Post on 25-Sep-2020
Assumption free modelling and monitoring of batch processes
F. Westad
• Background • Batch analysis background • Challenges • CAMO’s approach • Example case • Conclusion
Agenda
Background Batch processes are widely adopted in multiple industries
Batch process control is recipe driven and the operations are not adjusted to
accomodate raw material variations, changes to uncontrolable factors and other circumstances.
Univariate control charts are being used to monitor product characteristics and key process variables thoughout batch processing.
Background The problem with using univariate control charts for seperately monitoring key
variables is that most of the time these variables are not independent of each other and do not necessarily characterise adequately product quality
Product Quality is Multivariate
Process analytical technology has been introduced to monitor critical quality attributes
The output of the process analysers and their multivariate models is being used univariately...
Background
• Multivariate Batch Modelling is important for process development and process understanding: – Are the batches similar? – Can I find the reason why product quality for some batches is outside
the specifications? – Are there any effects from raw materials/season/operator/equipment?
• Multivariate Batch Monitoring is important for several reasons: – Quality control and event detection – Process improvement
• Traditional MVA- Two dimensional matrices (no time dimension)
• Batch MVA- Three dimensional data (time as a third dimension)
MVA and Batch Analysis
Bat
ch (I
)
Process Variables (J)
Variables
Obs
erva
tion
X
Bat
ch (I
)
Process Variables (J)
Batch data Unfolding strategies
1) Direct 3-way analysis
T1 T2 T4 T3 TK
J J J J J
… I
B3
J
K
B2
B1
B4
K
K
K
BI
K
. . .
Bat
ch (
I)
Variables (J)
X
3) Variable wise unfolding
2) Batch wise unfolding
On-line batch modelling & monitoring
• Data for a number of batches are collected • Step 1: Analyse all data (Explorative phase)
– Interpret variable structure; remove outliers – Create model on golden batches – Store model for on-line monitoring
• Step 2: On-line monitoring – Follow batch over time – Detect out-of-spec situations – Determine cause (e.g. residuals and contribution plots) – Take action (process control/feedback system required)
Challenges
The existing batch modelling approaches assume equal lengths of batches:
Same t0 and the same number of time points for each batch
Challenges Multiphase stages exhibit non-linear system dynamics which makes
modelling of phase transitions challenging
Wet product Free water drying
Bound water drying
The problem of unequal batches
• Both 3-way modeling and Time wise unfolding assume – Same number of time points for each batch – Batch process starts at time T0 for each
batch – Process evolves similarly in each batch, and
endpoint is reached at TK
• Workarounds when this is not the case – Replace Time with a Maturity index (e.g. %
conversion) – Use dynamic time warping functions – For 3-way: PARAFAC2
Non-linearity and phase transition When it’s not possible to fit a linear model on a non-linear batch
progression multiple local models can be deployed for each phase
Model 1
Model 2
Model 3
Summary of Challenges ...and the solution • It is not always feasible to control the starting point of a batch
process. • The progress of a chemical reaction or fermentation process
might not develop linearly over time. • In some cases the length and end point of a processing step
will be variable across batches. • CAMO has developed a method to estimate the batch
trajectory and confidence intervals in relative time – Removes dependence of the process time axis – Allows visualization of how the process evolves independent of
sampling rate – Enables plot of individual variables in relative time
CAMO’s approach: the procedure
• Perform PCA on all samples, validate across batch to find the optimal model dimension.
• Search for the optimal grid resolution. • Find samples inside the grids. • Make PCA on samples inside the grids only,
rescale and center from original data. • Estimate mean values for the samples inside
the grids based on the new model. • Update the model with the remaining
samples (if not outliers). Calculate the trajectory and deviation by interpolation.
• Calculate main PCA projection results and trajectory distance, distance to model and relative time.
-2 -1 0 1 2 3 4 5-1.5
-1
-0.5
0
0.5
1
1.5
Scores, PC1S
core
s P
C2
2D Score plot for all batches
Multivariate feature extraction and recalculation of trajectory based on relative time
CAMO’s approach
PCA on golden batches
Using CAMO grid methodology relative time trajectories are
calculated with a new PCA model
Mean trajectory and dynamic SD limits calculated
Visualising individual Process Varaiables
Raw data - Looks like the batches are different ... but in reality: The same trajectory
Monitoring a new batch
• Our approach has a particular advantage in the monitoring phase: – Independent of sampling rate (Even to calibration batches) – Displays batch progress in relative time – Able to model non-linear behaviour
• Details: – Monitor batch over time in score space – Detect out-of-spec situations
• Trajectory model distance • Distance to model • Contribution plot
– Take action (process control/feedback system required)
Monitoring a New Batch
• New Batch (Batch 5) ran outside dynamic control limits for portions of the process.
• Upon relative time drill down, we can see that Pressure and Temp B variables where high at that time point in comparison to golden operations
Variables
Pressure Temp A Temp B
Hot
ellin
g's
T² p
er v
aria
ble
0
1
2
3
4Contributions, sample : b5_104
Relative Time
-10 0 10 20 30 40 50 60 70 80 90 100 110
Mod
el D
ista
nces
, 2 C
ompo
nent
s
0
0.1
0.2
0.3
0.4
Trajectory Model Distances
Example Case
• Chemical reaction • 3 historical batches • Three variables: Reactant, intermediate and product
(predicted online with a model based on Spectroscopic data)
• PCA on the three batches • Projecting one new batch
Line plot Reactant, 3 batches
Consecutive Folded
Correlation loading plot
Not so exiting, but shows how the reaction progresses
2D score plot– historical batches The number of data points per batch does not affect the chemical
time in the 2D score space
Common starting point for all three batches
Common end point
2D score plot Scores, PC1
Does not reflect the relative reaction time!
2D score plot– trajectory model
95 % limit
Start
End
End
Trajectory
Score plot – PC2
In relative time As sample number
Line plot Reactant, 3 batches
Relative time Folded
Trajectory model distance
A one-dimensional representation of the limits in the
2D score plot
Trajectory F-Residuals
Projecting a new batch Score plot with limits (95%)
Independent of the sampling rate and number of points
Line plot of the raw data
In relative time As sample number
Number 55, reaction is finished
No progress
Trajectory model distance
Note how the end of the reaction is visualized correctly due to the relative time axis
Summary • CAMO’s new approach models the relative time. • New batches are monitored in relative time (not projected
as “sample number”) • The individual process variables can also be visualised in
relative time • There is no need to:
– Force the batches to a common length – Warp individual variables – Model against a maturity index (The relative time gives the
maturity directly) • A one-dimensional representation of the batch’s trajectory
with dynamic confidence intervals is a compact way to visualise for the operator
• The experienced user has access to scores, distance to model, residuals and contribution plots
THANK YOU!