-
ce
b
traan
Keywords:Froth otationImage analysisProcess modelingNeural
networks
ed tbe
er/collector dosage and pH) and the froth features (i.e. bubble
size, froth velocity, froth color and frothstability) along with
the metallurgical performances (i.e. copper/mass/water recoveries
and concentrate
ries, frluable
froth appearance. Today, machine vision systems can reliably
and
1996b; Morar et al., 2012; Vanegas and Holtham, 2008).The
primary control objectives of otation circuits are the met-
allurgical factors (i.e. recovery and concentrate grade) (Bergh
andYianatos, 1993). The on-line measurement and estimation of
thesevariables usually requires sophisticated instruments which
areexpensive to purchase and maintain (Liu and MacGregor,
2008).
opment of on-line machine vision based control systems.
2.1. Flotation tests
Laboratory experiments were conducted on a copper sulfrom
Qaleh-Zari copper mine, located in the south-east of Iran. Theore
was rst crushed to 2 mm in a jaw crusher and then furtherground in
a ball mill to d80 = 75 lm. The slurry from the ball millwas
transferred to a 2.5 L laboratory otation cell (see Fig. 1).The
slurry was conditioned with a certain amount of collector(Potassium
Amyl Xanthate) and frother (Aerofroth 65) for 2 and0.5 min,
respectively, just prior to otation.
Corresponding author. Tel.: +60 176343140.E-mail address:
[email protected] (A. Jahedsaravani).
Minerals Engineering 69 (2014) 137145
Contents lists availab
n
elsautomatically measure the froth characteristics from digital
imageswithin a short time and present the results to the operators
or inputthem to process control systems (Aldrich et al., 2010;
Holtham andNguyen, 2002; Kaartinen et al., 2006; Moolman et al.,
1996a, 1995,
2. Experimental
detailshttp://dx.doi.org/10.1016/j.mineng.2014.08.0030892-6875/
2014 The Authors. Published by Elsevier Ltd.This is an open access
article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/3.0/).de oreEffective
control of otation circuits is a difcult task owing to sev-eral
variables involved, unavoidable changes in ore characteristicsand
non-linear and dynamic nature of the process (Bonifazi et
al.,2002).
The otation circuits have traditionally been controlled by
theexperienced plant operators through monitoring changes in
the
1996; Kaartinen et al., 2006; Moolman et al., 1995; Morar et
al.,2012).
This paper presents the ndings of the laboratory test work
con-ducted to evaluate and model the relationship between the
frothvisual features and otation performance parameters. Such
inves-tigations can provide signicant contributions towards the
devel-1. Introduction
In the mineral processing industmon process for separation of
the vagrade) were determined for each run. The relationships
between the froth characteristics and perfor-mance parameters were
successfully modeled using the neural networks. The performance of
the devel-oped models was evaluated by the correlation coefcient
(R) and the root mean square error (RMSE). Theresults indicated
that the copper recovery (RMSE = 2.9; R = 0.9), concentrate grade
(RMSE = 1.07;R = 0.92), mass recovery (RMSE = 1.94; R = 0.94) and
water recovery (RMSE = 3.07; R = 0.95) can be accu-rately predicted
from the extracted surface froth features, which is of central
importance for controlpurposes. 2014 The Authors. Published by
Elsevier Ltd. This is anopenaccess article under the CCBY-NC-ND
license
(http://creativecommons.org/licenses/by-nc-nd/3.0/).
oth otation is a com-from gangue minerals.
Previous studies have shown that the froth visual
characteristicsreect changes in the process conditions and can be
used to predictthe metallurgical factors (Aldrich et al., 1997;
Banford et al., 1998;Bonifazi et al., 2000; Hargrave and Hall,
1997; Hargrave et al.,Available online 28 August 2014performance in
the batch otation of a copper sulde ore is discussed and modeled.
