Smart adaptive systems
in multivariable control and
diagnostics
Esko Juuso
Control Engineering Laboratory,
Department of Process and Environmental Engineering
University of Oulu
Finland
SIMS 2011
Västerås 29 Sept 2011
Outline
•
Fuzzy logic + LE
•
Data analysis
à Smart adaptive systems
–
–
•
Generalised norms
Generalised moments
Nonlinear scaling
–
–
–
•
Scaling functions
Constraints
Methodology based on skewness
Applications
–
–
–
–
•
Condition and stress indices
Operating conditions
Modelling and control
Intelligent analysers
Conclusions
SIMS 2011
Västerås 29 Sept 2011
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What is essential in fuzzy logic?
• Membership functions
• Meaning of the values
• How to define them?
– Data
– Expertise
• Automatic?
• Recursive?
• Rules?
– Expert systems?
– Is there any
structure?
– Is it just domain
expertise?
– Equations?
Neural networks?
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Fuzzy set systems à Linguistic equations
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+Automatic, adaptive
- Is it still understandable?
Increasing
complexity
complicated
simple
Set of rules
Adaptation
Decomposition
Clustering
Structured rules
Local models
Fuzzy relational models
Data-based systems
Self-organising
Tuning of rules
Linguistic fuzzy systems
Expertise
Trial and error
Tuning of membership
functions
+fast start
- tuning
in practice?
linear sets
nonlinear sets
Membership functions
SIMS 2011
Västerås 29 Sept 2011
Features: norms
• A generalised norm about the origin
t
M ap
p
= (t M ap )1/ p = (
p is a real number
N = t Ns
which is the lp norm
1 N (a ) p 1 / p
å xi ) ,
N i =1
t
M ap
p
º x (a ) .
p
• Special cases
– absolute mean
1
N
x (a )
1 N (a ) 2 1 / 2
å xi ) ,
N i=1
1
– rms value
N
x (a ) = x (ava ) =
2
(a )
= xrms
=(
åxa
i =1
( )
i
,
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Västerås 29 Sept 2011
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Features: norms
• equal sized sub-blocks à Recursive analysis
K St
M
p
a
p
ì 1
=í
î KS
å [(
KS
t
]
p 1/ p p
a i
M )
i =1
1/ p
ü
ý
þ
• A maximum from several samples
{
max( t M ap ) º max (t M ap )1i / p
i =1,..., K S
é 1
=ê
ë KS
ù
( M )ú
å
i =1
û
KS
t
1/ p
p
a i
,
}
• Increasing
p<q
(t M ap )1/ p £ (t M aq )1/ q
x (a )
-1
=
N
N
å
i =1
1
x i( a )
, … x (a )
1
=
1
N
N
å
i =1
x i( a ) , … x (a )
2
=(
1
N
N
å
2
x i(a ) ) 1 / 2
i =1
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LE: nonlinear scaling
à linear models (interactions)
Data
Meaning
Expertise
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Nonlinear scaling: constraints
- Monotonous
- Incresing
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Nonlinear scaling
Linear
Asymmetrical linear
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Second order polynomials
Tuning
(1) Core
[(cl ) j , (ch )]
(2) Ratios
é1 ù
a Î ê , 3ú
ë3 û
j
cj
•
Centre point
•
Corner points
é1 ù
a Î ê , 3ú
ë3 û
+
j
{min( x ), (c ) , (c ) , max( x )}
j
l
j
h
j
j
(3) Support [min( x j ), max( x j )]
•
1
(1 - a -j ) Dc -j ,
2
1
b -j = (3 - a -j ) Dc -j ,
2
1
+
a j = (a +j - 1) Dc +j ,
2
1
+
b j = (3 - a +j ) Dc +j
2
a -j =
Calculation
2 with x j ³ max( x j )
é
ê +
+2
+
ê - b j + b j - 4 a j (c j - x j )
- 2 with
c j £ x j £ max( x j )
ê
2a +j
Xj =ê
ê -2
ê - b j + b j - 4 a j (c j - x j )
- 2 with
min( x j ) £ x j £ c j
ê
2a j
ê
- 2 with x j £ min( x j )
êë
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Dynamic simulator
Fuzzy arithmetic
Extension principle (& fuzzy arithmetic)
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Variable time delay
Values of variables
Indices of variables
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Västerås 29 Sept 2011
Generalised moments
• Normalised moments
[
E ( X - E ( X ))
gk =
k
sX
• Skewness
k
g3 > 0
– Positive
– Symmetric
– Negative
g3 < 0
]
g3 = 0
• Generalised moment
(
k = 3 Skewness
k = 4 Kurtosis
E é X (a ) - t M ap
ê
gk = ë
k
sX
Central value
) ùúû
k
p
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Västerås 29 Sept 2011
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Data mining and modelling
We can analyse data
in various ways.
