Transcript Slide 1

Multivariate Statistical Monitoring And
Fault Diagnosis Of Two-Dimensional
Dynamic Batch Processes
YUAN YAO
DEPARTMENT OF CHEMICAL ENGINEERING
NATIONAL TSING HUA UNIVERSITY
26/10/2012
Multivariate Statistical
Monitoring of Batch Processes
2
PART 1
07:21
Batch Process
3
 Definition
 A process that leads to the production of finite quantities of
material by subjecting quantities of materials to an ordered set
of processing activities over a finite period of time using one or
more pieces of equipment (American National Standard)
 Applications
 Pharmaceuticals, polymers, biochemicals, food products and
specialty chemicals…
07:21
Why Batch Process Monitoring
4
 Requirement from global competition
 Consistent and high quality
 Operation safety
 Environmental guidelines
 Minimal energy and raw materials consumption
 To achieve this, process performance must be
monitored in real-time
07:21
Multivariate Statistical Process Monitoring
5
Normal
Operation
Data
Database
Process Data
Temp, Stroke,
Velocity,
Pressure, …
MSPC
Model
Current Batch Data
Online Monitoring and Fault
Diagnosis
Reaction - Score 1
5
4
3
2
Score 1
Feedback Control
and Optimization
-3 std. dev.
Average Batch
3 std. dev.
02p7-031
1
0
-1
-2
-3
0
100
200
300
400
500
Time (30 second intervals)
07:21
Multivariate Statistical Projection Techniques
6
 Multivariate statistical projection techniques
 Transformation of process variables into latent variables
Orthogonality
 Dimension reduction


Extraction of process information and knowledge
 The basic tools
 Principal component analysis (PCA)
 Partial least squares (PLS)
07:21
PCA and PLS
7
 PCA
 Coordinates transformation
 Dealing with single data set (I or O)
 Extraction of main variances
12
t1
11.5
p2=(0.707,-0.707)
11
t2
p1=(0.707,0.707)
10.5
 PLS
 Emphasize the covariance
between two data sets (I & O)
10
9.5
9
8.5
8
8
X
T
U
8.5
9
9.5
10
10.5
11
11.5
12
12.5
Y
07:21
PCA Decomposition
8
07:21
PCA-Based Monitoring and Diagnosis
9
 Multivariate Statistics
 SPE:
 Independence of
 T2

