1

Evolvable Fuzzy Systems

Plamen Angelov

Intelligent Systems Research LaboratoryDept of Communications SystemsInfoLab21, Lancaster University, UK

2

Lancaster University

One of the top 10% of the UK Universities

3

InfoLab21

•The Comms Systems and Computing Depts form an ICT force of 250 researchers•Research project income from Industry (Nokia, Philips, BAE Systems, QInetiq, Ford), Government (DTI, EPSRC), EC, Royal Society etc. £15M

4

DSP group

Research is focussed on the development of novel techniques in

• system modelling/identification

fuzzy rule based systems

• Intelligent collaborative Systems

• speech/image enhancement, compression, analysis and synthesis

• information fusion • NOKIA Lab• Intelligent Systems Lab

5

Intelligent Systems Lab

Collaborative mobile robots (5 Pioneer-3DX) with evolvable intelligence using embedded eTS systems for:prediction, classification and control

6

Outline

Models with Flexible Structure

Evolving Neuro-Fuzzy Models (eTS)

NOx emissions real-time modelling (DC)

Quality of crude oil distillation (CESPA)

Applications to speech processing (Nokia)

Autonomous vehicles (BAE, Qinetiq, J&S)

System on chip implementation (FPGA)

7

Outline

Controllers with evolvable structure

Application to EEG signals classification

Classification of Carcinoma Kidney Tissue Status based on Protein Expression Data

Biotech process applications

8

System Modeling

• predict object reactions;• control it;• detect faults;• study process performance

A. Conventional Models- First Principles Models- Black-box models

B. Fuzzy Models

9

Fermentation Process

n

D, P

X, S T, pH,

SI

DXXdt

dXX −= μ

)( SSDXqdtdS

IS −+−=

DPXqdtdP

P −=

A. First Principle Models

• Example: Fermentation process

transparent, close to nature (mass- and energy conservation in closed systems)

tedious, even impossible, (highly) non-linear

10

Hidden layer

wij wrj

• Linear state-space models

• Polynomial models

• ARMA models

• ANN

)()()1( kBukAxkx

S

X

µX

qS

P

+=+ )()()( kDukCxky +=

...)2()1(...)2()1()( 210210 +−+−+++−+−+= kybkybbkxakxaaky

...22

216

225

21421322110 +++++++= xxaxaxaxxaxaxaay

Black-box Models

11

Fuzzy Model Types

• Fuzzy parameters

• Fuzzy (in)equalities

• FRB models

• relational

• Mamdani

• Takagi-Sugeno or TSK

4~

43

~

32

~

2

~

1

~

0 φφφφψ aaaaa ++++=

),(~

1 kkk uxfx =+

IF (antecedent) THEN (consequence)

Rxy ο= ΥRN

iiRR

1=

=

)..()(...)(: 11

YisyTHENisXxANDANDisXxIFR nni

12

TSK Models (1985)

• TSK systems – important tool for system modeling and identification

Computational efficiency (local linearity)

Universal approximators

Good transparency

Convenient for data-driven design

)...()(...)(:

11

11

ininii

nni

bxaxayTHENisXxANDANDisXxIFR

+++=

13

TSK Fuzzy model of a Fermentation (concept)

X

time

Lag-phase LM1: Xk+1=a1Xk+b1

Growth phase LM2: Xk+1=a2Xk+b2

Saturation phase LM3: Xk+1=a3Xk+b3

μ

1

0 time

Saturation phase

Growth phase

Lag phase

LM1 LM2 LM3

y1

y2

x y

… yRN

Linear model 1

Linear model 2

Linear model RN

14

TSK in 2D Feature Space

• MIMO TSK in a 2D feature space

• eClustering

15

Data-driven learning

• Until 1990s fuzzy systems were designed based on ‘expert’ knowledge

• Data-driven design (’95) can include expert knowledge if it exists, but tries to extract knowledge from the data

• Recent tendency – data streams, on-line, real-time processes

16

The challengeSystems that posses Computational Intelligence usually rely on fixed rule-bases or NN

Trained off-line, do not adapt to environment

They do not develop their structure (evolve)

17

Example 1 current UAVsUnmanned Aerial Vehicles (UAV):

• limited flexibility

• limited control functions

• do not learn the new environment

Herta-1A UAV

Flew 08/18/06 →

over Scotland

18

Example 2 Mobile robotsMobile robots:

• Pre-programmed logic• Remotely controlled vehicles • Limited learning capabilities• Do not capture new knowledge

the de-miner ELTA →

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The challengeThe environment in which real systems (technological processes, robotic systems, transport vehicles) operate is (unpredictably) changing

The challenge - to develop systems capable of higher level adaptation to the environment and to internal changes (wearing, faults, regimes etc.)

