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SIMS 2011Västerås 29 Sept 2011
Smart adaptive systemsin multivariable control and
diagnosticsEsko Juuso
Control Engineering Laboratory,Department of Process and Environmental Engineering
University of OuluFinland
SIMS 2011Västerås 29 Sept 2011
Outline • Fuzzy logic + LEà Smart adaptive systems
• Data analysis– 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
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SIMS 2011Västerås 29 Sept 2011
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?
SIMS 2011Västerås 29 Sept 2011
Fuzzy set systems à Linguistic equations
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SIMS 2011Västerås 29 Sept 2011
Fuzzy relational modelsData-based systems
Self-organisingTuning of rules
Linguistic fuzzy systemsExpertise
Trial and errorTuning of membership
functions
linear sets nonlinear setsMembership functions
simple
complicatedSetofrules
+Automatic, adaptive- Is it still understandable?
+fast start- tuningin practice?
AdaptationDecomposition
ClusteringStructured rulesLocal models
Increasingcomplexity
SIMS 2011Västerås 29 Sept 2011
Features: norms• A generalised norm about the origin
which is the lp norm
• Special cases
– absolute mean
– rms value
sNN t=
,)1()( /1
1
)(/1 pN
i
p
ipp
p
p xN
MM å=
== aa
ta
t
.)(
pp
p xM aa
t º
,11
)()(
1
)( å=
==N
iiav x
Nxx aaa
,)1( 2/1
1
2)()(
2
)( å=
==N
iirms x
Nxx aaa
p is a real number
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SIMS 2011Västerås 29 Sept 2011
Features: norms• equal sized sub-blocksà Recursive analysis
• A maximum from several samples
• Increasing
[ ] ,)(1)(1/1
1
/1
1
/1pK
ii
p
S
pK
i
ppi
p
Sp
pKSS
S MK
MK
M úû
ùêë
é=
þýü
îíì
= åå==
at
at
at
{ }pi
p
Ki
p MMS
/1
,...,1)(max)max( a
ta
t
=º
qqpp MM /1/1 )()( at
at £ qp <
,1
1)(
1)(
å=
-= N
i ix
Nx
a
a 2/1
1
2)(
2
)( )1( å=
=N
iix
Nx aa,1
1
)(1
)( å=
=N
iix
Nx aa… …
SIMS 2011Västerås 29 Sept 2011
LE: nonlinear scalingà linear models (interactions)
Data
Meaning
Expertise
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SIMS 2011Västerås 29 Sept 2011
Nonlinear scaling: constraints
- Monotonous- Incresing
SIMS 2011Västerås 29 Sept 2011
Nonlinear scaling
Linear
Asymmetrical linear
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SIMS 2011Västerås 29 Sept 2011
Second order polynomialsTuning
(1) Core
(2) Ratios
(3) Support
• Centre point
• Corner points
• Calculation
}{ )max(,)(,)(),min( jjhjlj xccx
jc)](,)[( hjl cc
úûù
êëéÎ+ 3,
31
ja
)]max(),[min( jj xx
úûù
êëéÎ- 3,31
ja
+++
+++
---
---
D-=
D-=
D-=
D-=
jjj
jjj
jjj
jjj
cb
ca
cb
ca
)3(21
,)1(21
,)3(21
,)1(21
a
a
a
a
êêêêêêêêê
ë
é
£-
££---+-
££---+-
³
=---
+
+++
)min(2
)min(22
)(4
)max(22
)(4
)max(2
2
2
jj
jjjj
jjjjj
jjjj
jjjjj
jj
j
xxwith
cxxwitha
xcabb
xxcwitha
xcabb
xxwith
X
SIMS 2011Västerås 29 Sept 2011
Dynamic simulator
Extension principle (& fuzzy arithmetic)
Fuzzy arithmetic
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SIMS 2011Västerås 29 Sept 2011
Variable time delay
Indices of variables
Values of variables
SIMS 2011Västerås 29 Sept 2011
Generalised moments• Normalised moments
• Skewness– Positive– Symmetric– Negative
• Generalised moment
k = 3 Skewnessk = 4 Kurtosis( )[ ]
kX
k
kXEXE
sg
)(-=
03 >g
03 <g03 =g
( )k
X
k
p
p
k
MXE
sg
ata
úûù
êëé -
=
)(
Central value
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SIMS 2011Västerås 29 Sept 2011
Data mining and modelling
We can analyse datain various ways.
• Do we know wherewe are?
• Can we tell it in anunderstandable way?
• Can we use it?