residuals
Multivariate normal
distribution of scores
Original data space
X
Score space
TPT
+
Residual space
E
T2
SPE
 Typical monitoring and
diagnosis charts
 PLS-based monitoring
can be conducted in
similar way
Kourti (2006)
07:21
PCA Score Plot
10
Kourti et al. (1996)
Hodouin et al. (1993)
07:21
PCA loading Plot
11
Lu et al. (2004)
07:21
Normalization
12
 Removing means and equalizing variances
xi , j 
xi , j  x j
sj
(i  1,
, n; j  1,
, m)
 Benefits
 Eliminating the effects of variable units and measuring ranges
 Emphasize correlations among variables
07:21
An Example of Batch Process: Injection Molding
13
A cycle
Mold Close
Filling
Packing Holding
Plastication
Mold Open
Cooling
M
07:21
Batch Process Data Matrix
14
X (I  J  K )
batch  variable  time
07:21
Batch-wise Unfolding and Normalization
15
K
Batches
1
I
1
Variables
J
J
1
T1
JK
T2
T3
......
I
Nomikos and MacGregor (1994, 1995)
07:21
Time-wise Unfolding and Normalization
16
1
K
J
B1
K
B2
Batches
1
B3
1
Variables
J
IK
....
I
Wold et al. (1998)
07:21
Data From Penicillin Fermentation
17
Variable 1
Variable 2
8.86
Variable 3
102
14
8.855
12
100
8.85
10
98
8.845
Raw
8
8.84
96
6
8.835
94
4
8.83
92
2
8.825
8.82
0
50
100
150
200
250
300
350
400
450
90
0
50
100
150
200
250
300
350
400
450
2.5
0
0
50
100
150
200
250
300
350
400
450
1.5
2
0.58
1
1.5
1
0.5
0.5
Batch-wise Normalized
0.575
0
0
-0.5
0.57
-0.5
-1
-1.5
-1
-2
0.565
0
50
100
150
200
250
300
350
400
450
0.62
0.61
-2.5
0
50
100
150
200
250
300
350
400
450
1
3
0.5
2
50
100
150
200
250
300
350
400
450
50
100
150
200
250
300
350
400
450
0
1
0.59
0
4
0.6
Time-wise Normalized
-1.5
-0.5
0
-1
0.58
-1
-1.5
-2
0.57
-2
-3
0.56
-2.5
-4
0.55
0.54
-3
-5
0
50
100
150
200
250
300
350
400
450
-6
0
50
100
150
200
250
300
350
400
450
-3.5
0
07:21
After Batch-wise Normalization
18
Normal Probability Plot
0.999
0.997
Raw Data
0.99
0.98
0.99
0.98
0.95
0.90
0.95
0.90
0.75
0.75
Probability
Probability
Normal Probability Plot
0.999
0.997
0.50
0.25
0.50
0.25
0.10
0.05
0.10
0.05
0.02
0.01
0.02
0.01
0.003
0.001
0.003
0.001
0.5
1
1.5
Data
2
-1.5
1
1
0.8
0.8
Raw Data
0.6
0.4
0.2
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1
-1
20
40
60
Time lag
80
-1
-0.5
0
0.5
Data
1
1.5
2
2.5
0.6
0.4
0
Normalized Data
100
Normalized Data
0
20
40
60
80
100
Time lag
07:21
After Time-wise Normalization
19
Normal Probability Plot
0.999
0.997
Raw Data
0.99
0.98
0.99
0.98
0.95
0.90
0.95
0.90
0.75
0.75
Probability
Probability
Normal Probability Plot
0.999
0.997
0.50
0.25
0.50
0.25
0.10
0.05
0.10
0.05
0.02
0.01
0.02
0.01
0.003
0.001
0.003
0.001
0.5
1
1.5
Data
2
Normalized Data
-3
1
1
0.8
0.8
0.6
-2
-1.5
-1
Data
-0.5
0
0.5
1
0.6
Raw Data
0.4
-2.5
0.4
0.2
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1
-1
0
20
40
60
Time lag
80
100
Normalized Data
0
20
40
60
80
100
Time lag
07:21
Multiway PCA (MPCA)
20
 Properties
 PC score vectors contain information on batch-to-batch
variation
 Loading matrices reflect variable behaviour over time
t1
v1, v2, v3, …vJ
t2
tK
v1, v2, v3, …vJ
v1, v2, v3, …vJ
b1
b2
b3
Score vectors
bI
Loading matrices
Nomikos and MacGregor (1994, 1995)
07:21
Online Monitoring Based on MPCA
21
Nomikos and MacGregor (1994)
07:21
Features of MPCA
22
 Focus on between-batch variations
 Nonlinear and dynamic components are reduced or
eliminated
 Batch duration is required to be equalised
 Future measurements need to be estimated
07:21
Features of Time-wise MPCA
23
 Focus on through-batch behaviour
 Non-linear and dynamic components still exist in the
data
 Future measurements estimation is not needed
 Batches can be of different durations
07:21
Two-Stage Approach
24
Unfolding and
normalization
Time, K
Batches, I
t1
 Stage 1: Batch-wise
Variables, J
b1
b2
b3
bI
 Stage 2: rearrangement
b1
b2
bI
t1
t2
t3
tK
t1
t2
t3
tK
t2
v1, v2, …vJ v1, v2, …vJ
tK
v1, v2, …vJ
v1, v2, …vJ
Rearrangement
t1
t2
t3
tK
07:21
Features of The Two-Stage Approach
25
 No estimation of future observations
 No need to equalize batch durations
 Major nonlinear and dynamic components are
reduced or eliminated
07:21
Future Data Estimation in Online Monitoring
26
 Different estimation methods
 Zero deviations


