Sin ttulo de diapositiva

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PLS a versatile tool for industrial process
improvement
Alberto Ferrer, José M. Prats, Daniel Aguado,
Santiago Vidal-Puig
Multivariate Statistical Engineering Research
Group Dpt. Applied Statistics, O.R. Quality
Technical University of Valencia (Spain)
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Characteristics of modern data
Information??
Low rank Highly collinear Missing values Low
S/N
Help me!
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How to adapt to data-rich environments?
Multivariate projection methods PCA, PLS
Process is driven by a few underlying common
cause events
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Partial Least Squares Regression (PLSR)

• Predictive Model using latent variables
• T XW
• X TPT E
• U TB H
• Y UCT F XB F

X
T
X
T
PT
E


Maximize cov(ta,ua)r(ta,ua)?(ta)?(ua)
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PLS a versatile tool
PLS
Data mining tool
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PLS - soft sensorWaste water treatment plant
(WWTP)
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PLS - soft sensor

• Modern WWTPs collect large number of on-line
  measurements

Sensors for measuring process variables
Sensors for measuring key quality variables
Not usually available in small WWTPs
Do not directly provide information on process
performance
Develop a Soft-sensor
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PLS - soft sensor

• Case study SBR operated for EBPR

Process variables pH, dissolved oxygen (DO)
electric conductivity (Cond), oxidation reduction
potential (ORP), and temperature (Temp).
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PLS - soft sensor

• Data structure collected information

- Electronic sensors
- Quality control laboratory
x1 pH x2 Oxidation reduction potential x3
Conductivity x4 Dissolved Oxygen x5
Temperature
y1 Phosphorus concentration y2 Potassium
concentration y3 Magnesium concentration
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PLS - soft sensor

• Predictive model building

- Batch-wise unfolding correlation structure
modelling
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x1
x2
x1
Batch
x2
I
Built in by design.
Unfolded data matrices
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PLS - soft sensor

• Predictive model building

- 15 batches for model fitting and 5 for
validation
- A PLS-2 model was built (1700 X variables, 54 Y
variables)
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PLS - soft sensor

• Good accuracy of the developed model

- Observed versus predicted
Phosphorus
Potassium
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PLS - soft sensor

• Model application
• Drawback ? the model requires the entire
  trajectories of the explicative variables to be
  known. How can on-line predictions be obtained?

Evolving batch
Sol. imputation methods to fill in the future
observations (Missing data TSR (Arteaga Ferrer
2002))
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PLS - soft sensor

• Practical advantages of the predictive model

- Provides on-line accurate predictions for the 3
quality trajectories from the very beginning of
the batch (10 total time)
- Uses input data from inexpensive and
low-maintenance sensors installed in the reactor
- Can handle missing data
- By monitoring the residuals it is possible
Outlier detection ? avoiding dangerous
extrapolations
Model update assessment ? adapting process
changes
Cost-effective tool
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PLS-Discriminant Analysisfault detection on
image data
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PLS-Discriminant Analysisfault detection on
image data

• Methods
• Human inspection not feasible in practice low
  reliable.
• Traditional image analysis of the spectral or
  textural properties, extracting characteristics
  from the image subjective.

Multivariate image analysis (MIA) integrating
both textural and spectral information of the
pixels PLS-DA

• To capture the pixels linked to a specific
  defect Score Plot from PCA
• To fit PLS-DA models based on dummy images
  derived from these
• PCA based MIA models

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PLS discriminant analysis

• For each image...

• Procedure
• For each image...

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PLS discriminant analysis

• Procedure (Red channel)

• For each of the three channels, stack the
  shifted images, saving the spatial information
  related to the neighbouring pixels to a specific
  one, and creating a 3-way OOV data structure.

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PLS discriminant analysis

• Procedure

• By stacking the Unfolded Textural Image of each
  colour channel the 3-way spectro-textural
  internal data structure is obtained.

