Transcript Fuzzy Set Systems

Smart Adaptive Methods
in Modelling and Simulation
of Complex Systems
Esko Juuso
Control Engineering Group,
Faculty of Technology
University of Oulu
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
EUROSIM
Federation of European Simulation Societies
OULU
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
EUROSIM
Federation of European Simulation Societies
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Control Engineering Group
Competence Pyramid
Detection of operating conditions
- system adaptation
-fault diagnosis, condition monitoring, quality
Intelligent analysers
-sensor fusion
-software sensors
-trends
Intelligent control
-adaptation
-model-based
Measurements
-on-line analysers
-DSP
Intelligent actuators
- model-based
Dynamic simulation
- controller design, prediction
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Outline
•
Background
–
–
•
Modelling & Simulation
–
•
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Data + Knowledge + Decomposition
Linguistic equation (LE) systems
–
–
–
•
•
Soft computing: fuzzy set systems
Hard computing: statistical analysis
Generalised moments and norms
Nonlinear scaling
Genetic tuning
Application examples
Conclusions
Detection of operating conditions
Symptom generation
Classification and reasoning
-limit values, parameter esimates
-analytic, heuristic
-condition monitoring
-statistical process control (SPC)
-case-based reasoning (CBR), models
-fault and event trees
-cause-effect relationships
-novelty detection
Classification and reasoning methodologies
-rule-based, fuzzy, neural, support vector
-artificial immune systems
-qualitative models, search strategies
Soft sensors
-data-collection
-pre-processing
-normalisation and scaling
-interpolation
-data quality, outliers
-signal processing
-feature extraction
-sensor fusion
Nonlinear multivariable methodologies
- steady-state & dynamic
-decomposition, clustering, composite models
-mixed models
-development and tuning
-statistical, fuzzy, neural, genetic
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Nonlinear process control
- feedback
-fuzzy, neural, sliding mode
- adaptation (on-line, predefined)
- model-based (FF, IMC, MPC)
- high-level
Steady-state modelling: Data
Statistical analysis
• Interactions
– Linear, quadratic &
interactive Response
surface methodology
(RMS)
• Reduce dimensions
– Principal component
analysis (PCA)
– Partial least squares
regression (PLS)
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Artificial neural networks
• Linear networks
– Regression
– Recursive tuning
• Multilayer perceptron
– Nonlinear activation
• Learning
– Backpropagation
– Advanced optimisation
Steady-state modelling: Knowledge
Fuzzy arithmetics
• Extension principle
• Interval arithmetics
• Horizontal systems
Type-2 fuzzy sets
• Uncertainty about the
membership functions
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Rules and relations
• Linguistic fuzzy
• Takagi-Sugeno fuzzy
• Singleton
• Fuzzy relational models
Fuzzy set systems
Fuzzy
Fuzzy
Fuzzy
arithmetics
Fuzzy
rulebase
Fuzzy
Fuzzy
relations
Fuzzy
aritmetics
Fuzzification
Fuzzy
Crisp
Fuzzy
reasoning
Defuzzification
Fuzzy
Fuzzy
inequalities
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Crisp
Fuzzy
Steady-state modelling: Decomposition
Modelling
Clustering
• Subprocesses
• Hierachical
• Composite models
• Hierarchical
• Partitioning: K-means
• Fuzzy
– Linear parameter
varying (LPV)
– Piecewise affine (PWA)
– TS fuzzy models
– Ensemble of redundant
neural networks
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
– Fuzzy c-means (FCM)
– Subtractive
•
•
•
•
Neural: SOM
Shape (Gustafson-Kessel)
Robust
Optimal number
Complex applications: Fuzzy set systems
Data
mining
Domain expertise
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Expert Systems
EXPERTISE
+ Extracting expert knowledge
Chaos Theory
- Complexity
- Handling of uncertainty
- Testing
•Risk Analysis
•Economical factors
Knowledge-base
alternatives
Rules
Fuzzy Set Systems
+ Handling of uncerainty
+ Natural compromises
+ Easy to build (small systems)
+ Explanations
- Tuning (complex systems)
- (Doubts about stability)
Neuro-fuzzy
Linguistic Equations
+ Very compact
+ Combining knowledge
+ Generalisation
+ Adaptive tuning
+ Easier testing
- Structure Restrictions
Neural Networks
+ ”Automatic” Modelling
+ Black Box Modelling
+ Precision (small systems)
- Only for Fragments
- Explanations
- Safety
- Precision (complex systems)
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
DATA
Genetic Algorithms
+ Large search space
+ Global/local optimisation
+ Design
- Computer Time Consuming
- Not for Control (off-line)
NN Structures
Fuzzy set systems  Linguistic equation systems
Smart adaptive
applications
- Modelling
Linear
interactions
- Control
- Diagnostics
Meaning
How to define??
Hard computing??
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Adaptation of scaling functions
- Generalised norms and moments
- Constraints
- Case specific
Data
Data selection
- Outliers
- Suspicious
Domain expertise
Nonlinear scaling
- Feasible ranges
- Membership definitions
- Membership functions
Variable grouping
- 3-5 variables
- Include/exclude
- Correlation
- Causality
Linguistic relations
- Selected and scaled data
Adaptation
- Manual
- Neural
- Genetic
Linguistic equation alternatives
- Linear regression
- Case specific
Selected equations
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Selected variable groups
Manually defined equations
Final variable groups
Statistical analysis: norms
• A generalised norm about the origin