Current deviations


Assume future measurements to operate along the mean trajectory
Assume future measurements to continue at the same level as
present time
Missing data

Fill the future measurements based on variable correlations
Current time
Current
batch
NO future data
t
P(1xJK)
07:21
Batch Trajectory Synchronization
27
 Methods
 Cutting to minimum length
 Missing data
 Indicator variables
 Dynamic time warping (DTW)
 Estimation of batch progress
Rothwell et al. (1998)
Kourti (2003)
Nomikos and MacGregor (1995)
Kassidas et al. (1998)
Undey et al. (2003)
07:21
Dynamic PCA (DPCA)
28
 Conduct PCA on an expanded data matrix
Ku et al. (1995)
07:21
Batch Dynamic PCA (BDPCA)
29
Chen and Liu (2003)
07:21
Multiphase Batch Processes
30
 Motivations




Multiphase is an inherent nature of many batch processes
Each phase has its own underlying characteristics
Process can exhibit significantly different behaviors over different operation
phases
To develop a phase-based model to reflect the inherent process stage nature can
improve process understanding and monitoring efficiency
07:21
Sub-PCA
31
 Recognition of batch processes:
 A batch process can be divided into phase reflected by its
changing process correlation nature
 Despite that the process may be time varying, the correlation
of its variable will be largely similar within the same phase
 Three steps:
 Phase division in terms of process correlation
 Sub-PCA modeling
 Online monitoring
Lu et al. (2004)
07:21
Phase Division and Process Modeling
With Sub-PCA
32
07:21
Phase Division Results of Injection Molding
Process
33
Mold Close
Filling
V/P
Transfer
Packing-holding
Gate
Freeze
Cooling
(Plastication)
Mold Open
07:21
Extensions of Sub-PCA
34
 Phase-based monitoring of uneven-length batches
 Phase-based quality prediction and control
 Phase-based monitoring with transition information
…
07:21
Other Research Efforts
35
 Nonlinearity
 Multiscale
…
07:21
Two-Dimensional Dynamic
Batch Process Monitoring
36
PART 2
07:21
Batch process dynamics monitoring
37
 Batch process dynamics

batch1
batch3
Within batch dynamics
Short term

batch2
Batch-to-batch dynamics

Long term
Slow response variables, variations in materials, batch-wise control law, …
 Existing methods




PCA/PLS + time series model (Wold, 1994)
Dynamic PCA (DPCA) (Ku et al., 1995)
Batch Dynamic PCA/PLS (Chen & Liu, 2002)
MPCA/MPLS + prior batch information
(J.Flores-Cerrillo & MacGregor,2004)
 The long term dynamics are considered by including some prior batch
information
07:21
38
 Two-dimensional dynamic PCA (2D-DPCA)
 Score space monitoring based on 2D-DPCA
 Multiphase 2D batch process monitoring
 Subspace identification for 2D dynamic batch
process statistical monitoring
 Non-Gaussianity
07:21
Research motivations
39
 Features of 2D dynamic batch data
07:21
Two-dimensional dynamic PCA (2D-DPCA)
40
 A fact
 Cross- and 2D autocorrelations (dynamics) information is
reflected by the correlations among current measurements
and lagged variables in region of support (ROS)
 Idea
 Data matrix augmented by including all lagged variables in
ROS
 Performing PCA to extract correlation information (crosscorrelation and 2D dynamics)
 Monitoring based on SPE
 Advantages
 Better monitoring results with more dynamic information
built in the model
 No prediction of future measurement is needed
07:21
Key points of the 2D-DPCA algorithm
41
 Define data matrix as below
 X mT 1,n 1 




X T

m 1, K  r


X



T
X
i ,k




 T

 X I , K  r 
X iT,k  [x1T (i, k ),
, xTj (i, k ),
xTj (i, k )  [ x j (i, k  1),
, xTJ (i, k )],
, x j (i, k  n j (i )),
x j (i  1, k  rj (i  1)),
, x j (i  1, k ),
x j (i  m j , k  rj (i  m j )),
, x j (i  1, k  n j (i  1)),
, x j (i  m j , k ),
, x j (i  m j , k  n j (i  m j ))].
 Perform PCA on this augmented data matrix