SIMS 2011Västerås 29 Sept 2011
Detecting operating conditions
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lp Norms: cavitation
pp
p
p MM /1)( at
at =
Order of moment:p = 2.75 selected
Order of derivation:4 selected
Frequency range: as low as possible
Signal length = several sample times ß Phenomena
Sample time 3 s
SIMS 2011Västerås 29 Sept 2011
Features: norms• a generalised norm about the origin
• Example: cavitation
– Relative
– Relative
– Relative
One featureà Cavitation index
sNN t=,)1()( /1
1
)(/1 pN
i
p
ipp
p
p xN
MM å=
== aa
ta
t
)max( 75.24
3 M
)max( 14
3 M
)max( 24
3 M
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Nonlinear scaling
SIMS 2011Västerås 29 Sept 2011
Cavitation index
1)4( -<CI
1)4( ³CI
01 )4( <£- CI
10 )4( <£ CI
Severity
Not acceptable
Still acceptable
Usable
Good
VDI 2056)max(( 75.2
431
4)4( MrelativefIC
-=
Improvedsensitivity
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SIMS 2011Västerås 29 Sept 2011
Signal processing- Derivation- Integration
Feature extraction- Norms- Histograms
Interpolation
NonlinearScaling
LE models
Signals
Process measurements
Process measurements
Laboratory analysis
Condition indicesStress indices
Condition indices
Stress indices
Process Cases & Faults
Cavitation in water turbines
Only one feature needed!
SIMS 2011Västerås 29 Sept 2011
Lime kilns
Length > 100 mSlow rotation: rotation time 42-45 s
~ 4 m
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Nonlinear scaling
SIMS 2011Västerås 29 Sept 2011
Scaled norms
Impacts
LevelVDI 2056
Improvedsensitivity
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SIMS 2011Västerås 29 Sept 2011
Signal processing- Derivation- Integration
Feature extraction- Norms- Histograms
Interpolation
NonlinearScaling
LE models
Signals
Process measurements
Process measurements
Laboratory analysis
Condition indices
Stress indices
Condition indices
Stress indices
Process Cases & Faults
Supporting rolls of a lime kiln
Several fault typesTwo features needed!
SIMS 2011Västerås 29 Sept 2011
Condition and stress indicesMethodology
• Norms: a good order α + proper p and τ
• Nonlinear scaling– Scaling functions and constraints
– New methodology based on skewness
• Signal distributions
Applications• Cavitation
• One norm with optimised order
• Supporting rolls of a lime kiln– Two norms: level & impacts
Vibration severity criteria
)max(1
14
15 M
)max(25.4
25.44
15 M
)max(( 75.24
314
)4( MrelativefIC-=
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Modelling and simulation
• Normal operationà model• Deviations• Anomalies• Case based reasoning (CBR)
à Detecting operating conditions
SIMS 2011Västerås 29 Sept 2011
•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
Continuous brewing
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SIMS 2011Västerås 29 Sept 2011
Signal processing- Derivation- Integration
Feature extraction- Norms- Histograms
Interpolation
NonlinearScaling
LE models
Signals
Process measurements
Process measurements
Laboratory analysis
Condition indices
Stress indices
Condition indices
Stress indices
Process Cases & FaultsQuality
Continuous brewing
Several operating conditionsNormal modelFluctuations
SIMS 2011Västerås 29 Sept 2011
Web break sensitivity
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Web break sensitivity
SIMS 2011Västerås 29 Sept 2011
Signal processing- Derivation- Integration
Feature extraction- Norms- Histograms
Interpolation
NonlinearScaling
LE models
Signals
Process measurements
Process measurements
Laboratory analysis
Condition indices
Stress indices
Condition indices
Stress indices
Process Cases & FaultsEfficiency
Web break sensitivity
Several operating conditionsCase Based Reasoning (CBR)
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Trend Analysis in Diagnostics
Alarm
Very good
Warning
There was a problem, but things are now getting better?
SIMS 2011Västerås 29 Sept 2011
Condition indexSeverity
Not acceptable
Still acceptable
Usable
Good
VDI 2056
Improvedsensitivity
1)1( -<CI
1)1( ³CI
01 )1( <£- CI
10 )1( <£ CI
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SIMS 2011Västerås 29 Sept 2011
Deviation index
( ).)()()(31)( kIkIkXkI T
jTjj
Dj D++=
Recursive updatesfor scaling functions
SIMS 2011Västerås 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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SIMS 2011Västerås 29 Sept 2011
· Nonlinear· Start-up· Set point changes· Disturbances
· Irradiation· Malfunctioning
· No time for on-lineadaptation
· Nonlinear· Start-up· Set point changes· Disturbances
· Irradiation· Malfunctioning
· No time for on-lineadaptation
· Availability· Solar elevation· Clouds· Seasonal
differences· Demand
LE SimulationControl
Solar energy
The controller needs to be goodin the whole operating area!!(Oscillations –> slow opearation)
Solar collector field
SIMS 2011Västerås 29 Sept 2011
Considerable differences between loops! Cloudsà braking
Temperature
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SIMS 2011Västerås 29 Sept 2011
Model-based tuning
Working point model
Operating conditions
Dynamic models
Distributed parameter models
Special caseswith fuzzy set systems
Can we makeall these models
consistentwith each other?