Flotation experi-ments were conducted at a wide range of operating
conditions (i.e. gas ow rate, slurry solids%, froth-Prediction of
the metallurgical performanby image analysis and neural
networks
A. Jahedsaravani a,, M.H. Marhaban a, M. MassinaeiaDepartment of
Electrical & Electronic Engineering, Faculty of Engineering,
Universiti PubMining Engineering Department, University of Birjand,
P.O. Box 97175-376, Birjand, Ir
a r t i c l e i n f o
Article history:Received 1 May 2014Accepted 1 August 2014
a b s t r a c t
It is now generally acceptthis paper, the relationship
Minerals E
journal homepage: www.Malaysia, 43400 UPM Serdang, Selangor,
Malaysia
hat froth appearance is a good indicative of the otation
performance. Intween the process conditions and the froth features
as well as the processs of a batch otation system
le at ScienceDirect
gineering
evier .com/locate /mineng
-
2.2. Image processing
138 A. Jahedsaravani et al. /Minerals Engineering 69 (2014)
137145Fig. 1. Laboratory-scale batch otation cell and video camera
set-up.
Table 1Input and output variables of otation experiments.
Input variables Range Output variables
Gas ow rate (L/min) 51015 Cu recovery (Rcu);concentrate grade
(Gcu)Slurry solids (%) 242832
Frother dosage (ppm) 51015 Mass recovery (Rm);water recovery
(Rw)
Collector dosage (g/t) 203040 Froth bubble size (Db);froth
velocity (Vf)
pH 10.811.512.2 Froth color (Cf);bubble collapse rate (Crb)The
gas owrate was measured by a gas owmeter and manu-ally regulated by
a needle valve. The impeller speed was set at1200 rpm. The froth
depth in the cell was kept at a height of2 cm during the
experiment. After turning on the air, the frothlayer was formed and
the concentrates were collected at timeintervals of 0.5, 2 and 5
min. The froth was allowed to freely over-ow and the concentrates
were analyzed for their water, massrecovery and copper content. The
tailings were ltered and driedand their copper content was
determined.
A video camera was mounted on a metal structure with
anadjustable arm allowing lateral and vertical adjustment (as
shownin Fig. 1). The distance from the top of the cell to the video
cameralens was 20 cm. Lighting was provided by a single 50W
halogenlamp next to the camera, as indicated in Fig. 1. The video
and met-allurgical data collected until 2 min were compared at
differentexperiments. 25 frames per second and 3000 frames per each
testwere captured and analyzed individually and the mean value
ofeach feature was reported for each run (Moolman et al.,
1995).
The otation experiments were conducted at different operat-ing
conditions and concentrate copper grade (Gcu), copper recovery(Rcu
= CGcu/FFcu1), mass recovery (Rm = C/F), water recovery (Rw =
Cw/Cf
2) as well as the froth features were measured and reported
foreach test. The operating conditions and the range of variables
uti-lized in the otation experiments are listed in Table 1.
In view of the large number of variables involved and their
pos-sible interactions, a fractional factorial design was used to
reducethe number of experiments and determine the most
importantphysical and chemical parameters (Bradshaw et al., 1992).
Overall,81 runs were selected to be performed based on a fractional
facto-rial design proposed by Statistica software.
1 C: mass of concentrate (g); F: mass of feed (g); Fcu: feed Cu
grade (%); Gcu:concentrate Cu grade (%).2 Cw: mass of water in
concentrate (g); Cf: mass of water in feed (g).The most signicant
froth properties including bubble size dis-tribution, froth color,
froth velocity and bubble collapse rate wereextracted from the
images in each experiment. Some efcientimage processing algorithms
were developed to quantify these fea-tures. Note that the bubble
size distribution and froth color are sta-tic variables which are
computed from a single image while thefroth speed and bubble
collapse rate are dynamic variables whichare calculated from an
image pair. In practice, both static anddynamic froth features
should be computed in an on-line controlsystem.
2.2.1. Bubble size distributionIt has been demonstrated that the
bubble size (Db)3 at the froth
surface is strongly related to the operating conditions and the
pro-cess performance (Moolman et al., 1996a, 1996b). Various
tech-niques developed for bubble size measurement
includesegmentation (Cipriano et al., 1998; Mehrshad and
Massinaei,2011; Sadr-Kazemi and Cilliers, 1997; Wang et al., 2003),
texturespectrum (Nguyen and Thornton, 1995), wavelet texture
analysis(Liu et al., 2005), modied texture spectrum approach (Lin
et al.,2008) and using interfacial morphological information (Yang
et al.,2009). In practice, each of these methods has its respective
advanta-ges and disadvantages.