20

On-line identification

• What to do when new data do not fitinto the model with a chosen structure?

• Adaptive systems theory answer (’70s): adapt the parameters ONLY

• This may be an outlier

• Or it may bring new information(knowledge) – about a different regime, operation point, change etc.

• Thus update the structure

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Evolving Systems• Evolving systems – a possible solution

Evolving is adaptive in terms of both structure and parametersIncremental evolution of the fuzzy rules(clusters): update, replace, add new

What to evolve?• Consequent parameters (parameters of linear

sub-models);• Premise parameters (centers and widths of the

Gaussians);• Rule-base (rules, fuzzy sets/linguistic terms);

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TSK MIMO model

( ) ( )**11 ...........: i

nnii xtocloseisxANDANDxtocloseisxIFR

f(x)x y

Tnxxxx ],...,,[ 21= T

myyyy ],...,,[ 21=

)( ii fyTHEN = iTe

i xf π= ],1[ TTe xx =

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

inm

in

in

im

ii

im

ii

i

ααα

αααααα

π

...............

...

...

21

11211

00201ii af =

[ ]Tim

iiia 00201 ααα=

23

TSK MIMO model

∑=

=N

i

ii yy1

λ∑=

= N

j

j

ii

1

τ

τλ

{ }⎪⎩

⎪⎨⎧ == =

else

j lN

l

ji

0

maxarg1

ττλ

∏=

=n

jj

ij

i x1

)(μτ

( )22*4

ij

jixx

ij e σμ

−−

=

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TSK model as a FBFN

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eTS systems (2002)

Adapt parameters and evolve structure;eTS – eClustering (on-line version of the subtractive clustering) + a version of RLS

Applied so far to control, prediction, classification, speech error recovery etc.

Fuzzy rules and linguistic terms are not fixed and learning can start ‘from scratch’

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eTS systems (2002)

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Basic Principle

The approach can be summarised as:

Decomposition of the complex data space into overlapping local regions eClustering.avi

Joint identification of local (simpler) sub-systems in real-time

Forming the output of the system as a fuzzy blending of local outputs

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The concept of Potential

Key notion – spatial proximity in the input/output data space

iAkiA

Adk

PA

,1)1/(111

=Σ−+=

iBkiB

Bdk

PB

,1)1/(111

=Σ−+=

BA PP <

29

Potential update

Recursively calculated

Centers’ scatter up-date:

kkkkk k

kzPγβα 2)1)(1(

1)(−++−

−=

( )∑+

=

=mn

j

jkk z

1

2α

( )∑∑−

=

+

=

=1

1 1

2k

i

mn

j

jik zβ

jk

mn

j

jkk z Γ=∑

+

=1

γ

∑−

=

=Γ1

1

k

i

ji

jk z

0; 111 =+= −− βαββ kkk jk

jk

jk z 11 −− +Γ=Γ 01 =Γj

∑+

=−−−

−

−++−

−= mn

jjkkk

kk

zzzPzPk

zPkzP

1

2

1**

1*

1

*1*

)()(2

)()1()(

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Rule-base evolution

Form new rule:

Modify the rule:

Remove – based on similarity

PzP kk >)(

2min *

1

ij

j

ik

N

ixx

σ<−

=

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Input Output

Data Data

Real-time update (potential-based)

Rule-base

Rule-base evolution

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Learning

Identification criteria:

θψ Ty = ( ) ( ) ( )[ ]TTNTT πππθ ,...,, 21=

TTe

NTe

Te xxx ],...,,[ 21 λλλψ =

( ) ( ) min→Ψ−Ψ− θθ TTT YY

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Parameters learning

• Weighted RLS

)( 1

^

1

^^

−− −+= kTkkkkkk yC θψψθθ

kkTk

kTkkk

kk CCCCCψψ

ψψ

1

111 1 −

−−− +−=

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Basic procedure

1. First data - first rule center

2. Collect new data in real-time

3. Calculate Snew

4. Recursively up-date S*

5. Up-grade or modify the Rule-base

6. Estimate Consequent parameters

7. Form the final output

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Flow-Chart – part 1

Initialization; k←1; θ1←0; λ1←1; P*1←1

Begin

Get the input, xk

Generate yk

k ← k+1

Get the real output, ykreal

Generate potential, Pk (xk, ykreal)

Update the potential of the focal points, Pk

12

36

Flow-Chart – part 2

Update parameters θk

yes

no

Replace the rule x*i← xk

Initialize thereplaced rule

Form new cluster/ rule/ neuron/ x*(N+1) ← xk

Initialize it; θ(N+1);P*(N+1)

no

yes

21

⎟⎠⎞

⎜⎝⎛ <⎟

⎠⎞

⎜⎝⎛ >

==

ik

N

iki

k

N

ik PPORPP *

1

*

1minmax

2min *

1

σ<−

=

ikk

N

ixx

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eTS Systems Analysis

• Single algorithmic parameter – cluster radius

• evolutionary (inherits previous model structure), changes are gradual

• extracts accumulated spatial proximityinformation from the data;

