1406 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Correlation Analysis
Correlation between disparate datasets is required for a
couple of reasons. First, any causal relationships between
the characteristics of the ore and the ensuing process per-
formance should be explicitly encoded into the DES
model to tailor the model performance to better match the
observed behavior of the system. Second, to confirm that
the model outputs are reasonably accurate, the predicted
performance of the system should be reviewed to ensure
they match the downstream datasets. For example, if the
DES model accurately predicts the time it takes for ore to
traverse the primary crusher to the intermediate stockpile,
then the modeled tons, copper grade, and other geologic
attributes of the DES model should reconcile with opera-
tional data such as the conveyor scale weights or stockpile
tracking metrics.
To identify potential causal connections between the
ore and the crusher downtimes, ore control data on ore
hardness, total clay content, swelling clay content, pyrite
concentration, BWI, RQD, and two metrics related to size
was used to calculate correlations with unplanned down-
time events. As geology and operational data is noisy, a
series of weighted averages were calculated for every geo-
logic attribute. Similarly, many of the downtimes are of
short durations, so downtimes were summed over a range
of time periods. A series of cross correlations, including
time lags ranging from 15 minutes to 4 hours, were then
calculated comparing each combination of weighted-aver-
age ore attribute and cumulative downtime.
Any observed correlations may be considered genuine
if they meet the following requirements:
1. The associated p-value must be ≤0.1.
2. The peak correlation must be reasonably high
compared to the correlations observed for other
variables in the ore control dataset.
3. The number of instances must be reasonably high.
4. The correlation must be consistent regardless of the
weighted average window, process performance
window, and time lag parameters used for the cross
correlations calculation.
5. There must be a geologically plausible explanation
for the observed correlation.
RESULTS
The model was successfully able to predict the movement of
material from the entrance point at the primary crusher to
the intermediate ore stockpile. This includes the additional
geology-related attributes relevant to modeling future
components of the processing system. Outputs include
sequential files covering the time delay during processing,
tons, total copper, hardness, and the three components of
the foreign key linking the material loads to the original
data source. Therefore, the major goals of the study were
fulfilled.
However, this study was not able to quantify a direct
correlation between the hardness of ore delivered at the
crusher and unplanned downtime events attributed to hard
ore. Weak correlations appear to exist between hardness-
related downtimes and the size distribution variables. These
variables are being considered for use in constraining the
simulated production in the accompanying DES model
instead.
DISCUSSION
A key component of DES models is that they are stochas-
tic and involve many repetitions to capture the effects of
unpredictable and random behavior in the system. In prac-
tice many of the empirical distributions used here had a
very low degree of variability. In many cases this made fit-
ting a theoretical distribution challenging. For example, the
apron feeder speed data is tightly clustered and bimodal,
which is likely the result of a system that can operate on
two speed settings.
Table 3. Overview of distributions used to model downtime events
Downtime Category Type of Down Distribution Notes
Shift Change Scheduled 43200–60 +6.96e+03
*BETA(0.615, 4.42)
Scheduled every 12 hours, length varies
Shift Change MTTR 60 +6.96e+03 *BETA(0.615, 4.42) Scheduled every 12 hours, length varies
Planned Maintenance MTBF 60 +WEIB(4.86e+03, 0.287) Modeled as a random event since there are
many superimposed maintenance activities
included
Planned Maintenance MTTR 60 +WEIB(1.08e+03, 0.279)
Unplanned Maintenance MTBF –0.001 +EXPO(361) Excludes geology-related downs
Unplanned Maintenance MTTR –3.84e+03 +LOGN(4.16e+03, 487) Excludes geology-related downs
Correlation Analysis
Correlation between disparate datasets is required for a
couple of reasons. First, any causal relationships between
the characteristics of the ore and the ensuing process per-
formance should be explicitly encoded into the DES
model to tailor the model performance to better match the
observed behavior of the system. Second, to confirm that
the model outputs are reasonably accurate, the predicted
performance of the system should be reviewed to ensure
they match the downstream datasets. For example, if the
DES model accurately predicts the time it takes for ore to
traverse the primary crusher to the intermediate stockpile,
then the modeled tons, copper grade, and other geologic
attributes of the DES model should reconcile with opera-
tional data such as the conveyor scale weights or stockpile
tracking metrics.
To identify potential causal connections between the
ore and the crusher downtimes, ore control data on ore
hardness, total clay content, swelling clay content, pyrite
concentration, BWI, RQD, and two metrics related to size
was used to calculate correlations with unplanned down-
time events. As geology and operational data is noisy, a
series of weighted averages were calculated for every geo-
logic attribute. Similarly, many of the downtimes are of
short durations, so downtimes were summed over a range
of time periods. A series of cross correlations, including
time lags ranging from 15 minutes to 4 hours, were then
calculated comparing each combination of weighted-aver-
age ore attribute and cumulative downtime.
Any observed correlations may be considered genuine
if they meet the following requirements:
1. The associated p-value must be ≤0.1.
2. The peak correlation must be reasonably high
compared to the correlations observed for other
variables in the ore control dataset.
3. The number of instances must be reasonably high.
4. The correlation must be consistent regardless of the
weighted average window, process performance
window, and time lag parameters used for the cross
correlations calculation.
5. There must be a geologically plausible explanation
for the observed correlation.
RESULTS
The model was successfully able to predict the movement of
material from the entrance point at the primary crusher to
the intermediate ore stockpile. This includes the additional
geology-related attributes relevant to modeling future
components of the processing system. Outputs include
sequential files covering the time delay during processing,
tons, total copper, hardness, and the three components of
the foreign key linking the material loads to the original
data source. Therefore, the major goals of the study were
fulfilled.
However, this study was not able to quantify a direct
correlation between the hardness of ore delivered at the
crusher and unplanned downtime events attributed to hard
ore. Weak correlations appear to exist between hardness-
related downtimes and the size distribution variables. These
variables are being considered for use in constraining the
simulated production in the accompanying DES model
instead.
DISCUSSION
A key component of DES models is that they are stochas-
tic and involve many repetitions to capture the effects of
unpredictable and random behavior in the system. In prac-
tice many of the empirical distributions used here had a
very low degree of variability. In many cases this made fit-
ting a theoretical distribution challenging. For example, the
apron feeder speed data is tightly clustered and bimodal,
which is likely the result of a system that can operate on
two speed settings.
Table 3. Overview of distributions used to model downtime events
Downtime Category Type of Down Distribution Notes
Shift Change Scheduled 43200–60 +6.96e+03
*BETA(0.615, 4.42)
Scheduled every 12 hours, length varies
Shift Change MTTR 60 +6.96e+03 *BETA(0.615, 4.42) Scheduled every 12 hours, length varies
Planned Maintenance MTBF 60 +WEIB(4.86e+03, 0.287) Modeled as a random event since there are
many superimposed maintenance activities
included
Planned Maintenance MTTR 60 +WEIB(1.08e+03, 0.279)
Unplanned Maintenance MTBF –0.001 +EXPO(361) Excludes geology-related downs
Unplanned Maintenance MTTR –3.84e+03 +LOGN(4.16e+03, 487) Excludes geology-related downs