2446 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
model fitting, but also a higher parameter sensitivity to the
experimental design, specifically to the selection of the flo-
tation intervals in the batch tests. The rate constant proved
to be remarkably sensitive to the first two flotation intervals
as shown in Figure 4(b). When omitting these 2 datapoints,
the k values presented significant deviations regarding the
baseline. This effect was not observed when removing
time-recovery data from the third flotation interval. The
sensitivity of the Rectangular model was less significant
than that observed with the SFR model, and only notorious
when omitting the first datapoint [Figure 4(d)]. Removing
time-recovery data from the second flotation interval did
not lead to significant changes in the Rectangular f(k)s
with respect to the baseline. The Gamma model presented
higher robustness compared to the two-parameter mod-
els. The location, dispersion, and shapes of the estimated
Gamma f(k)s were not critically modified regarding the
baseline. This result suggests that this model structure is
the most stable of the three to represent R(t) and f(k) for
this dataset. It should be noted that the Gamma model has
an additional parameter, which makes it more sensitive to
overfitting. However, as the number of datapoints was not
comparable to the number of parameters, this phenom-
enon was not observed, which justified the stability of the
f(k) estimations.
Figure 5 shows the variability in the R∞ estimations
when removing one datapoint at a time, and assuming the
SFR [Figure 5(a)], Rectangular [Figure 5(b)] and Gamma
Figure 5. Cumulative distribution functions of the R
∞ estimations: (a) SFR model (b) Rectangular model (c) Gamma model
model fitting, but also a higher parameter sensitivity to the
experimental design, specifically to the selection of the flo-
tation intervals in the batch tests. The rate constant proved
to be remarkably sensitive to the first two flotation intervals
as shown in Figure 4(b). When omitting these 2 datapoints,
the k values presented significant deviations regarding the
baseline. This effect was not observed when removing
time-recovery data from the third flotation interval. The
sensitivity of the Rectangular model was less significant
than that observed with the SFR model, and only notorious
when omitting the first datapoint [Figure 4(d)]. Removing
time-recovery data from the second flotation interval did
not lead to significant changes in the Rectangular f(k)s
with respect to the baseline. The Gamma model presented
higher robustness compared to the two-parameter mod-
els. The location, dispersion, and shapes of the estimated
Gamma f(k)s were not critically modified regarding the
baseline. This result suggests that this model structure is
the most stable of the three to represent R(t) and f(k) for
this dataset. It should be noted that the Gamma model has
an additional parameter, which makes it more sensitive to
overfitting. However, as the number of datapoints was not
comparable to the number of parameters, this phenom-
enon was not observed, which justified the stability of the
f(k) estimations.
Figure 5 shows the variability in the R∞ estimations
when removing one datapoint at a time, and assuming the
SFR [Figure 5(a)], Rectangular [Figure 5(b)] and Gamma
Figure 5. Cumulative distribution functions of the R
∞ estimations: (a) SFR model (b) Rectangular model (c) Gamma model