• it is very robust and naturally excludes outliers, because their S is high

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Applications: Modeling

NOx emissions real-time modelling (Daimler-Chrysler)

Quality modelling of crude oil distillation (CESPA)

Lost packets estimation in VoIP (Nokia)

Autonomous systems (BAE, Qinetiq, J&S)

Fermentation processes on-line modeling

System on chip implementation (FPGA)

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Daimler Chrysler

NOx emissions modeling for a car engine (Daimler-Chrysler test engines, Dr. E. Lughofer)

NOx – 4s ahead prediction

667 training+824 testing samples at 1 Hz

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NOx: variables

4 input attributes:• N - engine rotation speed, rpm• P2 - pressure offset in cylinders, bar• Te - engine output torque, Nm• Nd – speed of the dynamometer

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Data, Nk-4 and P2k-5

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Data, Tek-5 and Ndk-6

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Data, Nk-6 and NOxk

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NOx accuracy (correlation)

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NOx Prediction

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eTS parameters

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Fuzzy Sets

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Fuzzy Rules

R1: IF( 4−kN is Medium) AND ( 52 −koffsetP is Low) AND ( 5−kTe is High) AND ( 6−kNd is …) AND ( 6−kN is Medium)

THEN 6156

145

1352

124

11

10 −−−−− +++++= kkkk

offsetkk NaNdaTeaPaNaaNOx

R1: IF( 4−kN is Low) AND ( 52 −koffsetP is Low) AND ( 5−kTe is Very Low) AND ( 6−kNd is …) AND ( 6−kN is Medium)

THEN 6156

145

1352

124

11

10 −−−−− +++++= kkkk

offsetkk NaNdaTeaPaNaaNOx

R1: IF( 4−kN is Medium) AND ( 52 −koffsetP is Medium) AND ( 5−kTe is High) AND ( 6−kNd is …) AND ( 6−kN is Low)

THEN 6156

145

1352

124

11

10 −−−−− +++++= kkkk

offsetkk NaNdaTeaPaNaaNOx

R1: IF( 4−kN is Low) AND ( 52 −koffsetP is Very Low) AND ( 5−kTe is Medium) AND ( 6−kNd is …) AND ( 6−kN is Medium)

THEN 6156

145

1352

124

11

10 −−−−− +++++= kkkk

offsetkk NaNdaTeaPaNaaNOx

R1: IF( 4−kN is Very High) AND ( 52 −koffsetP is Very Low) AND ( 5−kTe is Low) AND ( 6−kNd is …) AND ( 6−kN is Low)

THEN 6156

145

1352

124

11

10 −−−−− +++++= kkkk

offsetkk NaNdaTeaPaNaaNOx

R1: IF( 4−kN is Low) AND ( 52 −koffsetP is High) AND ( 5−kTe is Low) AND ( 6−kNd is …) AND ( 6−kN is Very High)

THEN 6156

145

1352

124

11

10 −−−−− +++++= kkkk

offsetkk NaNdaTeaPaNaaNOx

R1: IF( 4−kN is Low) AND ( 52 −koffsetP is Very High) AND ( 5−kTe is Very High) AND ( 6−kNd is …) AND ( 6−kN is Very High)

THEN 6156

145

1352

124

11

10 −−−−− +++++= kkkk

offsetkk NaNdaTeaPaNaaNOx

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Local model parameters

R\par a0 a1 a2 a3 a4 a5

R10.62122 0.57316 -0.79908 -0.10607 -3.8705 3.6797

R20.25019 0.24239 -0.29438 0.46455 -1.533 1.4712

R30.77561 0.12709 0.37604 0.078215 0.45054 -0.2973

R40.29341 0.45984 0.38647 0.27322 -0.55073 -0.30107

R5-0.27591 0.033233 -0.22574 0.44712 0.45803 0.46113

R60.42849 0.47549 -1.9812 -1.1318 -2.7612 -0.22697

R7-0.43818 0.6626 1.0395 2.8411 -0.0079526 -0.071655

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Rule Base EvolutionNumber of ADDED rules : 7

Number of MODIFIED rules : 6

Samples that originate new rules :

1 3 5 8 12 21 588

Final position of the focal points :

1 4 5 311 12 21 588

MODIFIED rules formed around samples :

2 4 41 53 57 311

Time of calculations (CPU): 1.0469 S

Variance Accounted For (VAF): 85.034

PERFORMANCE MEASURESCorrelation 0.92213MSE 0.0037546 RMSE 0.061275 NDEI 0.38991

51

Quality of crude oil

• CESPA oil refinery, Tenerfie, Spain

• 80000 bb/d

• Products: heavy naphta, kerosene, GOL

• Parameters: T95%; Pensky-Martens (inflammability analysis)