Extract simultaneously 2D auto-correlated and cross-correlated
relationships
 Monitoring: SPE



Residual space contains only noise
Satisfy statistical assumption of independence
Control limit of SPE can be estimated by Χ2 distribution
07:21
ROS determination problem
42
 ROS

A subset of lagged variables which can reflect process dynamics
(autocorrelations and lagged cross-correlations) correctly
 Difficulty in ROS determination

Variety of reasons causing batch process dynamics
No uniform shape or order for all batch processes
 Property of the lagged variables in ROS

Reasonable predictor variables which can be regressed to variables’
current values
 Key idea of ROS determination

Similar to the variable selection problem in regression model
building
07:21
ROS autodetermination based on backward
eliminations
43
 Initial ROS selection
 Lagged variables with significant correlations to current
samples


Simple regression method (Gauchi, 1995; Gauchi and Chagnon 2001)
Student t-test for the slope coefficient
 Target proper ROS determination
 Iterative stepwise elimination (ISE) (Boggia et al., 1997)



In each elimination cycle, the independent variable with the minimum
importance is eliminated
An index (e.g., PRESS, AIC) is used as a criterion to evaluate the
regression models built in iterations
The best choice of the ROS
the candidate region
corresponding to the best model
07:21
Procedure of 2D-DPCA with autodetermined
ROS based on backward eliminations
44
Getting normal history data
Initial ROS selection
Proper ROS determination
Getting new process data
2-D-DPCA modeling
Calculating SPE for new data
No
SPE control limits calculation
Out of control?
Yes
Fault diagnosis
07:21
Stepwise regression
45
 Major procedure





The predictor variable with the largest correlation with the criterion
variable enters the equation first, if it can pass the entry requirement
based on statistic significance
The other variable is selected based on the highest partial correlation,
if it can pass the entry requirement
The variables already in the equation are examined for removal
according to the removal criterion
The last two steps are run iteratively
Variable selection ends when no more variables meet entry and
removal criteria
 Advantages


More robust than backward elimination
Get rid of the redundant information provided by the candidate
variables and noises
07:21
ROS
autodetermination
based on forward
iterative stepwise
regressions
46
07:21
Case study I
47
 Batch process model
x1 (i, k )  0.8* x1 (i  1, k )  0.5* x1 (i, k  1)  0.33* x1 (i  1, k  1)  w1
x2 (i, k )  0.44* x2 (i  1, k )  0.67* x2 (i, k  1)  0.11* x2 (i  1, k  1)  w2
x3 (i, k )  0.65* x1 (i, k )  0.35* x2 (i, k )  w3
x4 (i, k )  1.26* x1 (i, k )  0.33* x2 (i, k )  w4
 Residuals of 2D-DPCA model
Residuals
0.02
x1
x2
1
0
-0.02
Auto-correlation
Histogram
0
0
50
100 150 200
-1
0.02
1
0
0
-0.02
0
50
100 150 200
Time
-1
0
10
20
30
0
10
20
Lags
30
07:21
Faults to detect
48
 Fault 1
 Fault 2
Correlation structure change of
x2 from batch 61