• Do we know where
we are?
• Can we tell it in an
understandable way?
• Can we use it?
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Detecting operating conditions
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lp Norms: cavitation
Order of moment:
p = 2.75 selected
Sample time 3 s
t
M ap
p
= (t M ap )1/ p
Frequency range: as low as possible
Order of derivation:
4 selected
Signal length = several sample times ß Phenomena
SIMS 2011
Västerås 29 Sept 2011
Features: norms
•
a generalised norm about the origin
t
•
M ap
p
= (t M ap )1/ p = (
1 N (a ) p 1 / p
å xi ) ,
N i =1
N =t Ns
Example: cavitation
– Relative
max( 3 M 42.75 )
– Relative
max( 3 M 42 )
– Relative
max( 3 M 41 )
One feature à Cavitation index
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Nonlinear scaling
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Cavitation index
I C( 4) = f 4-1 ( relative max( 3 M 42.75 )
Severity
VDI 2056
I C( 4) ³ 1
Not acceptable
0 £ I C( 4 ) < 1
Still acceptable
- 1 £ I C( 4) < 0
I C( 4) < - 1
Usable
Improved
sensitivity
Good
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Cavitation in water turbines
Signals
Signal processing
- Derivation
- Integration
Process measurements
Feature extraction
- Norms
- Histograms
Nonlinear
Scaling
Process measurements
Interpolation
Laboratory analysis
Condition indices
Stress indices
Condition indices
LE models
Stress indices
Only one feature needed!
Process Cases & Faults
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Västerås 29 Sept 2011
Lime kilns
~4m
Length > 100 m
Slow rotation: rotation time 42-45 s
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Nonlinear scaling
SIMS 2011
Västerås 29 Sept 2011
Scaled norms
Impacts
Improved
sensitivity
VDI 2056
Level
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Supporting rolls of a lime kiln
Signals
Signal processing
- Derivation
- Integration
Process measurements
Feature extraction
- Norms
- Histograms
Condition indices
Nonlinear
Scaling
Stress indices
Process measurements
Condition indices
Interpolation
LE models
Laboratory analysis
Several fault types
Two features needed!