In the current study, a marker-based watershed algorithm
wasdeveloped to quantify the bubble size distribution
(Jahedsaravaniet al., 2014). In this method, three sets of markers
were extractedfrom the pre-processed images and then the bubble
edges weredetected using a watershed transform. More details of the
devel-oped algorithm can be found in Jahedsaravani et al. (2014).
Fig. 2shows segmentation results of some sample froth images
takenat different process conditions. The results indicate that the
pro-posed algorithm is capable of accurately detecting bubbles of
dif-ferent sizes, which is often problematic.
2.2.2. Froth velocityFroth velocity (Vf)4 can be quantied by
tracking the bubbles
movement in consecutive frames. Block matching (Forbes,
2007),pixel tracing (Holtham and Nguyen, 2002) and bubble
tracking(Botha et al., 1999) are the most commonly used techniques
to mea-sure the froth velocity. In this work, the block matching
algorithmwas employed to estimate the froth velocity.
Because of varying froth velocity at different parts of the
cellsurface, two parallel blocks were chosen. In this algorithm,
rstlytwo blocks are selected in the rst frame (as source blocks)
andthen neighboring region (i.e. where the target block will
besearched there) is determined in the next frame in accordancewith
the maximum froth displacement recorded in the database(i.e. 20
pixels) (see Fig. 3). Red5 rectangles in Fig. 3 represent thesource
and target blocks in the rst and second frames, whilegreen
rectangle shows the neighboring region. Finally, the sourceblocks
are searched in the dened neighboring region in the sec-ond frame,
assuming the froth movement direction is towardsthe cell lip.
The searching process is a critical stage in a block
matchingalgorithm which may lead to wrong estimation of the bubble
dis-placement. Hence, the similarity between the source and
targetblocks (which is assumed to be in the neighboring region) is
calcu-lated by the two dimensional discrete cross correlation
as:
3 Bubble size (pixel): number of pixels forming diameter of
bubble.4 Froth velocity (pixel/s): rate of bubble displacement in
successive frames per unittime.5 For interpretation of color in
Fig. 3, the reader is referred to the web version of
this article.
-
Fig. 2. Segmentation of froth images by the developed
marker-based watershed algorithm.
First frame Second frame
Fig. 3. Froth velocity measurement by the block matching
algorithm.
A. Jahedsaravani et al. /Minerals Engineering 69 (2014) 137145
139
-
Fig. 4. Quantication of color feature from the froth images.
(For interpretation of the rethis article.)
Table 2Correlation coefcient between color channels and
metallurgical performances.
Metallurgical performances Color channels
R G B
Rcu 0.48 0.45 0.37Gcu 0.6 0.53 0.39Rm 0.62 0.58 0.43Rw 0.65 0.59
0.45
Fig. 5. Bubble collapse algorithm: (a) source block image (s1),
(b) translated block imdisappearing bubbles.
140 A. Jahedsaravani et al. /Minerals Engineering 69 (2014)
137145Ci; j XM1
m0
XN1m0Am;nBm i;n j
0 6 i < 2M 1 & 0 6 j < 2N 1 1
where A and B are the source and target blocks respectively,
the
ferences to colour in this gure legend, the reader is referred
to the web version ofblock size ism n (240 135), and the bar over B
denotes complexconjugation. The maximum value of matrix C shows how
similar thesource and target blocks are. The peak point among the
maximumvalues is an indicator of the froth movement (see Fig. 3).
Sometimesno froth motion is detected between two successive frames
(e.g. at
age (s2), (c) difference image (sb) and (d) number and location
of appearing and
-
Table 3Input and output variables of modeling procedure.
Inputs
Variables Range Mean
Db (pixel) 12.8729.86 17.46 3.5Vf (pixel/s) 38.67250.7 115.35
45.83Cf (intensity) 92.1119.07 106.42 6.9Crb 0.293.05 1.25 0.59
Table 4Correlation matrix between process and image
variables.
