472 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Selection of the Sensor Based on ROC Analyses
ROC graphs were generated to assess and compare the per-
formance of the four different sensors. The target calcite
grade selected to construct the graph depicted in Figure 4
was 80%. To construct the graph, for each of the sensors,
the cut-off thresholds were varied. The variation range of the
thresholds were selected considering the sensors responses.
In this way, the highest and the lowest responses of each
sensor were identified. Subsequently, the gaps between the
thresholds were determined in order to evaluate 150 dif-
ferent values that cover the range of responses of the sen-
sors. In Figure 4 it is shown that the sensors XRT and XRF
excelled in their performance.
Selection of the Sensor Based on SRL
The responses of the four sensors were correlated to the
assay calcite grades and graphs were constructed to deter-
mine if the linear models were appropriate. In Figure 5 are
presented the correlation equations of the different sensor
responses and the assay calcite grade of each specimen. As
shown by the R2 factor, the XRT and XRF responses were
the most accurate according to the actual grades.
Comparison Between SRL and ROC
In order to compare the performance of the two approaches
to process the data, 25 rocks randomly selected were clas-
sified using, in the case of SRL, the equations which cor-
relate the assay calcite grade and the sensor response, and
in the case of ROC, using the cut-off threshold identified
as the best one through the ROC graph (Figure 4).To select
the optimal cut-off threshold, for both XRT and XRF, it
was identified the combination of sensitivity and speci-
ficity in the ROC graph whose location was closer to the
“perfect classification point” (Figure 2). The target calcite
grade selected to make the comparison was 80%. Moreover,
it was carried out only with the XRT and XRF sensors as
both showed the best performance. In Table 1 are presented
these results.
Classifying the rocks through the SRL approach for
both, XRT and XRF, sensors, leads to a slightly higher
grade of calcite in the accepted material than sorting the
specimens by ROC. However, the recovery of calcite, in
the case of XRF is more than 20% superior with the ROC
approach than with SRL. Additionally, the mass of the
accepted material, with both sensors, is noticeable greater
when using the ROC approach. As a result of these obser-
vations, it could be concluded that processing the sensor
responses with ROC is more fruitful than with SRL, as the
performance of the sensor is improved.
Evaluation of the Sensors
Determining the concentrate grade based on sensor mea-
surements is crucial, particularly considering the superior
performance of the XRF and XRT sensors. To rapidly
determine the calcite grade and the calcite recovery of the
accepted fraction, graphs were created for both the F and
the C fraction.
Similar to the example presented in Figure 3, the top
33% of the mass of the specimens that belong to the C
fraction, characterized by the highest calcite grade based
on XRF measurements, will exhibit a grade of 84% and a
recovery of 37%. Meanwhile, the F fraction will possess a
calcite grade of 83% and a recovery of 36%.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
1-Specificity
XRF
XRT
Colorimeter
Laser
Figure 4. ROC graph for a target calcium carbonate grade of
80%
Table 1. Comparison between SRL and ROC approaches for a target calcite grade of 80%
Accepted Material Rejected Material
Grade, %Recovery, %Mass, %Grade, %Recovery, %Mass,%
XRT SRL 84.8 37.0 33.6 73.0 63.0 66.4
ROC 83.8 51.4 47.2 70.9 48.6 52.8
XRF SRL 84.5 37.1 33.9 73.2 62.9 66.1
ROC 82.2 60.8 57.0 70.1 39.2 43.0
Sensitivit
Selection of the Sensor Based on ROC Analyses
ROC graphs were generated to assess and compare the per-
formance of the four different sensors. The target calcite
grade selected to construct the graph depicted in Figure 4
was 80%. To construct the graph, for each of the sensors,
the cut-off thresholds were varied. The variation range of the
thresholds were selected considering the sensors responses.
In this way, the highest and the lowest responses of each
sensor were identified. Subsequently, the gaps between the
thresholds were determined in order to evaluate 150 dif-
ferent values that cover the range of responses of the sen-
sors. In Figure 4 it is shown that the sensors XRT and XRF
excelled in their performance.
Selection of the Sensor Based on SRL
The responses of the four sensors were correlated to the
assay calcite grades and graphs were constructed to deter-
mine if the linear models were appropriate. In Figure 5 are
presented the correlation equations of the different sensor
responses and the assay calcite grade of each specimen. As
shown by the R2 factor, the XRT and XRF responses were
the most accurate according to the actual grades.
Comparison Between SRL and ROC
In order to compare the performance of the two approaches
to process the data, 25 rocks randomly selected were clas-
sified using, in the case of SRL, the equations which cor-
relate the assay calcite grade and the sensor response, and
in the case of ROC, using the cut-off threshold identified
as the best one through the ROC graph (Figure 4).To select
the optimal cut-off threshold, for both XRT and XRF, it
was identified the combination of sensitivity and speci-
ficity in the ROC graph whose location was closer to the
“perfect classification point” (Figure 2). The target calcite
grade selected to make the comparison was 80%. Moreover,
it was carried out only with the XRT and XRF sensors as
both showed the best performance. In Table 1 are presented
these results.
Classifying the rocks through the SRL approach for
both, XRT and XRF, sensors, leads to a slightly higher
grade of calcite in the accepted material than sorting the
specimens by ROC. However, the recovery of calcite, in
the case of XRF is more than 20% superior with the ROC
approach than with SRL. Additionally, the mass of the
accepted material, with both sensors, is noticeable greater
when using the ROC approach. As a result of these obser-
vations, it could be concluded that processing the sensor
responses with ROC is more fruitful than with SRL, as the
performance of the sensor is improved.
Evaluation of the Sensors
Determining the concentrate grade based on sensor mea-
surements is crucial, particularly considering the superior
performance of the XRF and XRT sensors. To rapidly
determine the calcite grade and the calcite recovery of the
accepted fraction, graphs were created for both the F and
the C fraction.
Similar to the example presented in Figure 3, the top
33% of the mass of the specimens that belong to the C
fraction, characterized by the highest calcite grade based
on XRF measurements, will exhibit a grade of 84% and a
recovery of 37%. Meanwhile, the F fraction will possess a
calcite grade of 83% and a recovery of 36%.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
1-Specificity
XRF
XRT
Colorimeter
Laser
Figure 4. ROC graph for a target calcium carbonate grade of
80%
Table 1. Comparison between SRL and ROC approaches for a target calcite grade of 80%
Accepted Material Rejected Material
Grade, %Recovery, %Mass, %Grade, %Recovery, %Mass,%
XRT SRL 84.8 37.0 33.6 73.0 63.0 66.4
ROC 83.8 51.4 47.2 70.9 48.6 52.8
XRF SRL 84.5 37.1 33.9 73.2 62.9 66.1
ROC 82.2 60.8 57.0 70.1 39.2 43.0
Sensitivit