Comparison of
Statistical & Mechanistic Models
for Process Monitoring
2013 AIChE Annual Meeting
Paul Nomikos
Senior Research Scientist
Research & Development
E-mail: [email protected]
© INVISTA S.à r.l. November 2013
Data-To-Value Framework
Data
Knowledge
Value
More than
enough!
Modeling
Improvements
Mechanistic
Process
Knowledge
Based
Product
Literature
Sophisticated
Process/Product
Historians
Safety
Statistical
Modeling Principles
Models should be generic, informative, and simple.
A driving force for continuous improvement.
All models are wrong! Some are useful.
Capture effects that are important for the model’s use.
Modeling without well defined goals is like paying taxes!
They never end, and you are never happy with them.
Mechanistic & Statistical Models
Mechanistic
Statistical
Fundamental Principles
Process Variability
State Observes
(Kalman Filters)
PCA, PLS
Hard and Time Consuming
to Develop
Easy to Develop
Few Assumptions
Computational Intensive
Computational Intensive
Problematic Calculations
Simple Calculations
Easy to Maintain
Data Driven
Batch Polymer Reactors
VENT
Heating
INLET
Time
Time
Heating
OUTLET
Time
The Need … and the Problem
VENT
Heating
Real Time Release
of Product on Aim
INLET
Zero Waste
Global Distribution
Heating
OUTLET
Minimum number of batches to detect a quality upset:
Batches
O
Lab
Quality
x
O
O
x
O
O
x
O
O
O
Lab Analysis Delay
Cost : A significant amount of
polymer can be out of
specifications.
O
Action
Pressure
Mechanistic Model
Based on First Principles.
Differential equations that incorporate
kinetics, thermodynamics, etc.
Quality predictions
Time
Temperature
Time
Time
Kalman Filter formulation is optimal
but Engineering Knowledge can
simplify things.
On-line measurements allow for 50%
reduction of the full model.
No need for energy balance.
Process Knowledge allowed to solve
issues of measurement error and
initial conditions.
Mechanistic Model
Quality Batch SIMulator
INPUT
On-line Measurements
Pressure
Vent Rate
Temperature
QBSIM
First Principles
Math-Modeling
OUTPUT
Quality Measurements
Viscosity
Functional Groups
Solvent Loss
Lab Measurements
Lab Quality A
60
55
50
0
20
40
60
80
100
20
40
60
80
100
Lab Quality B
44
42
40
38
0
Batch
Mechanistic Model
Predicted Quality A
Predicted (o) Quality Measurements
55
54
53
Predicted Quality B
52
0
20
40
20
40
60
80
100
60
80
100
43
42
41
40
0
Batch
Mechanistic Model
Quality A
Predicted (o) vs. Actual (*) Quality Measurements
56
54
52
0
20
40
20
40
60
80
100
60
80
100
Quality B
44
42
40
38
0
Batch
Statistical Model – Correlation
Upper limit
Mean
Variable 2
Variable 1
Lower limit
People can normally handle
2 variables at a time …
maybe 1 …
Statistical Model – PCA/PLS
8
Variable 3
First PC
PCA is one of the better
Statistical methods to
summarize multivariate
data for analysis and
monitoring.
6
4
2
Second PC
0
6
6
4
Variable 2
4
2
2
0
0
Variable 1
PLS is an expansion of
PCA for regressing Xdata (process) to Y-data
(product).
Statistical Model – PCA/PLS
Shadow Analogy …
A human image is multidimensional (3D,
color, texture, etc.)
A shadow is a 2D
representation, but it
still contains a lot of
information as long as
the light source is at
the right angle!
Statistical Model – Batch Processes
Variation explained by MPCA
K
Time
Batches
1
Average Trajectory
X
Actual Measurement
from a single batch.
I
MPCA
J
Measurements
New Batch
Q
D-Index = D / Dlimit
Q-Index = Q / Qlimit
Origin +
D
Normal Operating Region
Reduced Space
* T-score
Time
Model of Process Variability
New way to summarize
huge amounts of data.
Simple charts.
Identification of root cause
for process / product upset.
Statistical Model
Principal Component Analysis
INPUT
On-line Measurements
About 20 measurements
around the reactor.
PCA
Statistical
Monitoring
OUTPUT
Process Indexes
Process Behavior is Quality!
D-Index
Q-Index
Lab Measurements
Lab Quality A
60
55
50
0
20
40
60
80
100
20
40
60
80
100
Lab Quality B
44
42
40
38
0
Batch
Statistical Model
SPC Autoclave
D INDEX
3
2
1
0
0
20
40
20
40
60
80
60
80
Q INDEX
3
2
1
0
0
Batch
Statistical Model
Contribution Plots & Comparison Graphs
8
6
4
2
0
TIME
TIME
30
Heating Medium
20
10
0
0
2
4
6
8
VARIABLE
10
12
14
TIME
Process Improvements
Mechanistic Model
Statistical Model
Temperature
TIME
TIME
4
10
Standard Deviation
Solvent Loss Rate
3.5
3
2.5
2
1.5
5
1
0
0.5
TIME
0
TIME
Real Time Release Benefits
Since 1997:
• Production has
increased by 250%
• Yield losses have
decreased by 65%
• Value:
$2MM/yr
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Yield Losses
• Lab Measurements
have decreased by 70%
Expansion II
Production
Expansion I
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Year
RTR
Implementation
Comparison of Mechanistic vs. Statistical Model
Mechanistic - Development
2 years (model) + 2 months (on-line)
Statistical – Development
1 week (model) + 1 month (on-line)
Robust – Easy to Maintain
Data Driven – Maintenance needs effort
Stubborn Witness
In Depth Quality Understanding
Detects and Asses Product Upsets
Allows for Product Standards and Metrics
Mechanistic
Run Time / Batch = 30 sec
Easy to Relate and Maintain
Willing Witness
In Depth Process Understanding
Detects Process Upsets
Allows for Process Standards and Metrics
Statistical
Run Time / Batch = 5 sec
Cultural Shock – Maintenance needs effort
Statistical & Mechanistic Models
Both statistical and mechanistic models offer tremendous advantages
for process improvements and in process/product monitoring and control.
Their proper use allows to analyze and to use productively the information
contained in the enormous amount of on-line process measurements
collected every day in industry.
All models have a common assumption:
Observable events !