SIMS 2011Västerås 29 Sept 2011
Multilevel LE control of a solar collector field
LE control Adaptation Braking
Prediction Cascadecontrol
AsymmetrySmooth, efficient operation
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PI type LE controller
Working point
Linguistic values of- effective irradiation- temperature difference- ambient temperature
Nonlinear scaling of the error
Nonlinear scaling of the change of error
LE Controller: Adaptive Scaling
Cascade control
Smart actionsto avoid oscillations
SIMS 2011Västerås 29 Sept 2011
Predictive braking action
Braking rate coefficient- initial error- braking constant
LE Controller: Adaptive ScalingAsymmetrical action
&Working pointcontrol
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CascadeControl
(wp)
Too lowsetpoint fortemperature
Test results
SIMS 2011Västerås 29 Sept 2011
Cascade controlreduces overshootefficiently.
Cascade control is notstrong enough toreduce overshoot
Inlet temperature changesconsiderably
Irradiation disturbances
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Clear weather
SIMS 2011Västerås 29 Sept 2011
Cloudy weather
Slightly lower temperatures
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Power on a clear day
Fast start-up
Occational situations with very high working point
SIMS 2011Västerås 29 Sept 2011
Power on a cloudy day
Occational situations with very working point
Several start-ups in coudy conditions
Slightly lower power
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Energy collectionHigh efficiency in energy collection
High energycollectioneven on cloudydays
SIMS 2011Västerås 29 Sept 2011
Linguistic values of- effective irradiation- temperature difference- ambient temperature
Intelligent analysers
• Working point
• 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
àSmart actions
SIMS 2011Västerås 29 Sept 2011
Smart adaptive systems
ControlDecision making
What is really controlled?
ControlDecision makingControl
Decision making
On-line modelling- identification
Performanceanalysis
Adaptationadaptation mechanisms,gain scheduling, scaling
Intelligent analyser(Software sensor)Intelligent analyser
(Software sensor)Intelligent analyser(Software sensor)
Process understandingàModelling à more efficient (new)measurements
MeasurementTechnology
High-level control & Diagnosticsweighting of stragies, switching,
cascade control,plant-wide control, expertise
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Complex Models
• Interactive• Multimodel• Process phases with different models
• Biosystems• Nature
SIMS 2011Västerås 29 Sept 2011
Activated sludge plantVariables
• 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 volumeindex (DSVI)
• Poor setling (bulking)– Lack of nutrients– Lack of oxygen
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Cascade modelling
• PCA, Takagi-Sugeno, RBF, LVQ, nerofuzzy, LETS, ...• Process knowledge
X
SIMS 2011Västerås 29 Sept 2011
Variables• Control
– sludge age,– COD/nutrient rate,– sludge loading,– recycle ratio
• treatment efficiency =reduction of– total nitrogen,– total phosphorus,– total COD
• Effective time delays– flow rates– kinetics
• Data pre-processing• Interpolation
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Shortage of nutrientsToo much nutrients
High oxygenLow oxygen
High temperatureLow temperature
High flowLow flow
Very good
Low reduction
Settling problems
Very good
Warnings
SIMS 2011Västerås 29 Sept 2011
Submodels
Water treatment
Fuzzy LE blocks
BioMass
Load
- Load- Nutrients- Oxygen- Temperature
Condition ofthe biomass
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Multimodel system for water treatment
BioMass 1
BioMass 2
BioMass 3
BioMasspopulation
Weight factors are model parameters
e.g. very good, normal, problematic
SIMS 2011Västerås 29 Sept 2011
Signal processing- Derivation- Integration
Feature extraction- Norms- Histograms
Interpolation
NonlinearScaling
LE models
Signals
Process measurements
Process measurements
Laboratory analysis
Condition indices
Stress indices
Condition indices
Stress indices
Process Cases & FaultsEfficiency
Wastewater treatment
Several operating conditionsChanges with time
slow + fast
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Water treatment
• Compact LE models
• New scaling approach– Skewness & generalised norms– Improved sensitivityà 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
Multimodel system
Interactive models
LE models
SIMS 2011Västerås 29 Sept 2011
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Smart use of intelligent systems
IntelligentFunctions & features
(analysis,modelling, control,
diagnosis,…)
Methodologies(intelligent,
statistics, learning,optimisation,…)
Connections (OPC, agents, HLA, wireless, industrial ethernet, …)
Hybridsystems
Application-specific components and smart systemsà new functionalities
SIMS 2011Västerås 29 Sept 2011
Conclusions
• Expertise• Data
• Fuzzy reasoning• Statistical analysis
• Generalised norms andmoments
Smart adaptive systems• Interactions
– Fuzzy set systems– Linguistic equations
• Meaning– Membership functions– Membership definitions
• Nonlinear scaling