The Correlation between Macroscopic Image and Object Properties with Bubble Size in Flotation
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Procedure
2.2. Semiautomated Image Processing
2.3. Region Properties and Their Association with Bubble Size
3. Results
4. Conclusions
- Several image and object properties showed moderate or strong correlations, linear and non-linear, with the Sauter diameter.
- The maximal information coefficient was successfully used to detect non-linear associations between image and object properties with bubble size. These associations were not clearly detected with the coefficient of correlation. The strongest associations were observed with the median of the spatial bandwidth, median of the equivalent diameter, relative standard deviation of the aspect ratio, and median of the number of objects per unit area.
- After removing churn-turbulent conditions and linearizing non-linear associations, a multivariable linear model was proposed, which was able to estimate bubble size in the range 1.3–6.7 mm. This model was obtained from four predictors: median of the circularity, relative interquartile range of the equivalent diameter, relative standard deviation of the number of elements per unit area, and median of the spatial bandwidth. These predictors were chosen from the best subset of all possible linear models, minimizing PRESS.
- The linear model was successfully tested on 72 independent datasets, which showed the generalizability of the model structure.
Author Contributions
Funding
Conflicts of Interest
Appendix A
Appendix B
Appendix C
Title | p-Values | 95% Confidence Intervals |
---|---|---|
Constant | 0.0453 | (0.0242, 2.25) |
C50 | 0.000420 | (−2.78, −0.822) |
EDIQR | 6.90 × 10−11 | (0.573, 0.997) |
NRSD | 2.14 × 10−5 | (0.843, 2.19) |
BW50 | 1.11 × 10−43 | (3.22, 3.76) |
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Type of Frother | Location | Frother Concentrations, ppm | Superficial Gas Rate, cm/s |
---|---|---|---|
MIBC | 1 and 2 | 0, 2, 4, 8, 16 | 0.5, 1.0, 1.5, 2.0, 2.5 |
AeroFroth® 70 | 1 | 0, 2, 4, 8, 16, 32 | 0.4, 1.2, 2.0 |
OrePrep® F-507 | 1 | 0, 2, 4, 8, 16, 32 | 0.4, 1.2, 2.0 |
Flotanol® 9946 | 1 | 0, 2, 4, 8, 16, 32 | 0.4, 1.2, 2.0 |
Type of Frother | Location | Frother Concentrations, ppm | Superficial Gas Rate, cm/s |
---|---|---|---|
AeroFroth® 70 | 2 | 0, 2, 4, 8, 16, 32 | 0.8, 1.6 |
0, 2, 8, 32 | 0.4, 1.2, 2.0 | ||
OrePrep® F-507 | 2 | 0, 2, 4, 8, 16, 32 | 0.8, 1.6 |
0, 2, 8, 32 | 0.4, 1.2, 2.0 | ||
Flotanol® 9946 | 2 | 0, 2, 4, 8, 16, 32 | 0.8, 1.6 |
0, 2, 8, 32 | 0.4, 1.2, 2.0 |
Property | Variable Symbol | Statistical Index |
---|---|---|
Shadow Fraction | SF | Median Relative Standard Deviation Relative Interdecile Range Relative Interquintile Range Relative Interquartile Range |
C | ||
Aspect Ratio, major axis length/minor axis length | AR | |
Eccentricity | E | |
Perimeter, mm | P | |
Solidity | S | |
, mm | ED | |
Number of Objects per mm2, 1/mm2 | N | |
Spatial Bandwidth, pxl/mm | BW |
Title | P50 | SFRIQQR | ED50 | NRSD | BW50 | EC50 | ARRSD | C50 | ECRIDR | N50 | AR50 | BWRSD |
---|---|---|---|---|---|---|---|---|---|---|---|---|
R | 0.838 | 0.831 | 0.829 | 0.822 | −0.820 | 0.766 | 0.762 | −0.750 | −0.730 | −0.717 | 0.700 | 0.650 |
MIC | 0.942 | 0.794 | 0.960 | 0.859 | 1.000 | 0.813 | 0.969 | 0.754 | 0.798 | 0.953 | 0.813 | 0.477 |
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Vinnett, L.; Cornejo, I.; Yianatos, J.; Acuña, C.; Urriola, B.; Guajardo, C.; Esteban, A. The Correlation between Macroscopic Image and Object Properties with Bubble Size in Flotation. Minerals 2022, 12, 1528. https://doi.org/10.3390/min12121528
Vinnett L, Cornejo I, Yianatos J, Acuña C, Urriola B, Guajardo C, Esteban A. The Correlation between Macroscopic Image and Object Properties with Bubble Size in Flotation. Minerals. 2022; 12(12):1528. https://doi.org/10.3390/min12121528
Chicago/Turabian StyleVinnett, Luis, Iván Cornejo, Juan Yianatos, Claudio Acuña, Benjamín Urriola, Camila Guajardo, and Alex Esteban. 2022. "The Correlation between Macroscopic Image and Object Properties with Bubble Size in Flotation" Minerals 12, no. 12: 1528. https://doi.org/10.3390/min12121528