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Robust approach for on-lineparticle size estimation in a wet
Hugo Garcs H. and Daniel Sbrbaro H.
Universidad de Concepcin, Chile.
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Outline
Introduction.
Grinding database analysis.
Robust approach for particle size estimtion.
Performance.
Conclusions and final remarks.
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Introduction
Virtual sensor performs on-line particle size estimationbased on grinding operational variables: fresh ore feedrate m [ton/hour], sump water rate s [m3/hour],
cyclone feed density d [gr/cc] and pressure at thecyclone battery p [kg/cm2].
Virtual sensor can overcome several problems in
n ustr a p ants operat on, suc as: Real sensor is out of service due to failure or maintenance.
Intrinsic delay measuring complex process variable(chromatograph, PSA).
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Grinding database analysis
Outlier: inconsistent measurement with most
of the data set.
Outliers detection based on Hampel Identifierin target variable of grinding plant: percentage
. .
2
1+= imed yy
( )||. medy yymedianMAD = 48261
y
med
MAD
ykyky
=)()(~
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Grinding database analysis
medy
+med
y
medy
Outliers detection results in grinding target variable based on Hampel Identifier
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Robust approach for particle size
estimation
Outliers detection procedure assigns a state to
each measurement. This information is usedin a robust model where each category has an
- .
)()()( kkkyT
ii =
T
iiiiiik ][)(
43210 = : parameters vector
Tkpkdkslkmk ])(~)(~)(~)(~[)( = 1 : measurements vector
(robust scaled with Hampel Id.)
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Robust approach for particle size
estimation
)()()( kkkyT =11
)(k
)( ky)()()( kkkyT = 22
)()()( kkkyT =33
)( kf65
)( kf65)(
ky
)(ke
Robust model for online estimation of particle size in grinding plant
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Robust approach for particle size
estimation
Decision block compares of i-th inner
models to select final output.
Decision block realize selection according to
)( kyi
detection procedure.
Example: if and performs an
estimation in normal caterogy, then finalparticle size estimation is provided by .
)(),( kyky 21 )( ky3
)( ky2
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Robust approach for particle size
estimation
+>med
yky )(1
+> medyky )(2
+> medyky )(3
+
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Performance
Particle size estimation in validation data set, robust and normal approach
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Performance
MSE [%] R [0/1]
Performance indexes validation data set
o us mo e . .
Conventional model 6.5788 0.7698
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Conclusions and final remarks Particle size estimation, i.e: virtual sensing, backup and replace original
PSA real sensor for 12 hours (720 samples at 1 minute rate), keepingavailable critical process variable in grinding plant for data based taskssuch as real time optimization and/or process monitoring.
In order to not discard outlier measurements corresponding to abnormaloperational conditions, a robust approach with linear sub-models and finaldecision block is developed.
Outliers detection procedure based on Hampel Identifier labelsmeasurements in different categories to train different linear models,mprov ng per ormance respec o conven ona near mo e n va a on
data set. Further work will consider a robust model based on neural networks or
support vector machines to take into account nonlinear interactionsbetween operational variables and will integrate outliersdetection/training algorithms for the different model structures.
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Thanks for your attention