942 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Figure 15 demonstrates that bubble characteristics
(froth velocity) interact with reagents (ZnSO4), with feed
Cu at 0.16%, feed flowrate at 274 TPH, feed Pb at 2.19%,
Cu rougher 1 froth velocity at 8.3 cm/s, dichromate addi-
tion at 147 ccm, and Pb cleaner 1 bubble texture at 0.42.
Figure 15 shows a saddle point, where the recovery
increases by either decreasing ZnSO4 and increasing froth
velocity or increasing ZnSO4 and decreasing froth velocity.
In a summary, neural networks can often find optimal
models for any given training set, given enough nodes, but
are correspondingly easy to overfit. Traditional tests like
ANOVA or T-tests are difficult to apply to neural networks.
Decision trees present similar difficulties but can be easier
to interpret. Still, both neural networks and decision trees
can provide excellent insight into the overall behavior of
complex flotation.
Table 8. Model Parameter Estimates
Term Estimate Prob |t| VIF
Intercept 89.26 0.0001 .
Assays|Mill Feed Copper Scaled –8.58 0.0001 3.4
Assays|Mill Feed Flowrate –0.01 0.5449 3.4
Assays|Mill Feed Lead Scaled 1.29 0.0001 6.9
Copper\Rougher 1|Froth Velocity –0.20 0.0001 3.8
Lead\Circuit ZnSO4 Flowrate|Flowrate 0.003 0.001 7.4
Lead\Cleaner 2 Bichromate Flowrate|Flowrate –0.02 0.0001 5.1
Lead\Cleaner 1|Bubble Texture –3.71 0.0461 2.4
Lead\Cleaner 1|Froth Velocity 0.24 0.047 8.1
(Assays|Mill Feed Flowrate–259.713)*(Copper\Rougher 1|Froth Velocity–13.8332) 0.01 0.0001 2.3
(Assays|Mill Feed Flowrate–259.713)*(Lead\Circuit ZnSO4 Flowrate|Flowrate–3487.43) 0.00003 0.0121 2.8
(Assays|Mill Feed Copper Scaled–0.18341)*(Lead\Cleaner 2 Bichromate
Flowrate|Flowrate–115.054)
–0.13 0.0001 4.2
(Lead\Circuit ZnSO4 Flowrate|Flowrate–3487.43)*(Lead\Cleaner 2 Bichromate
Flowrate|Flowrate–115.054)
–5.4e–5 0.004 2.3
(Lead\Cleaner 2 Bichromate Flowrate|Flowrate–115.054)*(Lead\Cleaner 2 Bichromate
Flowrate|Flowrate–115.054)
–0.000349 0.0001 5.7
(Lead\Cleaner 1|Bubble Texture–0.42369)*(Lead\Cleaner 1|Bubble Texture–0.42369) 133.89 0.0004 2.5
(Lead\Circuit ZnSO4 Flowrate|Flowrate–3487.43)*(Lead\Cleaner 1|Froth
Velocity–10.8551)
–0.0028 0.0057 6.0
(Lead\Cleaner 2 Bichromate Flowrate|Flowrate–115.054)*(Lead\Cleaner 1|Froth
Velocity–10.8551)
–0.0046 0.0125 2.1
Figure 14. Impact of mill feed rate and dichromate addition
on the Pb recovery
Figure 15. Impact of ZnSO4 and Pb cleaner 1 froth velocity
on Pb recovery
Figure 15 demonstrates that bubble characteristics
(froth velocity) interact with reagents (ZnSO4), with feed
Cu at 0.16%, feed flowrate at 274 TPH, feed Pb at 2.19%,
Cu rougher 1 froth velocity at 8.3 cm/s, dichromate addi-
tion at 147 ccm, and Pb cleaner 1 bubble texture at 0.42.
Figure 15 shows a saddle point, where the recovery
increases by either decreasing ZnSO4 and increasing froth
velocity or increasing ZnSO4 and decreasing froth velocity.
In a summary, neural networks can often find optimal
models for any given training set, given enough nodes, but
are correspondingly easy to overfit. Traditional tests like
ANOVA or T-tests are difficult to apply to neural networks.
Decision trees present similar difficulties but can be easier
to interpret. Still, both neural networks and decision trees
can provide excellent insight into the overall behavior of
complex flotation.
Table 8. Model Parameter Estimates
Term Estimate Prob |t| VIF
Intercept 89.26 0.0001 .
Assays|Mill Feed Copper Scaled –8.58 0.0001 3.4
Assays|Mill Feed Flowrate –0.01 0.5449 3.4
Assays|Mill Feed Lead Scaled 1.29 0.0001 6.9
Copper\Rougher 1|Froth Velocity –0.20 0.0001 3.8
Lead\Circuit ZnSO4 Flowrate|Flowrate 0.003 0.001 7.4
Lead\Cleaner 2 Bichromate Flowrate|Flowrate –0.02 0.0001 5.1
Lead\Cleaner 1|Bubble Texture –3.71 0.0461 2.4
Lead\Cleaner 1|Froth Velocity 0.24 0.047 8.1
(Assays|Mill Feed Flowrate–259.713)*(Copper\Rougher 1|Froth Velocity–13.8332) 0.01 0.0001 2.3
(Assays|Mill Feed Flowrate–259.713)*(Lead\Circuit ZnSO4 Flowrate|Flowrate–3487.43) 0.00003 0.0121 2.8
(Assays|Mill Feed Copper Scaled–0.18341)*(Lead\Cleaner 2 Bichromate
Flowrate|Flowrate–115.054)
–0.13 0.0001 4.2
(Lead\Circuit ZnSO4 Flowrate|Flowrate–3487.43)*(Lead\Cleaner 2 Bichromate
Flowrate|Flowrate–115.054)
–5.4e–5 0.004 2.3
(Lead\Cleaner 2 Bichromate Flowrate|Flowrate–115.054)*(Lead\Cleaner 2 Bichromate
Flowrate|Flowrate–115.054)
–0.000349 0.0001 5.7
(Lead\Cleaner 1|Bubble Texture–0.42369)*(Lead\Cleaner 1|Bubble Texture–0.42369) 133.89 0.0004 2.5
(Lead\Circuit ZnSO4 Flowrate|Flowrate–3487.43)*(Lead\Cleaner 1|Froth
Velocity–10.8551)
–0.0028 0.0057 6.0
(Lead\Cleaner 2 Bichromate Flowrate|Flowrate–115.054)*(Lead\Cleaner 1|Froth
Velocity–10.8551)
–0.0046 0.0125 2.1
Figure 14. Impact of mill feed rate and dichromate addition
on the Pb recovery
Figure 15. Impact of ZnSO4 and Pb cleaner 1 froth velocity
on Pb recovery