878 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
The trained SVR models are used for optimization of a
simulated grinding circuit using a non–dominated sorting
genetic algorithm (NSGA–II). The NSGA–II utilizes the
elite strategy, non–dominated sorting and crowding dis-
tance comparison to generate better populations at every
iteration that are non–dominated in nature and are evenly
distributed in the pareto front. For studying the variation
in optimal solutions due to variation in feed and operat-
ing conditions, three different cases of ore grades (Lee et
al., 2020) as well as three different cases of ball filling are
studied. Multi–objective optimization to maximize midsize
passing and throughput using NSGA–II algorithm is found
to execute ~10 times faster using the ML models rather
than the design space data points. The ML models also
serve as non–linear interpolation equations, hence allowing
intermediate values to be selected between the design space
data points.
The optimal solution for the maximization of through-
put and maximization of normalized midsize percentage
passing and minimization of specific power are obtained
using the NSGA II algorithm. Figure 7 shows the pareto
front of the throughput vs midsize percentage passing space
for three different grades of ore based on their hardness.
CONCLUSIONS
Unlike previous grinding models that focused on PSD or
power draw separately, a novel grinding model combining
a population balance model for product PSD and semi-
empirical models for mill holdup and power draw was
proposed. A semi-empirical model for mill holdup was
developed using published experimental data.
Holdup was found to be linearly proportional to the
slurry flow rate in some previous works and to square root
of the slurry flow rate in others. After testing various for-
mulations, a representation of holdup as a function of
scaled flow rate, Q' =Slurry flow rate/Mill volume, showed
good agreement with published data. It was observed that
for 0.1Q'2, holdup varies linearly with Q' and for Q'8,
holdup varies as a square root of Q'. This holdup model
facilitates estimation of mean residence time, τ, as well as
slurry filling, U which are used as inputs to the PSD and
the power draw models.
The grinding model was validated with the published
experimental and the observed accuracy was satisfactory.
ML models were developed for midsize passing and
mill throughput using SVR with the synthetic data gener-
ated by simulating a typical closed circuit grinding opera-
tion. Multi-objective optimization was carried out using
these models and optimal solutions for three different cases
Figure 7. Optimization results for midsize passing vs throughput for ball filling, J=0.3. Lines represent the pareto front
obtained through optimization and the points represent the operating space used for optimization
The trained SVR models are used for optimization of a
simulated grinding circuit using a non–dominated sorting
genetic algorithm (NSGA–II). The NSGA–II utilizes the
elite strategy, non–dominated sorting and crowding dis-
tance comparison to generate better populations at every
iteration that are non–dominated in nature and are evenly
distributed in the pareto front. For studying the variation
in optimal solutions due to variation in feed and operat-
ing conditions, three different cases of ore grades (Lee et
al., 2020) as well as three different cases of ball filling are
studied. Multi–objective optimization to maximize midsize
passing and throughput using NSGA–II algorithm is found
to execute ~10 times faster using the ML models rather
than the design space data points. The ML models also
serve as non–linear interpolation equations, hence allowing
intermediate values to be selected between the design space
data points.
The optimal solution for the maximization of through-
put and maximization of normalized midsize percentage
passing and minimization of specific power are obtained
using the NSGA II algorithm. Figure 7 shows the pareto
front of the throughput vs midsize percentage passing space
for three different grades of ore based on their hardness.
CONCLUSIONS
Unlike previous grinding models that focused on PSD or
power draw separately, a novel grinding model combining
a population balance model for product PSD and semi-
empirical models for mill holdup and power draw was
proposed. A semi-empirical model for mill holdup was
developed using published experimental data.
Holdup was found to be linearly proportional to the
slurry flow rate in some previous works and to square root
of the slurry flow rate in others. After testing various for-
mulations, a representation of holdup as a function of
scaled flow rate, Q' =Slurry flow rate/Mill volume, showed
good agreement with published data. It was observed that
for 0.1Q'2, holdup varies linearly with Q' and for Q'8,
holdup varies as a square root of Q'. This holdup model
facilitates estimation of mean residence time, τ, as well as
slurry filling, U which are used as inputs to the PSD and
the power draw models.
The grinding model was validated with the published
experimental and the observed accuracy was satisfactory.
ML models were developed for midsize passing and
mill throughput using SVR with the synthetic data gener-
ated by simulating a typical closed circuit grinding opera-
tion. Multi-objective optimization was carried out using
these models and optimal solutions for three different cases
Figure 7. Optimization results for midsize passing vs throughput for ball filling, J=0.3. Lines represent the pareto front
obtained through optimization and the points represent the operating space used for optimization