In Exp. #6 (S=1:3:5:3:1), the proportion of middle-seized pellets (12 mm<size<16 mm) is the largest. In Exp. #7 (S=1:5:4:3:1), the proportions of small-seized pellets (size≤12 mm) is the largest. In Exp. #8 (S=1:3:4:5:1), the proportions of large-seized (size≥14 mm) pellets are the largest.
In Fig. 12, comparisons between surface PSD and whole PSD of pellet beds with different size distributions are shown. It can be seen that the cumulative percentages of whole particles are larger than surface pellets, and the average PSD errors σ are more than 4.1%, indicating that error still exists when the size distributions change. The biggest error (6.6%) occurred in Exp. #6 where the proportion of small-sized particles (size≤12 mm) is the highest, which illustrates that the proportion of small-seized pellets is one of the main factors that influence the error. The main reason is that small-seized pellets are usually dropped into the bottom or covered by large pellets and won’t be detected by the vision-based method. In Fig. 13, the PSD results of surface pellets, bottom pellets, and whole pellets are shown, using pellets in ROI #1 of Exp #7 as an example. It can be seen that large particles (white particles: 18 mm, green particles: 16 mm) are easy to be recognized from the surface layer, whereas most of the small particles (red particles: 10 mm, blue particles: 12 mm) are located at the bottom layer. Therefore, a higher proportion of small-sized pellets can lead to higher error.
The camera is mostly installed above conveyor to measure the size distribution of green pellets, while some researchers installed camera near the discharge of the conveyor. To find a suitable location for camera, the influence of camera location on PSD measuring error is investigated. Three different camera locations are studied, including location #1 (camera installed above the conveyor), location #2 (camera installed in front of dropping pellets), location #3 (camera installed behind dropping pellets), as shown in Section 2.2. Pellets in different ROIs from Exp #2 are used, and the patch number of point clouds in each ROI is 16.
In Fig. 14, comparisons between surface PSD and whole PSD of pellets in Exp #2, with camera installed in different locations. It is shown that, the cumulative percentage of whole PSD is larger than surface PSD of pellets when camera is installed in location #1 (above the conveyor). On the contrary, the cumulative percentage curve of surface PSD is in good agreement with the whole PSD of pellets when the camera is installed near the discharges, indicating that the measured PSD of surface pellets well reflect the PSD of whole pellets. The difference in PSD measuring results by cameras installed in location #2 (in front of dropping pellets) and location #3 (behind dropping pellets) can be neglected. The reason is that the dropping pellets are not affected by segregation, and only a few small pellets are covered by large pellets. Thus, more small pellets can be detected when 3D camera is installed near the discharge.
Table 3 shows PSD measuring errors of simulated pellets in Exp #1–#8 with camera installed in different locations, the max PSD error σ is up to 12.3% due to the particle segregation and overlap. However, it is reduced to less than 3.1% when camera is installed in front of or behind dropping pellets. Results show that PSD measuring error can be reduced when camera is installed near the discharge of conveyor.
| Camera locations | Error in Different simulation groups (%) | Min error (%) | Max error (%) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Exp#1 | Exp#2 | Exp#3 | Exp#4 | Exp#5 | Exp#6 | Exp#7 | Exp#8 | |||
| Location#1 | 5.2 | 7.3 | 8.2 | 10.1 | 12.3 | 4.1 | 6.6 | 4.1 | 4.1 | 12.3 |
| Location#2 | 1.2 | 2.1 | 2.5 | 2.9 | 3.1 | 1.1 | 1.5 | 1.5 | 1.1 | 3.1 |
| Location#3 | 1.4 | 1.8 | 2.6 | 2.7 | 3.0 | 1.2 | 1.7 | 1.2 | 1.2 | 3.0 |
In general, the accuracy of the statistical results can be enhanced by increasing the number of data samples. It is motivated us to investigate whether the PSD measuring error can be reduced by collecting more patches of point clouds of green pellets. Pellets in Exp #1–#8 of DEM experiments are taken as an example. Different patch number of point clouds (N=128, 64, 32, 16, 8, 4) can be obtained by generating point clouds of pellets in ROI #1–#2 using different sampling intervals (T=0.25 s, 0.5 s, 1 s, 2 s, 4 s, 8 s). Noted that pellets in ROI #3 is not discussed here because the difference between ROI #3 and ROI #2 is small.
In Fig. 15, the PSD measuring errors of pellets in Exp #1–#8 are shown, using different patch numbers of point clouds. It can be seen that the PSD measuring error in each ROI is basically reduced with the increasing patch number of point clouds. To quantitatively evaluate the effectiveness of patch number on PSD error, the decline rate Δ of PSD errors is calculated by
| (11) |
where error4, error128 is the PSD errors when patch number is 4 and 128, respectively. In Table 4, the decline rates of PSD errors when patch number is increased from 4 to 128 are shown. It can be seen that for dropping particles in ROI #2, the PSD measuring error σ is reduced by more than 8.1% with the number of point clouds is increased from 4 to 128, indicating that capturing more point clouds number better reflects the PSD of whole pellets. For pellets in ROI #1, the PSD measuring error is gradually reduced by more than 7.4% when the number of point clouds increases from 4 to 128. Results show that increasing the patch number of point clouds can effectively reduce the PSD measurement error. However, the PSD measuring error won’t be decreased by increasing the patch number when there are overlapping parts between the collected point clouds when the sampling interval is relatively short. In industrial sites, it is recommended to capture more point clouds by configuring shorter sampling intervals or increasing the sampling time of the camera, so that the measured surface PSD is closer to the whole PSD of pellets. It is noted that it is important to ensure that there is no overlap between each point clouds when using a shorter sampling interval.
