smart adaptive methods in modelling and simulation of complex systems

COMOD 2014St. Petersburg, Russia, 2-4 July 2014

Smart Adaptive Methods in Modelling and Simulation

of Complex SystemsEsko Juuso

Control Engineering Group,

Faculty of Technology

University of Oulu


EUROSIM Federation of European Simulation

Societies OULU



Societies


Detection of operating conditions- system adaptation

-fault diagnosis, condition monitoring, quality

Dynamic simulation- controller design, prediction

Intelligent analysers-sensor fusion

-software sensors-trends

Intelligent control-adaptation

-model-based

Measurements-on-line analysers

-DSP

Intelligent actuators- model-based

Control Engineering Group

Competence Pyramid


Outline• Background

– Soft computing: fuzzy set systems– Hard computing: statistical analysis

• Modelling & Simulation– Data + Knowledge + Decomposition

• Linguistic equation (LE) systems– Generalised moments and norms– Nonlinear scaling– Genetic tuning

• Application examples• Conclusions


Symptom generation

-limit values, parameter esimates-analytic, heuristic

-condition monitoring-statistical process control (SPC)

Nonlinear process control

- feedback-fuzzy, neural, sliding mode

- adaptation (on-line, predefined)- model-based (FF, IMC, MPC)

- high-level

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

Classification and reasoning methodologies

-rule-based, fuzzy, neural, support vector-artificial immune systems

-qualitative models, search strategies

Classification and reasoning

-case-based reasoning (CBR), models-fault and event trees

-cause-effect relationships-novelty detection

Detection of operating conditions


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)

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

Rules and relations• Linguistic fuzzy• Takagi-Sugeno fuzzy• Singleton• Fuzzy relational

modelsType-2 fuzzy sets• Uncertainty about the

membership functions


Fuzzification

Fuzzyreasoning

Fuzzyrulebase

Defuzzification

Fuzzy

Crisp

Fuzzy

Crisp

Fuzzy

Fuzzy relations

Fuzzy set systems


Steady-state modelling: Decomposition

Modelling

• Subprocesses• Hierachical• Composite models

– Linear parameter varying (LPV)

– Piecewise affine (PWA)

– TS fuzzy models– Ensemble of

redundant neural networks

Clustering

• Hierarchical• Partitioning: K-means• Fuzzy

– Fuzzy c-means (FCM)– Subtractive

• Neural: SOM

• Shape (Gustafson-Kessel)

• Robust• Optimal number


Complex applications: Fuzzy set systems

Domain expertise

Datamining


Expert Systems+ Extracting expert knowledge

- Complexity- Handling of uncertainty- Testing

Fuzzy Set Systems+ Handling of uncerainty+ Natural compromises+ Easy to build (small systems)+ Explanations - Tuning (complex systems)- (Doubts about stability)

Linguistic Equations+ Very compact+ Combining knowledge+ Generalisation+ Adaptive tuning+ Easier testing

- Structure Restrictions

Genetic Algorithms+ Large search space+ Global/local optimisation+ Design

- Computer Time Consuming- Not for Control (off-line)

Neural Networks+ ”Automatic” Modelling+ Black Box Modelling+ Precision (small systems)- Only for Fragments- Explanations- Safety- Precision (complex systems)

EXPERTISE

DATA

Neuro-fuzzyNN Structures

Knowledge-basealternatives

Rules

Chaos Theory•Risk Analysis•Economical factors


Fuzzy set systems Linguistic equation systems

Meaning

Linear interactions

Smart adaptiveapplications- Modelling- Control- Diagnostics

How to define??

Hard computing??