x2 (i, k )  0.67* x2 (i  1, k )  0.8* x2 (i, k 1)
0.47* x2 (i  1, k  1)  w2

A small process drift on variable
x2 from batch 61

Adding a signal that increases
slowly with time and batch
5
0
Batch 61
-5
0
5
50
100
150
200
50
100
150
200
50
100
150
200
100
150
200
0
Batch 63
-5
0
5
0
Batch 66
-5
0
5
0
Batch 70
-5
0
50
Time
07:21
Monitoring of correlation structure change
49
 2D-DPCA
 MPCA with prior batch
information
90
-2
10
Faulty
Normal
80
70
-4
Batch 82
SPE
SPE
10
50
-6
10
Batch 61
(Faulty)
Batch 60
(Normal)
40
Batch 62
(Faulty)
-8
10
0
60
100
200
300
400
Batch*Time
500
600
30
0
20
40
Batches
60
80
07:21
Monitoring of small process drift
50
 2D-DPCA
 MPCA with prior batch
information
200
-2
10
Faulty
Normal
-3
150
10
-4
SPE
SPE
10
100
-5
Batch 69
10
50
-6
10
-7
10
0
Batch 60
(Normal)
100
Batch 61
(Faulty)
200
300
400
Batch*Time
Batch 62
(Faulty)
500
600
0
0
20
40
Batches
60
80
07:21
51
 Two-dimensional dynamic PCA (2D-DPCA)
 Score space monitoring based on 2D-DPCA
 Multiphase 2D batch process monitoring
 Subspace identification for 2D dynamic batch
process statistical monitoring
 Non-Gaussianity
07:21
Score information in dynamic batch processes
52
 Discussions on SPE and T2


Concern about different kinds of information
Complementarities of each other
 Risk of not using score information in monitoring

Possible missing alarm
 Scores from dynamic (including 2D dynamic) PCA
model

Not satisfy the statistical assumption for control limits calculation



Autocorrelations
Lagged cross-correlations
Reasonable T2 control limits can not be achieved unless the
dynamics in score values are filtered

2D multivariate autoregressive (AR) score filters


Extracting score dynamics with AR filters
Calculating T2 with filtered scores
07:21
2D multivariate AR score filters
53
 Requirements in filter design
 2D
 Multivariate
 Suited to different dynamic structure in score space
 No existing filter can be directly used
 Filter design
 Score ROS autodetermination
 Filter calculation
tˆ (i, k )   (  a (0, d )t (i, k  d )  
j
J
qd1 ( i )
d1 1
d3 1
pd1
d1
3
d1
3
qd1 ( i  d 2 )

d 2 1 d3  f d1 ( i  d 2 )
ad1 (d 2 , d3 )td1 (i  d 2 , k  d3 ))
t jf (i, k )  t j (i, k )  tˆj (i, k )
07:21
2D-DPCA based modeling and monitoring in
both score and residual SPE
54
Getting normal
history data
ROS selection for
2-D-DPCA
modeling
2-D-DPCA
modeling
Getting new
process data
SPE control limits
calculation
Yes
Calculating SPE
for new data
Calculating T2 for
new data
Out of
?
control
2-D multivariate
AR score filters
design
T2 control limits
calculation based
on filtered scores
Out of
?
control
No
Yes
No
Fault diagnosis
07:21
Case study II
55
 Batch process model
x1 (i, k )  0.8* x1 (i  1, k )  0.5* x1 (i, k  1)  0.33* x1 (i  1, k  1)  w1
x2 (i, k )  0.44* x2 (i  1, k )  0.67* x2 (i, k  1)  0.11* x2 (i  1, k  1)  w2
x3 (i, k )  0.65* x1 (i, k )  0.35* x2 (i, k )  w3
x4 (i, k )  1.26* x1 (i, k )  0.33* x2 (i, k )  w4
 Faults to detect



Fault 1: a correlation structure change in x2 starting from batch 61
Fault 2: a drift starting from batch 61
Fault 3: a drift in the trajectory of x2 only in batch 61


Only affecting SPE in batch 61
Affecting T2 in batch 61 and the following batches
07:21
Dynamics in scores
56
PC1
Lagged cross-correlations
between scores in time directions
PC2
PC3
PC4
PC1
PC2
PC3
PC4
07:21
Dynamics in filtered scores
57
PC1
Lagged cross-correlations
between filtered scores in time
directions
PC2
PC3
PC4
PC1
PC2
PC3
PC4
07:21
Monitoring results of fault 1
58
10
10
T
T
2
2
1
1
0.1
0.1
60
61
60
61
Batch number
Batch number
Unfiltered scores
Filtered scores
07:21
Monitoring results of fault 2
59
10
10
T
2
T
2
1
1
0.1
0.1
60
61
Batch number
Unfiltered scores
60
61
Batch number
Filtered scores
07:21
Monitoring results of fault 3
60
100
2
10
T
SPE
100
10
1
1
60
61
62
63
64
60
61
62
63
Batch number
Batch number
SPE
T2
64
07:21
61
 Two-dimensional dynamic PCA (2D-DPCA)
 Score space monitoring based on 2D-DPCA
 Multiphase 2D batch process monitoring
 Subspace identification for 2D dynamic batch
process statistical monitoring
 Non-Gaussianity
07:21
Multiphase 2D dynamic batch processes
62
 Characteristics
 The structures of variable cross-correlations and 2D dynamics
may change from phase to phase

