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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