Process variables Image variables
Db Vf Cf Crb
Gas ow rate 0.29* 0.68* 0.22* 0.31*
pH 0.64* 0.35* 0.64* 0.65*Frother dosage 0.28* 0.25* 0.10
0.15Collector dosage 0.16 0.15 0.09 0.00Slurry solids% 0.07 0.17
0.09 0.12
* Signicant at 95% condence level.
Table 5Correlation matrix between metallurgical performances and
image variables.
Metallurgical performances Image variables
Db Vf Cf Crb
Rcu 0.71 0.51 0.48 0.23Gcu 0.72 0.76 0.6 0.39Rm 0.69 0.88 0.62
0.43Rw 0.71 0.89 0.65 0.43
Table 6Correlation matrix between image variables.
Image variables Db Vf Cf Crb
Db 1.00 0.56 0.52 0.39Vf 1.00 0.60 0.27Cf 1.00 0.64Crb 1.00
Fig. 6. Correlation between bubble size, froth velocity and
bubble collapse rate.
A. Jahedsaravani et al. /Minerals Engineering 69 (2014) 137145
141low air ow rates), therefore for detecting the peak value at
zeropoint of displacement, the neighboring area is dened from a
pixelahead of the source block, so the width of search area is 21
pixels.
2.2.3. Froth colorIt has been accepted that the froth color
(Cf)6 is an indicative of
the concentrate grade and recovery (i.e. the bubble loading) in
theotation cells (Aldrich et al., 2010). The froth color can be
measuredthrough extraction of the red, green and blue (RGB) values
from colorimages. In the current study, the mean value of the R, G
and B valueswere calculated for quantifying the froth color (see
Fig. 4). Finally,the mean of R channel which has the maximum
correlation withmetallurgical factors was chosen as representative
of froth color(see Table 2) (Kaartinen et al., 2006). To avoid the
effect of reec-tance and shadow, both extremely dark and bright
intensity valueswere excluded from the calculation.
2.2.4. Bubble collapse rateBubble collapse rate (Crb)7 at the
froth surface is an indicator of
froth stability. The froth stability is quantied by analyzing
consec-utive frames and detecting the rate of change in the
appearance ofthe images. In this work, the bubble collapse rate was
calculatedfrom the difference between reectance and shadow created
at thefroth surface, as a result of bubble appearing and
disappearing insuccessive frames, along with the froth velocity
information (seeFig. 5) (Kaartinen et al., 2006). Initially, the
target block in the secondframe is sent back to the source block in
the rst frame. After that,the difference between the rst frame and
the translated frame iscomputed. Finally, the bubble collapse rate
is calculated by applyinga threshold value followed by a size lter
to eliminate the noise.
Each bubble has its own white spot where pixel
intensitiesincrease almost up to 255 (in 8 bit RGB color space).
Bubbleappearing process leads to white spot formation while bubble
dis-appearing process leads to generation of dark regions where
pixelintensities tend to 0. Assume that a bubble is collapsed in
consec-utive frames so the white spot in the rst frame converts to
thedark spot in second frame. If the rst image be subtracted
fromthe second image then a bright region appears in location of
bubblecollision. Hence, the target block (i.e. s2 obtained by the
froth veloc-ity algorithm) was translated back to its rst position
where thesource block (i.e. s1) is. So
s2x s2xd 2
Outputs
Variables Range Mean
Rcu 6795.65 85.91 6.23Gcu 3.7223.24 9.45 3.84Rm 2.825.76 12.82
5.11Rw 1.8445.83 21.19 10.33where s2 and s2 are the translated and
target blocks respectively andd is block displacement obtained by
the froth velocity algorithm.Then, the absolute difference of two
images was computed as
Sb js1 s2j 3where sb is difference image. So, bright regions are
appeared in theresulting image. Two features of the bright regions
distinguish themfrom obtained noise in the difference image.
Actually, the appeared
6 Froth color (intensity): mean of gray level values of red
channel.7 Bubble collapse rate: rate of bubble collapse (appearing
and disappearing
bubbles) in consecutive frames.