Linguistic relations- Selected and scaled data

Data Data selection- Outliers- Suspicious

Nonlinear scaling- Feasible ranges- Membership definitions- Membership functions

Adaptation of scaling functions- Generalised norms and moments- Constraints- Case specific

Variable grouping- 3-5 variables- Include/exclude- Correlation- Causality

Selected variable groups

Domain expertise

Linguistic equation alternatives- Linear regression- Case specific

Adaptation- Manual- Neural- Genetic

Selected equations Final variable groups

Manually defined equations


Statistical analysis: norms• A generalised norm about the origin

which is the lp norm

• Special cases

– absolute mean

– rms value

• Positive and negative values

sNN

,)1

()( /1

1

)(/1 pN

i

p

ipp

p

p xN

MM

.)(

pp

p xM

,1

1

)()(

1

)(

N

iiav x

Nxx

,)1

( 2/1

1

2)()(

2

)(

N

iirms x

Nxx

p is a real number


Generalised norms• equal sized sub-blocks

• A maximum from several samples

• Increasing

,)(1

)(1

/1

1

/1

1

/1

pK

ii

p

S

pK

i

ppi

p

Sp

pKSS

S MK

MK

M

pi

p

Ki

p MMS

/1

,...,1)(max)max(

qqpp MM /1/1 )()(

qp

,1

1)(

1

)(

N

i ix

Nx

2/1

1

2)(

2

)( )1

(

N

iix

Nx ,

1

1

)(

1

)(

N

iix

Nx

… …

Recursive analysis!


Generalised moments• Normalised moments

• Skewness– Positive– Symmetric– Negative

• Generalised moment

• Locally linear if possible• Corrections for corner points• Core • Support

k = 3 Skewnessk = 4 Kurtosis

kX

k

k

XEXE

)(

03

03 03

k

X

k

p

p

k

MXE

)(

Central value

)](,)[( hjl cc

)]max(),[min( jj xx


LE: nonlinear scaling linear models (interactions)

Data

Meaning

Expertise

Knowledge-based information: labels to numbers


Second order polynomialsTuning

(1) Core

(2) Ratios

(3) Support

• Centre point

• Corner points

• Calculation

)max(,)(,)(),min( jjhjlj xccx

jc

)](,)[( hjl cc

3,3

1j

)]max(),[min( jj xx

3,3

1j

jjj

jjj

jjj

jjj

cb

ca

cb

ca

)3(2

1

,)1(2

1

,)3(2

1

,)1(2

1

)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


LE models: Dynamic simulator


Genetic tuning

• Membership definitions– Parameters

– No penalties

• Normalised interactions


Lagphase

Exp.phase

Steadystate

Decision system

X

X

X +

Integration

Prediction

Fuzzy weighting


Submodels

CO2 forecast

OTR forecast

DO forecast

Measurements

Volumetric mass transferCoefficient, kLa

Fuzzy LE blocks

Note: 3 phases & 3 models / phase 9 interactive dynamic models!


LE Application examples: Control

• Energy: – Solar power plant

• Environment: – Water circulation & wastewater treatment

• Pulp&Paper: – Lime kilns

Length > 100 mSlow rotation: rotation time 42-45 s

~ 4 m


• Setpoint tracking

• Cloudy conditions

• Optimisation

Solar thermal power plantSolar thermal power plant

www.psa.es

Principle: lower irradiation lower temperaturesOperator can choose the risk level: smooth … fast

Clouds High temperature are risky Cloudy conditions are detected from fluctuations of irradiation Working point is limited Further limitations for the setpoint

Constrained optimisation:-Temperature (< 300 oC)

- Temperature increase (< 90 oC)


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 adaptationSmooth adjustable operation A good basis for optimised operation within a Smart Grid

MODEL-BASEDCONTROL


LE Application examples: Diagnostics

• Stress indices– Cavitation

• Condition indices– Lime kiln

• Fatigue


Conclusions

• Soft computing– Expertise– Fuzzy reasoning

• Hard computing– Data– Statistical analysis

• Generalised norms and moments

Complex systems• Interactions

– Fuzzy set systems– Linguistic equations

• Meaning– Membership definitions Membership functions

• Nonlinear scaling



Societies

34th Board Meeting in Vienna, February 2012,

NSS became an observer member of EUROSIM


EUROSIM 2016September 13-16, 2016, Oulu,

Finland

The 9th EUROSIM Congress on Modelling and Simulation

Oulu City Theatre

30

smart adaptive methods in modelling and simulation of complex systems

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