Not proper to build a single 2D-DPCA model for the whole
batch operation
 Difficulties in phase division and modeling
 To take 2D dynamics into consideration in phase division, the
correlations between current measurements and lagged
measurements in ROS need to be extracted, which means ROS
determination is necessary before phase division
 Without phase division, different phase ROS cannot be
determined
07:21
Batch process data
normalization
Regarding the whole batch
duration as a single phase
ROS determination in
each divided phase
Iterative phase division
Building augmented time-slice data
matrices based on the ROS of each phase
Time-slice 2D-DPCA
modeling
Clustering
New phase(s)
divided?
Yes
No
Transition identification in
each phase
Getting steady phase and
transition information
Major steps of multiphase
2D-DPCA modeling
Phase and transition 2DDPCA modeling
Calculation of SPE and T2
control limits for monitoring
63
07:21
Case study III
64
 A two-phase 2D dynamic batch process
 Phase I
x1 (i, k )  0.8* x1 (i, k  1)  0.3* x1 (i  1, k )  0.5* x1 (i 1, k  1)  w1 (i, k )
x2 (i, k )  0.9* x2 (i, k  1)  w2 (i, k )
x3 (i, k )  0.4* x3 (i, k  1)  0.25* x1 (i, k )  0.35* x2 (i, k )  w3 (i, k )

Phase 2
x1 (i, k )  0.8* x1 (i, k  1)  0.3* x1 (i  1, k )  0.5* x1 (i  1, k  1)  w1 (i, k )
x2 (i, k )  0.67* x2 (i, k  1)  0.11* x2 (i  1, k )  0.44* x2 (i  1, k  1)  w2 (i, k )
x3 (i, k )  0.4* x3 (i, k  1)  0.25* x1 (i, k )  0.35* x2 (i, k )  w3 (i, k )
 Fault to detect
 A small drift in the trajectories of x2 starting from batch 81
07:21
Monitoring results
65
10
Faulty
Normal
Faulty
Normal
1
SPE
SPE
1
0.1
0.1
0.01
80
81
Batch number
Multiphase 2D-DPCA
80
81
Batch number
Regular 2D-DPCA
07:21
66
 Two-dimensional dynamic PCA (2D-DPCA)
 Score space monitoring based on 2D-DPCA
 Multiphase 2D batch process monitoring
 Subspace identification for 2D dynamic batch
process statistical monitoring
 Non-Gaussianity
07:21
Motivations
67
 Shortcoming of lagged variable model structure

Too many variables which make the contribution plots messy and
hard to read
 Solutions


Reducing the number of variables
Summarizing the process dynamics information with a small number
of state variables (subspace identification (SI)) instead of the lagged
variables in ROS
Extracting variable correlations and dynamics for process
monitoring
Building 2D-DPCA model using the state variables and the current
variables
07:21
SI-2D-DPCA
68
 Canonical variate analysis (CVA) for SI
 An application of canonical correlation analysis (CCA) on SI



Extracting the relationship between past (lagged measurements in ROS)
and future (current measurements)
Finding the sets of orthogonal canonical latent variables in both data
spaces which are most correlated
Achieving good prediction accuracy using fewest latent variables
 SI-based 2D-DPCA
 Applying 2D-DPCA on an expanded matrix


