XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 877
Furthermore, the effect of slurry filling on power draw
is elucidated using data from different pilot scale mills.
Figure 6 shows the results for pilot mill data (Soleymani
et al., 2016). The maximum relative error obtained is
±11.16%.
Grinding Circuit Optimization using Machine
Learning Models
Since large sets of data from laboratory or industrial scale
mills is not readily available, we have created synthetic data
using the grinding model presented in the previous section.
The PSD, flow rate and slurry concentration of FF along
with the sump water added are treated as independent vari-
ables. Initial values of ball mill output PSD (fBO), ball mill
slurry concentration (c) and cyclone underflow volumetric
flow rate (QUf) are unknown. Hence guesses are provided
for each steady-state data point. The system of equations is
solved using the least squares method .
The mass flow rate of fines from the cyclone is consid-
ered as the throughput of the grinding circuit. The mid-
size passing is the fraction of solids passing through the
188-micron sieve size. Synthetic data is generated by simu-
lating the integrated grinding circuit for a range of values
of the independent variables listed in Table 2 with a total
of 3,125 combinations. The steady state values obtained
from the integrated model by solving the system of linear
equations. Obtaining the solution to the system of non-
linear equations using least squares method is an iterative
approach and requires multiple evaluations of the given
set of non-linear equations till the solution is converged.
Therefore, model-based optimization using physics-based
models is computationally expensive. Computationally less
intensive machine learning (ML) models are commonly
used instead. The converged solutions are checked for feasi-
bility and the feasible data points are used for training ML
models for midsize passing and throughput. It was found
that support vector regression (SVR) models achieved the
highest accuracy in describing the data with test-R2=0.85
and 0.96 for midsize passing and throughput, respectively.
SVR based models are robust, automatically control solu-
tion complexity and effective with dense as well as sparse
datasets. SVR is also computationally economical compared
to more intricate artificial neural network–based models.
Figure 6. Effect of slurry filling (U) on power draw (Soleymani et al., 2016)
Table 2 Process variables and their limits used for
optimization
Parameter Symbol Minimum Maximum
Slurry concentration C 0.6 0.694
Ball filling J 0.3 0.345
Fresh feed (kg/min) FF 2.15 43.04
Ball Mill speed ϕ 0.6 0.8
Ball Mill filling V
B 0.18 1.0
Furthermore, the effect of slurry filling on power draw
is elucidated using data from different pilot scale mills.
Figure 6 shows the results for pilot mill data (Soleymani
et al., 2016). The maximum relative error obtained is
±11.16%.
Grinding Circuit Optimization using Machine
Learning Models
Since large sets of data from laboratory or industrial scale
mills is not readily available, we have created synthetic data
using the grinding model presented in the previous section.
The PSD, flow rate and slurry concentration of FF along
with the sump water added are treated as independent vari-
ables. Initial values of ball mill output PSD (fBO), ball mill
slurry concentration (c) and cyclone underflow volumetric
flow rate (QUf) are unknown. Hence guesses are provided
for each steady-state data point. The system of equations is
solved using the least squares method .
The mass flow rate of fines from the cyclone is consid-
ered as the throughput of the grinding circuit. The mid-
size passing is the fraction of solids passing through the
188-micron sieve size. Synthetic data is generated by simu-
lating the integrated grinding circuit for a range of values
of the independent variables listed in Table 2 with a total
of 3,125 combinations. The steady state values obtained
from the integrated model by solving the system of linear
equations. Obtaining the solution to the system of non-
linear equations using least squares method is an iterative
approach and requires multiple evaluations of the given
set of non-linear equations till the solution is converged.
Therefore, model-based optimization using physics-based
models is computationally expensive. Computationally less
intensive machine learning (ML) models are commonly
used instead. The converged solutions are checked for feasi-
bility and the feasible data points are used for training ML
models for midsize passing and throughput. It was found
that support vector regression (SVR) models achieved the
highest accuracy in describing the data with test-R2=0.85
and 0.96 for midsize passing and throughput, respectively.
SVR based models are robust, automatically control solu-
tion complexity and effective with dense as well as sparse
datasets. SVR is also computationally economical compared
to more intricate artificial neural network–based models.
Figure 6. Effect of slurry filling (U) on power draw (Soleymani et al., 2016)
Table 2 Process variables and their limits used for
optimization
Parameter Symbol Minimum Maximum
Slurry concentration C 0.6 0.694
Ball filling J 0.3 0.345
Fresh feed (kg/min) FF 2.15 43.04
Ball Mill speed ϕ 0.6 0.8
Ball Mill filling V
B 0.18 1.0