| Pellet location | Decline rate of PSD errors in different exp (%) | Min value (%) | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Exp#1 | Exp#2 | Exp#3 | Exp#4 | Exp#5 | Exp#6 | Exp#7 | Exp#8 | ||
| ROI#1 | 17.4 | 15.8 | 8.6 | 7.4 | 9.3 | 30.4 | 17.9 | 29.4 | 7.4 |
| ROI#2 | 28.9 | 14.6 | 9.7 | 8.1 | 12.5 | 26.2 | 24.7 | 30.2 | 8.1 |
The above simulation results illustrate that the error between surface PSD and whole PSD of green pellets on conveyor cannot be neglected due to the particle segregation and overlap. However, it can be reduced by installing the camera near the discharge or increasing the patch number of captured point clouds. To verify the simulation results, physical experiments are performed to analyze the PSD measuring error of green pellets on a conveyor.
Considering that the whole PSD of green pellets is difficult to obtain in industry, the physical experiments are conducted in the laboratory. The vision acquisition system with a 3D camera installed above the conveyor is adopted (see Fig. 16), which consists of a computer, a conveyor belt, a 3D camera. To obtain the point clouds of green pellets captured by cameras installed in different locations, two groups (#a, #b) of green pellets are adopted. For group #a, the green pellets are densely stacked on the conveyor belt (pellet thickness is 10 cm), which is used to evaluate the performance of PSD measurement by camera installed above on conveyor. For group #b, the green pellets are sparsely dispersed on the conveyor to simulate the dropping pellets, so that the performance of PSD measurement by camera installed near the discharge can be evaluated. The performance of camera location #2 (in front of pellets) and location #3 (behind dropping pellets) won’t be compared here because the difference in their PSD measuring results can be neglected. The acquisition processes of cloud points of green pellets are as follows. First, drop green pellets into the conveyor, and set the sampling frequency of 3D camera. Then, open the conveyor controller and start the acquisition of point clouds. End the acquisition of point clouds after all pellets are dropped from the conveyor. By use of the 3D vision acquisition system and the two groups of pellets, a total of 128 point clouds of pellets are obtained (64 point clouds for each group), as shown in Fig. 17. For the two groups, their surface PSD are measured by vision-based method, and their whole PSD are measured by manual sieving method.
In Fig. 18, the measured surface PSD and whole PSD of green pellets in two groups are shown. For dense pellets in group #a, the cumulative percentage of whole PSD is larger than surface PSD of pellets, and the PSD measuring error is 10.5%. On contrary, for sparse pellets in group #b, the surface PSD is in good agreement with whole PSD of pellets, and the error is reduced to 0.5%. Results verified that PSD measuring error cannot be neglected when camera is installed above the conveyor, however, it can be reduced by installing the camera near discharge.
In Fig. 19, the PSD measuring errors of green pellets using different patch numbers of point clouds are shown. PSD measuring error gradually decreased when the number of point clouds images increased from 4 to 64. Specifically, PSD error decreased from 7.3% to 6.2% of particles in group #a, and it decreased from 2.7% to 1.6% of particles in group #b, illustrating that the PSD measuring error can be obtained by adopting more numbers of point clouds. The above results are consistent with our simulation results in Section 3, illustrating the effectiveness of the proposed simulation methods. Therefore, it is recommended to install camera near the discharge and capture more point clouds of dropping pellets, so that the measured surface PSD can better reflect the whole PSD of pellets.
3D vision technologies have been widely used in the PSD measurement of green pellets on conveyors. However, such methods only measure the surface PSD of pellets on conveyor. It is still unknown whether surface PSD can reflect the whole PSD of particles. In the present work, a novel analysis method is proposed to investigate the PSD measuring error of green pellets using DEM simulation and a point cloud transformation method. Comparative experiments are performed to investigate the PSD measuring error of green pellets with different parameters, including different size distributions, pellet thicknesses, camera locations, and point cloud numbers. The main conclusions of our work are as follows:
(1) The proposed method is effective in evaluating the PSD measuring error of green pellets on conveyors.
(2) For pellet beds with different thicknesses, PSD error gradually increased from 5.2% to 12.3% as the thickness increased from 3 cm to 11 cm.
(3) For pellet beds with different size distributions, the highest error (6.6%) occurred when the proportion of small-sized pellets (size ≤12 mm) is the largest.
(4) For cameras installed in different locations, PSD error is up to 12.3% when camera is installed above conveyor, while it is reduced to less than 3.1% when camera is installed near the discharge of conveyor.
(5) With the increasing patch number of point clouds from 4 to 128, PSD error can be reduced by more than 7.4%.
(6) Physical experiments of PSD measurement on green pellets verified the effectiveness of our simulation results.
In our future work, more experiments will be conducted to measure the PSD error of pellets under different pellet parameters (total number, size range, size distribution). By analyzing a large amount of experimental data, we aim to propose a correction method to further reduce the PSD error, which helps to increase the accuracy of PSD measuring results of green pellets in the steel industry.