M p
p
 ( M p )1 / p
N   Ns
1 N ( ) p 1 / p
 (  xi
) ,
N i 1
p is a real number
which is the lp norm

M p
p
 x ( ) .
p
• Special cases
– absolute mean
x
– rms value
x
( )
1
( )
2
1 N ( )
  xi ,
N i1
( )
rms
1 N ( ) 2 1/ 2
 (  xi ) ,
N i1
x
x
• Positive and negative values
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
( )
av
Generalised norms
• equal sized sub-blocks 
K S
p
M
p
 1

 KS
 (
KS

i 1
p
M  )i
1/ p

1/ p
p


• A maximum from several samples

max(  M p )  max ( M p )1i / p
i 1,...,K S
 1

 KS

( M  )i 

i 1

KS

1/ p
p
Recursive analysis!

• Increasing
pq
( Mp )1/ p  ( Mq )1/ q
x ( )
1

N
N

i 1
1
xi( )
, … x ( )
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
1
1

N
N

i 1
( )
i
x
, … x
( )
2
1
(
N
N
x
i 1
( ) 2 1/ 2
i
)
,
Generalised moments
•
•
Normalised moments
k 
3  0
Positive
Symmetric
Negative
3  0
3  0
Generalised moment

E  X ( )   M p

k  
k
k
p
Locally linear if possible
Corrections for corner points
[(cl ) j , (ch )]
Core
[min(x j ), max(x j )]
Support
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Central value
 
X
•
•
•
•

k = 3 Skewness
k = 4 Kurtosis
Xk
Skewness
–
–
–
•

E  X  E ( X )
k
LE: nonlinear scaling
 linear models (interactions)
Data
Meaning
Expertise
Knowledge-based information: labels to numbers
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Second order polynomials
Tuning
(1) Core
[(cl ) j , (ch )]
(2) Ratios
 j   , 3
3 
1

1
cj
•
Centre point
•
Corner points

 j   , 3
3 
min(x ), (c ) , (c ) , max(x )
j
l
j
h j
j
(3) Support [min(x j ), max(x j )]
•
1
a j  (1   j ) c j ,
2
1
b j  (3   j ) c j ,
2
1
a j  ( j  1) c j ,
2
1
b j  (3   j ) c j
2
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Calculation
2 with x j  max(x j )

 
2


b

b
 j
j  4 a j (c j  x j )
 2 with
c j  x j  max(x j )


2a j
Xj 
 
2


b

b
 j
j  4 a j (c j  x j )
 2 with
min(x j )  x j  c j

2a j

 2 with x j  min(x j )

LE models: Dynamic simulator
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Genetic tuning
• Membership definitions
– Parameters
– No penalties
• Normalised interactions
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Decision system
Fuzzy weighting
Lag
phase
X
Exp.
phase
X
Steady
state
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
+
Prediction
Integration
X
Submodels
Fuzzy LE blocks
Measurements
CO2
forecast
Volumetric mass transfer
Coefficient, kLa
OTR
forecast
DO
forecast
Note: 3 phases & 3 models / phase  9 interactive dynamic models!
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
LE Application examples: Control
• Energy:
– Solar power plant
• Environment:
– Water circulation & wastewater treatment
~4m
• Pulp&Paper:
– Lime kilns
Length > 100 m
Slow rotation: rotation time 42-45 s
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Solar thermal power plant
•
Setpoint tracking
Principle: lower irradiation  lower temperatures
Operator can choose the risk level: smooth … fast
•
Cloudy conditions
www.psa.es
Clouds  High temperature are risky  Cloudy conditions are detected from
fluctuations of irradiation Working point is limited  Further limitations for the setpoint
•
Optimisation
Constrained optimisation:
-Temperature (< 300 oC)
- Temperature increase (< 90 oC)
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Solar thermal power plant
• Intelligent control
– Adaptation, braking, asymmetrical action
– Automatic smart actions
– Disturbances are handled well if the working
point is on a good level
• Intelligent indices
– react well to disturbances (clouds, load, …)
• Model-based limits for the working point
 Better adaptation
 Smooth adjustable operation
 A good basis for optimised
operation within a Smart Grid
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
MODEL-BASED
CONTROL
LE Application examples: Diagnostics
• Stress indices
– Cavitation
• Condition indices
– Lime kiln
• Fatigue
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Conclusions
• Soft computing
– Expertise
– Fuzzy reasoning
• Hard computing
– Data
– Statistical analysis
• Generalised norms and
moments
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
Complex systems
• Interactions
– Fuzzy set systems
– Linguistic equations
• Meaning
– Membership definitions
 Membership functions
• Nonlinear scaling
EUROSIM
Federation of European Simulation Societies
34th Board Meeting in Vienna, February 2012,
NSS became an observer member of EUROSIM
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
EUROSIM 2016
September 13-16, 2016, Oulu, Finland
The 9th EUROSIM Congress on Modelling and Simulation
Oulu City Theatre
COMOD 2014
St. Petersburg, Russia, 2-4 July 2014
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