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!