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PLS discriminant analysis

• Procedure selecting the defects to be modelled

Image defining the disease
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PLS discriminant analysis

• Procedure creating the dummy images associated

Image defining the disease
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PLS discriminant analysis

• Procedure

New image (not necessary the same dimensions)
Selection in the same Score Space, but aligning
Good results, but one model for each disease
(time consuming) and possibility of superposing
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PLS discriminant analysis

• Procedure

Whereas using PCA model requires searching for
discriminating latent variables
... the PLS-DA model directly points out the
directions that best discriminate between the
defects of interest
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PLS discriminant analysis
Predicted Y image from y1 (not affected)

• Procedure

MIA strategy
PLS-DA
Inverted predicted Y image from y2 (affected)
X
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PLS discriminant analysis

• Procedure

Error
Real
Dummies after thresholding
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PLS discriminant analysis

• Procedure

we can appreciate the difference between the
prediction carried out by each of the classes
Repeating the procedure for a new image, and
applying the corresponding thresholds to each
predicted images
Affected area (pits) 6.61
Affected area (non sane) 25.64
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PLS discriminant analysis

• Procedure

Combining both types of predictions, it is
possible to create a new image describing all the
events present in the image
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PLS discriminant analysis

• Conclusions

A combination of the well known selection of
characteristics approach based on MIA has been
applied together with a PLS-DA model, in order to
clearly isolate the pixels related to one disease
that affects the oranges. This combination has
emerged as an efficient way for computing,
locating and displaying the pixels related to the
disease. Advantages over the MIA PCA based
selection of characteristics, not only in terms
of time, but also in terms of discrimination
capabilities (this model is precisely focused on
the segregation of the different types of
information appearing in a data set but, however,
it seems very interesting to show its potential
in multivariate image analysis).
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PLS - Time Seriesmodelling dynamic systems
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PLS-time series goal
The objective of this case study is to present
the capabilities of Partial Least Squares Time
Series (PLS-TS) methodology for the estimation of
the transfer function (TF) model of an industrial
polymerisation process (for controller design)
Settling time of the process
FIR model
Y Output
X Input
Process dynamics
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PLS-TS process description
The case study involves a commercial-scale
petrochemical process that produces large volumes
of a polymer (high-density polyethylene). The
variables we have considered are Data from
several manufacturing periods are available
2 INPUTS VARIABLES Temperature Tt Ethylene Flow
Et
2 OUTPUTS VARIABLES Melt Index MIt Productivity
Index APREt
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How to model process dynamics with PLS?
by expanding X matrix with lagged variables
...
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PROCESS DESCRIPTION
Three manufacturing periods were investigated.
APREt

• Melt Index (MIt) is sampled every 2 hours at
  reactors outlet
• and measured at laboratory

• Productivity Index (APREt) is worked out by
  energy balance every 2 hours

• Temperature and Ethylene Flows (Tt-1,Et-1) are
  measured as the average of reactors temperatures
  and ethylene flows during the 2 hours before t

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PLS-TS phases of model building

• Initial exploratory analysis of data

• Study of the nature of the series and their
  dynamics.
• Determination of number of differences to get
  stationary series and
• number of lags to consider in the formulation
  of the model
• Process fault detection (residual and score plots
  from preliminary
• PLS models).

• Pre-treatment of data

• Original matrix of input variables X is expanded
  with new lagged
• variables for every input.

• Transfer Function Model identification

- A PLS-TS model is estimated for every output
variable. PLS Coefficient Plots and Loading Plots
useful for pruning.

• Final model estimation

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PLS-TS model building process
INITIAL DATA SET 2 variables X 2 variables Y
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FIR vs ARIMAX models
ARIMAX models
FIR models
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PLS-TS exploratory data analysis
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PLS-TS exploratory data analysis fault
diagnosis via contribution plots
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PLS-TSTransfer function model identification
F.I.R.
PLS Regression Coefficients Plot
The PLS regression coefficients plot
facilitates the identification of the transfer
function. We can use it combined with the
Box-Jenkins methodology
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PLS Model Estimation
DifAPRE MODEL Lag Selection
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PLS Model Estimation
DifMI MODEL Lag Selection
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PLS-TS conclusions
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PLS a versatile tool for industrial process
improvement
aferrer_at_eio.upv.es
Thanks for your attention!