Data-driven Methods for
Monitoring, Fault Diagnosis,
Control and Optimization
John MacGregor
ProSensus, Inc.
McMaster University
Ali Cinar
Illinois Institute of Technology
Overview
• An overall theme: Making use of historical plant
data
• Empirical models
• Optimization
• Control
John MacGregor
• Monitoring and fault diagnosis
• Fault tolerant control
Ali Cinar
Models
• Mechanistic
– Structure from theory / Parameters from data
– Advantages are well known
– Problems:
• Assumptions that may be poor; theory for many y’s not known
• May not incorporate many of measured variables
• Examples: Y’s or X’s that are images or PAT sensors
• Empirical
– Structure and parameters from data
– Advantages are again well known:
– Problems:
• Structure is often imposed and unrealistic, no interpretability nor
any causality
Latent Variable Models - Concepts
Measured variables
Latent variable space
t2
t1
X
T
Summary statistics: T2 and SPE
(c) 2004-2010, ProSensus, Inc.
Latent variable regression models
Two data matrices:
X and Y
X
X = TPT + E
T
Y
Y = TCT + F
Symmetric in X and Y
• No hypothesized relation between X and Y
• Both X and Y are functions of the latent variables, T
• Choice of what is X and Y depends upon objectives
(c) 2004-2010, ProSensus, Inc.
Why Latent Variable Models?
• Low dimensional models
– Define the space containing most of the information
• Simultaneously model both the X and Y spaces
– Model structure truly determined by the data
– This makes models unique and interpretable
– Provides causal models in the low dimensional LV space
• Allows for active use of the model (eg. optimization)
– Allows for
• easy handling of missing data
• Easy detection of abnormal observations (*)
• Other regression methods (MLR, ANN, etc) do not share these
advantages when using historical data.
– Non-unique, uninterpretable, non-causal
Optimization in Latent Variable Spaces
• For active use of model, must have causality
– Active use
optimization / control / diagnosis
• Historical plant data generally do not contain causal
information on individual variables
– Nor will any model built from these data
• But latent variable models do provide causality in the
low dimensional LV space (t1, t2, …)
– Y = TCT
X= TPT
(t’s define Y and X)
– T = XW* (To change T must move combinations of x’s)
• Optimization in low dimensional LV space
– Then X and Y obtained from LV’s
• Illustrate concept with 2 industrial examples
Optimization: Injection molding process
• GE water systems (2003)
– Polyurethane film manufacture very sensitive to
humidity, temperature and raw material variations
– Operators periodically readjusted the process largely by
trial and error
• Inject ~50 parts; measure ~10 quality variables; make
adjustments
– Injection velocity profiles, timing sequences, etc.
• Iterate until within specification
– Provided a good set of data for LV modeling
• Nonlinear PLS model
– 20 raw material properties; 26 process variables; 10 quality variables
• Models for both Y and Variance (Y)
Optimization: Injection molding process
Min  y
T
ˆ
ˆ
ˆ
ˆ (tnew )




y
(
t
)
Q
y

y
(
t
)

y
des
new
1
des
new
 (t new )Q2 y
T
t new,a
a1, 2 ,..4
– Constraints:
• Humidity , temp and raw material properties constrained to
their currently measured values
• SPE < ϵ; T2 < T299% These ensure validity of model
– Applied only when multivariate control limits violated
– Results:
5
Readjustment in one step
Improved quality
Reduced scrap
Operational since 2004
3 39 3
38 6
7
35
34
0
t[2
]
•
•
•
•
20
21
28
-5
25
2
6
30
2327
2
4
-1 0
2
9

Optimization of a batch polymerization
Pilot plant data (Air Products & Chemicals)
End Properties (13)
Z
batches
variables
Recipe & Initial Conditions
X
Variable Trajectories
• Very high dimensional optimization
problem
• Easily solved in low dimensional LV
space
Y
Optimization for new product quality
• Constraints or desired values are specified for the 13 y’s
• Minimize batch duration
• Optimization done in the three dimensional LV space
Min  y
des
T
T
 yˆ (t new )  Q1  ydes  yˆ (t new )   q2T 2  q3 SPE  q4 xˆ
tn ew, a
a 1, 2 , 3
( yˆ , xˆ , SPE , T 2 )  PLS (t )
SPE  a1
T 2  a2
Cxˆ  a3
Dyˆ  a4
Multiple solutions for Z, X
-all satisfying the y specifications,
but with different batch times.