-
142 A. Jahedsaravani et al. /Minerals Engineering 69 (2014)
137145bright regions are brighter and bigger than noise so a
thresholdvalue (keeping the bright regions) followed by a size lter
(main-taining the bigger regions) leads to noise elimination and
measuringthe bubble collapse rate.
2.7. Process modeling
The relationship between the image features and
metallurgicalperformances were modeled by the neural networks. The
perfor-mance of the developed models was evaluated by the
correlationcoefcient (R) and the root mean square error (RMSE)
calculatedfrom the following expressions:
R covyi; yivaryi varyi
p 4
RMSE 1n
Xni1
yi yi2vuut 5
where yi and yi are the observed (actual) and model
outputs,respectively.
Fig. 7. Correlation between image variab3. Results and
discussion
3.1. Relationship between process variables, metallurgical
parametersand froth features
Estimation of the metallurgical performances from the
visualfroth features and feedback control of the process by
manipulatingthe operating variables is the ultimate goal of a
machine visionbased control system (Holtham and Nguyen, 2002;
Kaartinenet al., 2006). Input and output variables employed in the
modelingprocedure are given in Table 3. Inputs are the froth
featuresextracted from the images and the outputs are the
metallurgicalfactors measured in each experiment.
The correlation matrix between the process and image variablesis
shown in Table 4. The results suggest that the most
signicantprocess variables in terms of their inuence on the froth
featuresare pH, gas ow rate and frother dosage. An increase in the
gas owrate lead to forming more mobile and unstable froths with
largebubbles owing to enhanced bubble surface area ux.
The pH is a key factor which affects the otation
selectivity.More stable and runny froths with ne bubbles observed
at highpH values can be related to the increased slurry viscosity
as well
les and metallurgical performances.
-
ls Engineering 69 (2014) 137145 143A. Jahedsaravani et al.
/Mineraas to the change in ionic strength of the solution (Tucker
et al.,1994). Furthermore, pH is sometimes as a frother modier
andsome frothers require a higher pH to retain a more lasting
frothingpower (Bulatovic, 2007).
As expected, the froth mobility and stability increase in
thepresence of frothers owing to their role in hindering the
bubblecoalescence.
The correlation matrix between the metallurgical performancesand
image variables are listed in Table 5. It should be noted that
allthe correlations obtained are signicant at 95% condence
level.The results indicate that the bubble size and froth velocity
havethe most signicant correlations with the metallurgical
factors,which is of central importance for on-line control of the
otationcircuits. This is in agreement with plant experience and
some com-mercially available on-line machine vision systems
(Holtham andNguyen, 2002).
The correlationbetween the imagevariables are shown inTable 6and
Fig. 6. All the correlations achieved are signicant at 95%
con-dence level. There is a negative correlation between the bubble
sizeand froth velocity and a positive correlation between the
bubble size
Fig. 8. Relationship between image variables and metallurgical
parameters.
Fig. 9. Structure of the developed feed forward neural network
for Gcu model.
-
ls EnTable 7Performance evaluation of the developed neural
network model.
Metallurgical performances Training data R (correlation
coefcient)
Checking data Testing data
RCu 0.90 0.88 0.9GCu 0.97 0.92 0.92Rm 0.97 0.93 0.94Rw 0.97 0.95
0.95
144 A. Jahedsaravani et al. /Mineraand bubble collapse rate. The
results reveal that ner bubbles aremore stable and move faster than
the coarse bubbles.
Figs. 7 and 8 show the correlation between the froth featuresand
the copper recovery and concentrate grade. The results indi-cate
that ner bubbles and more mobile froths result in increasedcopper
recovery, which causes the secondary effects of an increasein the
mass and water recoveries and a decrease in the
concentrategrade.
The froth color is an indicator of thequantity and
typeofmineralsloaded on the bubbles. There is a negative
correlation between thecolor feature and concentrate grade which is
mainly due to a largeamount of gangue minerals recovered by
entrainment.
Froth stability or bubble collapse rate is a function of
bubbleloading and water hold-up in the froth zone.