Stress indices
Process Cases & Faults
SIMS 2011
Västerås 29 Sept 2011
Condition and stress indices
Methodology
•
Norms: a good order α + proper p and τ
•
Nonlinear scaling
– Scaling functions and constraints
– New methodology based on skewness
• Signal distributions
Applications
•
Cavitation
•
•
I C( 4) = f 4-1 ( relative max( 3 M 42.75 )
One norm with optimised order
Supporting rolls of a lime kiln
–
Two norms: level & impacts
max(
15
max(
15
M 41 )
1
M
4.25
4
4.25
)
Vibration severity criteria
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Västerås 29 Sept 2011
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Modelling and simulation
•
•
•
•
Normal operation à model
Deviations
Anomalies
Case based reasoning (CBR)
à Detecting operating conditions
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Västerås 29 Sept 2011
Continuous brewing
•1. case
NS NS PS PS PS PS PS
•2. case
PS PS NS NS NS NS NS
•3. & 4. case PB PB NS NS NS NS NS
•Fuzzy rules
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Västerås 29 Sept 2011
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Continuous brewing
Signals
Signal processing
- Derivation
- Integration
Process measurements
Feature extraction
- Norms
- Histograms
Several operating conditions
Normal model
Fluctuations
Nonlinear
Scaling
Process measurements
Interpolation
Laboratory analysis
Condition indices
Stress indices
Condition indices
LE models
Stress indices
Process Cases & Faults
Quality
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Västerås 29 Sept 2011
Web break sensitivity
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Web break sensitivity
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Web break sensitivity
Signals
Process measurements
Signal processing
- Derivation
- Integration
Feature extraction
- Norms
- Histograms
Several operating conditions
Case Based Reasoning (CBR)
Nonlinear
Scaling
Process measurements
Interpolation
Laboratory analysis
Condition indices
Stress indices
Condition indices
LE models
Stress indices
Process Cases & Faults
Efficiency
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Västerås 29 Sept 2011
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Trend Analysis in Diagnostics
Alarm
Warning
Very good
There was a problem, but things are now getting better?
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Condition index
Severity
VDI 2056
I C(1 ) ³ 1
0 £ I C( 1 ) < 1
- 1 £ I C(1 ) < 0
I C( 1 ) < - 1
Not acceptable
Still acceptable
Usable
Improved
sensitivity
Good
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Västerås 29 Sept 2011
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Deviation index
I Dj ( k ) =
(
)
1
X j (k ) + I Tj (k ) + DI Tj ( k ) .
3
Recursive updates
for scaling functions
SIMS 2011
Västerås 29 Sept 2011
Modelling and simulation in Control
• Dynamic models
• Time delays
• Control design
• Model based control
–
–
–
–
–
–
Feedforward
IMC
MPC
Switching
Special cases
…
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Solar collector field
LE
Simulation
Solar
energy
Availability
Solar elevation
Clouds
Seasonal
differences
· Demand
·
·
·
·
The controller needs to be good
in the whole operating area!!
(Oscillations –> slow opearation)
Control
·
·
·
·
Nonlinear
Start-up
Set point changes
Disturbances
· Irradiation
· Malfunctioning
· No time for on-line
adaptation
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Västerås 29 Sept 2011
Temperature
Considerable differences between loops!
Clouds à braking
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Model-based tuning
Dynamic models
Working point model
Distributed parameter models
Can we make
all these models
Operating conditions
consistent
with each other?
Special cases
with fuzzy set systems
SIMS 2011
Västerås 29 Sept 2011
Multilevel LE control of a solar collector field
Smooth, efficient operation
LE control Adaptation
Prediction
Braking
Asymmetry
Cascade
control
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LE Controller: Adaptive Scaling
PI type LE controller
Nonlinear scaling of the change of error
Nonlinear scaling of the error
Working point
Cascade control
Linguistic values of
- effective irradiation
- temperature difference
- ambient temperature
Smart actions
to avoid oscillations
SIMS 2011
Västerås 29 Sept 2011
LE Controller: Adaptive Scaling
Asymmetrical action
&
Working point
control
Predictive braking action
Braking rate coefficient
- initial error
- braking constant
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Test results
Cascade
Control
(wp)
Too low
setpoint for
temperature
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Västerås 29 Sept 2011
Irradiation disturbances
Cascade control
reduces overshoot
efficiently.