Supervisory MPC of Batch Processes
• Objective: Control final product quality
– Product quality only measured upon completion of batch
– Control problem is thus one of
1.
2.
3.
Predicting final quality from all the initial and evolving data
Making optimal mid-course corrections at several decision
points during the batch (QP)
Different objectives at each decision point
– PLS models have been shown to be ideal for modeling
batch trajectory data and predicting final quality
•
•
•
Build from historical batch data
Plus some DOE runs at the decision points
Closed-loop identification used for subsequent implementations
Supervisory MPC of Batch Processes
• Commercial systems in food industry
> 100,000 batches controlled
> 99.9% up-time
> 50% reduction in std dev of all final quality attributes
- 20-40% increases in productivity
0.08
0.07
• LV models also allow MSPC
monitoring throughout the
batch.
with ABC
0.06
0.05
0.04
0.03
• This helps make controller
robust to faults
– e.g. wireless temp sensor
failure – default controllers.
without ABC
0.02
0.01
0
-0.4
-0.2
0
SP
0.2
0.4
0.6
0.8
1
Final quality attribute
1.2
1.4
Summary (first part)
• Latent variable models provide powerful ways
to use historical operating data
– Can make use of all measured variables
– Provide unique, interpretable models for analysis
– Provide causality in the LV space for optimization,
control
• Industrial examples used to illustrate this
– Provide monitoring and diagnosis capabilities
(next part)
Implementation and Automation of
Process Supervision
• Many variations of PCA: PCA, MBPCA, DPCA, …
• Many techniques: PCA, PLS, Independent Component
Analysis (ICA), …
• The Irish potato famine - single kind of potato (Lumper)
Diversity provides robustness
• Develop a SPM, FD and control system that uses many
alternate techniques
– How to decide which technique works better for a
given situation? Add a management layer
– How to improve decision-making with experience?
Use distributed AI
Adaptive, Decentralized Process
Supervision
Develop an agent-based monitoring, fault
detection, diagnosis, and control system to:
– Coordinate alternative techniques for
reliable and accurate fault detection,
diagnosis (FDD) and control
– Improve performance via:
o context-dependent performance
assessment and decision-making
o multi-level learning
o adaptation
Distributed Artificial Intelligence
• Implement with Agent-Based Systems (ABS)
• Decision-making is decentralized and divided
into hierarchical layers
• Agents:
– are autonomous software entities
– observe their environment
– act on their environment according to predefined
rules/algorithms
– may adapt by changing their rules/interpretation
based on their environmental conditions at run
time
MADCABS: Monitoring
Analysis Diagnosis and Control
with Agent-Based Systems
• MADCABS is built using
a hierarchical layout,
with physical
communication layer,
process supervision
layer and agent
management layer
Management Layer for agent
performance evaluation and
priority assignment
Process supervision and control
agents.
This layer needs performance
evaluation.
MADCABS' Physical
Layer
Sensors
Actuators
Basic information flow:
Collection of raw data from plant
Preprocessing, monitoring,
diagnosis, control
Mapping control actions back to process
Simulator
Evaluation of technique and agent
performance
output: simulated
system data
example: solver.dll in
our case
Plant (real or
simulated)
Process Monitoring
 Calculates the performances:
Accumulated
performances
fault detection agents
are summed to find
• Statistical
processof monitoring
techniques
the total performance of the monitoring agent
used
 Builds new statistical models:
– Principal component analysis (PCA)
When all monitoring agents are performing badly or the process
– Dynamic
PCA (DPCA)
operating
mode changes.
– Multi-block PCA (MB-PCA)
Monitoring Organizer
Process
Fault Detection