Z  [Y
X]
Y: matrix of process data
X: matrix of states
07:21
Case study V
69
 Batch process model
x1 (i, k )  0.8* x1 (i  1, k )  0.5* x1 (i, k  1)  0.33* x1 (i  1, k  1)  w1
x2 (i, k )  0.44* x2 (i  1, k )  0.67* x2 (i, k  1)  0.11* x2 (i  1, k  1)  w2
x3 (i, k )  0.65* x1 (i, k )  0.35* x2 (i, k )  w3
x4 (i, k )  1.26* x1 (i, k )  0.33* x2 (i, k )  w4
 Fault
 Variable correlation structure change from the start of batch 61
x2 (i, k )  0.3* x2 (i 1, k )  0.85* x2 (i, k 1)  0.05* x2 (i 1, k 1)  w2
07:21
Subspace identification
70
 CVA
y p  x(i, k )
CCA
y f  [x(i, k 1), x(i 1, k ), x(i 1, k 1)]
 Canonical correlations
◦ r: a vector indicating canonical correlations
0.96875
0.92461
5.3462e
-007
3.6441e- 5.1788e- 1.955e007
008
008
1.955e008
0
0
0
0
0
07:21
Monitoring results
71
10
SPE
SPE
1
0.1
0.1
0.01
60
1
62
61
Batch
2D-DPCA using states variables
60
61
62
Batch
2D-DPCA using lagged variables
07:21
Fault diagnosis results
72
35
x(i,j)
y(i,j)
100
30
y(i,j)
y(i,j-1)
y(i-1,j)
y(i-1,j-1)
SPE contribution
SPE contribution
25
20
15
10
10
1
5
0
y1
1
y2
2
y3
3
y4
4
x1
5
Variable
2D-DPCA using states variables
x2
6
y1
y1 6y2 7y3 y4
y3 y4
y2 3
y1 14
y3 y4
y3 y4
y2 15
y2 11
1 2
4 5
8 y1
9 10
12 13
16
Variable
2D-DPCA using lagged variables
07:21
73
 Two-dimensional dynamic PCA (2D-DPCA)
 Score space monitoring based on 2D-DPCA
 Multiphase 2D batch process monitoring
 Multi-time-scale dynamic PCA
 Subspace identification for 2D dynamic batch
process statistical monitoring
 Non-Gaussianity
07:21
Handling non-Gaussianity
74
 Non-Gaussianity in batch process data
 Dynamics
Break the statistical
 Multiple operation phases
hypothesis of
 …
Gaussian distribution
 Solutions
 Score filter, phase division, …
Or
 Control limits estimation from non-Gaussian information

2D-DPCA + Gaussian mixture model (GMM)
07:21
Case study: penicillin fermentation
75
FC
pH
Acid
Fermenter
Substrate tank
Base
FC
T
Cold water
Hot water
Air
 A two-phase benchmark batch process
 Phase I: batch preculture for biomass growth
 Phase II: fed-batch phase with continuous substrate feed
 Batch-to-batch dynamics
 Disturbances in substrate feed rate vary from batch to batch in a correlated
manner
07:21
Monitoring results of a temperature controller fault
76
 Conventional 2D-DPCA
Normal
Normal
Faulty
Faulty
1000
100
T
2
SPE
10
100
1
10
0.1
3
4
5
Batch
3
5
4
Batch
07:21
Monitoring results of a temperature controller fault
(Cont.)
77
 Non-Gaussian 2D-DPCA
Normal
Faulty
Negative log likelihood
1000
100
10
3
4
5
Batch
07:21
Conclusions
78
 A first study of batch process dynamics in two dimensions
 A first combination of PCA technique and 2D model structure
 ROS autodetermination
 2D multivariate AR score filters for score space monitoring
 An iterative procedure to determine the phase division points and the ROS
for each phase
 Combination of SI technique and 2D-DPCA model structure for clearer
fault diagnosis
 Handling non-Gaussianity
07:21
Prospects
79
 Trajectory alignment on 2D dynamic batch process data
 2D batch process data filtering
 Multiple sampling rate
 Quality prediction for 2D batch processes
 Non-stationary 2D dynamics
 Different scales of batch dynamics in two directions
07:21
Thank you!
80
07:21