Cascade control is not
strong enough to
reduce overshoot
Inlet temperature changes
considerably
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Clear weather
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Cloudy weather
Slightly lower temperatures
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Power on a clear day
Occational situations with very high working point
Fast start-up
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Power on a cloudy day
Occational situations with very working point
Slightly lower power
Several start-ups in coudy conditions
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Energy collection
High efficiency in energy collection
High energy
collection
even on cloudy
days
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Intelligent analysers
• Working point
Linguistic values of
- effective irradiation
- temperature difference
- ambient temperature
• Predictive braking coefficient
• Change of working point
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Intelligent analysers
• Fast change of inlet temperature
• Too fast increase of outlet temperature
• Too high temperature difference
à Smart
actions
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Västerås 29 Sept 2011
Smart adaptive systems
High-level control & Diagnostics
On-line modelling
weighting of stragies, switching,
cascade control,
plant-wide control, expertise
- identification
Adaptation
adaptation mechanisms,
gain scheduling, scaling
Measurement
Technology
Performance
analysis
Intelligent analyser
Intelligent analyser
(Software
sensor)
Intelligent
analyser
(Software sensor)
(Software sensor)
Process understanding
àModelling à more efficient (new)
measurements
Control
Control
Decision
Control making
Decision making
Decision making
What is really controlled?
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Västerås 29 Sept 2011
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Complex Models
• Interactive
• Multimodel
• Process phases with different models
• Biosystems
• Nature
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Activated sludge plant
Variables
• Load
–
–
–
–
suspended solids (SS),
chemical oxygen demand (COD),
biological oxygen demand (BOD)
concentrations of nitrogen and phosphorus
• Additional nitrogen and phosphorus needed
• Biomass population ???
– sludge volume index (SVI) or diluted sludge volume
index (DSVI)
• Poor setling (bulking)
– Lack of nutrients
– Lack of oxygen
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Cascade modelling
X
• PCA, Takagi-Sugeno, RBF, LVQ, nerofuzzy, LETS, ...
• Process knowledge
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Västerås 29 Sept 2011
Variables
• Control
–
–
–
–
sludge age,
COD/nutrient rate,
sludge loading,
recycle ratio
• treatment efficiency =
reduction of
– total nitrogen,
– total phosphorus,
– total COD
• Data pre-processing
• Interpolation
• Effective time delays
– flow rates
– kinetics
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Shortage of nutrients
Too much nutrients
High oxygen
Low oxygen
High temperature
Low temperature
High flow
Low flow
Very good
Low reduction
Warnings
Settling problems
Very good
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Submodels
Fuzzy LE blocks
BioMass
Load
- Load
- Nutrients
- Oxygen
- Temperature
Condition of
the biomass
Water treatment
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Multimodel system for water treatment
BioMass
population
BioMass 1
BioMass 2
Weight factors are model parameters
e.g. very good, normal, problematic
BioMass 3
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Västerås 29 Sept 2011
Wastewater treatment
Signals
Process measurements
Signal processing
- Derivation
- Integration
Feature extraction
- Norms
- Histograms
Several operating conditions
Changes with time
slow + fast
Nonlinear
Scaling
Process measurements
Interpolation
Laboratory analysis
Condition indices
Stress indices
Condition indices
LE models
Stress indices
Process Cases & Faults
Efficiency
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Multimodel system
Water treatment
Interactive models
LE models
• Compact LE models
• New scaling approach
– Skewness & generalised norms
– Improved sensitivity à warnings
• Variable time delays
• Detection of operating conditions
– Early detection of changes à control actions
• Hybrid models are needed
– Uncertainty (features of influent, microbial composition)
– Mechanistic + Data-based + Intelligent
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Smart use of intelligent systems
Application-specific components and smart systems à new functionalities
Hybrid
systems
Intelligent
Functions & features
(analysis,
modelling, control,
diagnosis,
…)
Methodologies
(intelligent,
statistics, learning,
optimisation,…)
Connections (OPC, agents, HLA, wireless, industrial ethernet, …)
SIMS 2011
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Conclusions
• Expertise
• Data
Smart adaptive systems
• Interactions
– Fuzzy set systems
– Linguistic equations
• Fuzzy reasoning
• Statistical analysis
• Meaning
• Generalised norms and
moments
• Nonlinear scaling
– Membership functions
– Membership definitions
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