More stable froths (with low bubble collapse rate) result in
theincreased recovery and poor concentrate grade owing to
moreentrained gangue particles recovered.
Fig. 10. Observed vs. predicted values of the mRMSE
Total data Training data Checking data Testing data Total
data
0.89 2.52 2.9 2.9 2.640.96 1.09 1.39 1.07 1.130.96 1.26 1.38
1.94 1.40.97 2.51 2.9 3.07 2.66
gineering 69 (2014) 1371453.2. Modeling relationship between
froth features and metallurgicalperformances
Neural network is a robust computational technique for model-ing
of complex non-linear systems which are not easily modeledwith
conventional methods (Fausett, 1994). In this work, a threelayer
feed-forward perceptron neural network was employed formodeling the
process. It should be mentioned that 70% of datawas randomly
selected for training, 15% for checking and 15% fortesting.
Determination of the number of hidden layer neurons (HN) is akey
stage in design of an effective neural network. The
correctselecting the HN is essential to avoid over/under-training.
In otherwords, a large number of neurons applied in the hidden
layer leadto over-training, as the weight of hidden layer neurons
increasesprogressively, and decreasing the generalization
capability of sys-tem while few neurons employed may lead to
insufcient training.
etallurgical performances for testing set.
-
In the current work, the number of hidden layer neurons
wascomputed by a simple technique developed by Doukim et al.(2010).
In this method, at rst, the number of hidden layer neuronsis
computed using the binary search mode (i.e. HN = 1, 2, 4, 8,
etc.)and then several networks with these values are trained and
thebest-tted one (with the lowest RMSE value) is chosen.
Afterwards,a sequential search in the vicinity of HN is performed
in order toobtain the smallest value of HN. This method is repeated
for everyoutput and the best results are reported. HN was chosen as
9, 7, 7
Bonifazi, G., Massacci, P., Meloni, A., 2002. A 3D froth surface
rendering and analysistechnique to characterize otation processes.
Int. J. Miner. Process. 64, 153161.
Botha, C., Weber, D., Van Olst, M., Moolman, D., 1999. A
practical system for real-time on-plant otation froth visual
parameter extraction, Africon, 1999 IEEE.IEEE, 103106.
Bradshaw, D., Upton, A., OConnor, C., 1992. A study of the
pyrite otation efciencyof dithiocarbamates using factorial design
techniques. Miner. Eng. 5, 317329.
Bulatovic, S.M., 2007. Handbook of Flotation Reagents, Elsevier
Science &Technology Books.
Cipriano, A., Guarini, M., Vidal, R., Soto, A., Seplveda, C.,
Mery, D., Briseno, H., 1998.A real time visual sensor for
supervision of otation cells. Miner. Eng. 11, 489499.
A. Jahedsaravani et al. /Minerals Engineering 69 (2014) 137145
145and 8 for Cu/mass/water recovery and Cu grade
models,respectively.
The structure of developed neural network for the
concentrategrade (Gcu) model is presented in Fig. 9. This network
has an inputlayer (with 4 neurons), a hidden layer (with 8 neurons)
and an out-put layer (with 1 neuron).
Assessment factors of the predictive accuracy of the
proposedneural networks models are given in Table 7. Fig. 10 shows
scatterplots of the observed versus predicted values of the
metallurgicalperformances for the testing data. The results show
that the devel-oped neural networks can successfully model the
complicated rela-tionship between the input and output variables.
Furthermore, theprocess performance parameters can be accurately
predicatedfrom the froth visual features. The predicted variables
can be usedas inputs to a feedback control system.
4. Conclusion
In the present paper, the relationship between the froth
imagevariables (as inputs) and the metallurgical factors (as
outputs) ofa batch otation process was successfully modeled using
neuralnetworks. Accurate and reliable algorithms were developed
formeasuring the froth characteristics including the bubble size
dis-tribution, froth color, froth velocity and bubble collapse
rate. Astrong correlation between the froth visual features
particularlythe bubble size and froth velocity and performance
factors weredetected, which is of great signicance for control
purposes. Theimportance of such investigations is that a signicant
contributiontowards the development of a machine vision based
control systemfor industrial applications is made.
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