938 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Model statistics, given in Table 4, confirm the validity of
the neural network model generated. Mean absolute devia-
tion is significantly smaller than the range of the response
variable, showing that the underlying trend is identified.
Additional hidden nodes would allow higher R2 values, but
this must be balanced against potential overfitting.
In Figure 6, higher Fe grades correlate with more Cu
in the Pb concentrate. However, at low Fe grades the Cu
grade is not associated with increased separation difficulty.
Fe and Cu are often correlated with harder ores, leading to
less efficient grinding and less liberated material.
In Figure 7, higher Pb grades correlate with lower Cu
in the Pb concentrate. More Pb available results in more Pb
in the Pb concentrate, reducing the impact of any lost Cu
on the Pb concentrate. Historically, it is easier to separate
Pb/Cu when the ratio of Pb to Cu in the feed is higher,
clearly shown on the lower right of Figure 7s plot.
Neural network models are strong exploratory tools for
highly multidimensional data, especially when the degree
of complexity is unknown, and can provide insight into
even very complex behaviors in the process.
Decision trees can also evaluate complex data without
requiring underlying assumptions. Figure 9 shows a deci-
sion tree model fit to the same data, with all rows of mill
assay data as x-axis to split, or “prune the tree”. Decision
trees are relatively straightforward to interpret based on
what variables are used to divide the data but have similar
flexibility for complex data as neural networks.
Figure 7. Cu in the Pb Con vs Feed Cu and Feed Pb. In this
contour the Feed Zn and Feed Fe are fixed at 0.56% and
1.69% respectively
Feed Pb
Feed Zn
Feed Cu
Feed Fe
Cu in Pb Conc
Figure 8. Neural network architecture used for Figures 6 and 7. Activation function is tanh
Table 4. Model statistics for neural network model reported
in Figures 6–8
Measures Training Validation
R2 0.46 0.45
RASE 0.52 0.58
Mean Abs Dev 0.34 0.35
-LogLikelihood 367.25 213.74
SSE 129.11 82.63
Sum Freq 485 243
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