signalsare
based
the consensus formed
• Gives
Fault out-of-control
detection agents
theon
monitoring
between
agents
statisticsfault
for detection
PCA, DPCA
and MB-PCA
 Observes
performances
of statistics
fault detection agents under
– Hotelling’s
T2 and SPE
Fault detection agents
different fault magnitudes and keeps history
1.
PCA_SPE
 Triggers diagnosis agent
2
Fault detection organizer
2.
3.
4.
5.
6.
Process
PCA_T
MB-PCA_SPE
MB-PCA_T2
DPCA_SPE
DPCA_T2
Fault Diagnosis
Diagnosis Manager
Consensus Fault Decision
Fault Detection
Organizer
Diagnosis Training
Agent
Diagnosis
Agent
Fault
Identification
Agents
Process
Database
Fault Diagnosis: Identification techniques
• Contribution Plots
SPE
– Variable
contributions to
monitoring statistics
T2 and SPE
• Fishers Discriminant
Analysis (FDA)
• Partial Least
Squares
Discriminant
Analysis (PLSDA)
SPE = eeT
Fault Type 1
Fault Type 2
Observation
X
Y
For an out-of-control observation:
1s Error SPE = ∑e ,
FaultPrediction
Type 1
Squared
Variance
between
classes j
max
j = 1, …, number of variables N
Variance
within
classes
Fault
Type 2
1s
Variable Contributions
Classifynew
newobservation
observation
Classify
basedon
onthe
theclass
closeness to the
based
existing clusters
membership
X1
y =X3BPLS x X5
Fault Diagnosis (Identification) Agents
Project the new fault
data on the model and
determine the most
likely fault class
PCA_SPE
PCA_T2
MB-PCA_SPE
MBPCA_T2
DPCA_SPE
DPCA_T2
[X1,X4,X7]
[X1,X4]
[X1,X4]
[X1,X4,X7,X8]
[X1,X4,X6]
[X1,X4]
Contribution
Map
FDA PLSDA
Estimator
Identification
(Discrimination)
Agents
Process
Fault Signature for F1
[X1,X4]
Contribution Maps
[X1,X4] : [F1, F1, …]
Agent Performance Management Layer
Performance Evaluation:
• Record the performance of the agent and the
state metrics that define the state of the system
when that performance is observed.
[State Metrici, i=1,…,I ] = f (performance)
• Compare the current state of the system to
recorded states, and estimate the performance
of the agent for the current state based on its
performance for similar states in history.
Performance History Space
Agent A
State Metric 2
Pest,A
Agent B
Agent C
New Data Point:
What would the performances
of each agent be for this
state?
Pest,C
State Metric 1
Pestimate
For each agent:
- Identify performances at closest
state points.
- Obtain a performance estimate for the
current state point by interpolation.
d1
P1 P2
d3
d2
P3
Pest,B
Diagnosis Performance History
• Record:
– Fault signature
• Fault signatures are the process variables significantly
contributing to the inflation of the monitoring statistic
• Fault signatures are available once the fault is detected
– Performance of the agent for that fault signature
• Performance is recorded only after diagnosis is confirmed
• Use the history to find:
– Agents that are the best performers for the current fault
signature.
Diagnosis agent uses the estimated performances of
fault identification agents for the potential fault to form
the consensus diagnosis decision
Adaptation:
Performance-Based Consensus Analysis
- Agents update their built-in knowledge and
methods they use
- Discriminant agents update their models
with current data
Adaptive
FDA
Adaptive
PLSDA
Contribution Map
Estimator
Over time, after a diagnosis decision is confirmed
for a fault type, the misclassifications are used to
update the models of the adaptive instances
Plant or simulator
Fault-tolerant Control Structures
System Identification
MPC Control
Single centralized
control system
PID control
Set of Controllers
Controller Performance
Assessment
Monitoring and
Diagnosis
Decentralized control:
. Local coordinated MPCs
. Local MPCs integrated
with local FDD modules
using ABS
Summary/Conclusions
• Latent variable models provide powerful ways
to use historical operating data
• Data-driven methods are well-suited for
distributed process supervision
• Learning and adaptation in monitoring, FDD
and control enable fault- tolerant control
• MADCABS provides an environment for
adaptive fault diagnosis and fault-tolerant
control
• There are alternative approaches – Vive la
difference!
Acknowledgements
• IIT & ANL:
•
•
•
•
•
•
•
•
•
•
•
Fouad Teymour
Cindy Hood
Michael North
Arsun Artel
Inanc Birol
David Mendoza
Sinem Perk
QuanMin Shao
Derya Tetiker
Eric Tatara
Cenk Undey
Financial Support by National Science
Foundation CTS-0325378 of the ITR
program.
• McMaster University &
ProSensus
•
•
Many of my former grad students at
McMaster
The ProSensus team