• Off-line, once a day lab test

52

Quality of crude oil

The aim is to predict daily:• Temperature of the heavy Naphtha when it

evaporates 95% liquid volume, ASTM D96

• Temperature of the kerosene when it evaporates 95% liquid, ASTM D96

• Pensky Martens inflammability analysis of the Kerosene

• Temperature of the GOL when it evaporates 85% liquid, ASTM D96

53

T of heavy naphtha

Temperature of the heavy Naphtha when it evaporates 95% liquid volume In a distillation tower, mainly depends on

• The pressure of the tower

• Amount of product taking off

• Density of the crude

• Temperature of the column overhead

• Temperature of the Naphtha Extraction

54

T of kerosene

Temperature of kerosene when it evaporates 95% liq. vol. depends on:

• The pressure of the tower• Amount of product taking off, Naphtha and KNO• Density of the crude• Temperature of the column overhead• Steam introduced in GOL stripper ratio to KNO• Temperature of the Kerosene Extraction• Temperature of the Naphtha Extraction

55

Pensky-Martens

Inflammability analysis of the Kerosene concern the light part of the kerosene, and therefore it depends mainly in the Naphtha above and the steam injected in the kerosene stripper.

• The pressure of the tower• Amount of product taking off• Density of the crude• Temperature of the column overhead• Temperature of the Naphtha Extraction• Steam introduced in Kerosene stripper, ratio to KNO

56

T of gas oil

Temperature of GOL when it evaporates 95% depends on:

• The pressure of the tower• Amount of product taking off, Naphtha and KNO• Density of the crude• Temperature of the column overhead• Steam introduced in GOM stripper, ratio to GOM• Temperature of the GOL Extraction• Temperature of the Kerosene Extraction• Temperature of the Naphtha Extraction

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Fuzzy sets, Heavy naphtha

58

Fuzzy sets, Heavy naphtha

59

Prediction of Thn

• Error in the order of 2-3oC (the Thn is in the range of 100-160oC.

• The precision is comparable with the precision of the laboratory off-line test and can be done in real-time.

60

QoS improvement in VoIP

• Voice communication using Packet basedcommunication networks is becoming common place (e.g Internet)⇒ The future is Mobile IP based Comms

• GSM Air interface is hostile environment:due to urban, multi-path interference error rates/packet losses can be high

61

QoS improvement in VoIP

• QoS requires error concealment • Approach – real-time novel error

concealment approach using eTSmodels suitable for VoIP over GSM with “severe” packet losses (100 to 200 mSof Speech, getting towards word loss level) that

• minimise transmission bandwidth• minimise system delays• maximise speech quality (QoS)

62

Speech processing coders

• Modern Speech commissions digitise analog speech signal & use speech coding techniques to reduce the transmission bandwidths (reduced operator fixed costs)

• speech Coding applies DSP techniques to speech segments (~20 mS) in order to

• identify and isolate “perceptually” important characteristics of the voice signal

• then digitize and quantize them • Transmit the quantized/digital values.

63

LPC parameters

• Vocoder are a class of parametric coder that use a parametric model of the vocal tract

• Linear Prediction coding is a widely used method for representing the frequency shaping attributes of the vocal tract

• The short term spectral envelop is modeled by all pole Linear Predicting Filter

• This yields a small number of parameters (10)

64

The approach

• LPC is typically 10th Order• 10 LPC filter coefficients are generated

per frame (20mS speech segments) • LPC Filter Coefficients are usually

transformed into the Line Spectral Frequencies (LSP) before quantization

• modelling different aspects of speech\language but in the parameter domain(not necessarily the time domain)

65

Source speech LSP

0

0.5

1

1.5

2

2.5

3

3.5

0

420

840

1260

1680

2100

2520

2940

3360

3780

4200

4620

5040

5460

5880

6300

6720

7140

7560

7980

LSP0LSP1LSP2LSP3LSP4LSP5LSP6LSP7LSP8LSP9

-10000

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

1

1579

3157

4735

6313

7891

9469

1104

7

1262

5

1420

3

1578

1

1735

9

1893

7

2051

5

2209

3

2367

1

2524

9

2682

7

2840

5

2998

3

3156

1

Source speech LSP

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Preliminary results

eTS is able replace around 100 mS of lost unquantized speech with small losses (state of art is currently around 40mS)eTS when continuously executed ( always replace the LSP) can improve the overall speech quality of low bit rate codec

Un quantisedLSPs

Predictor

VPredLSP

VLSP

Rest of Decoding

Quantised LSPs

10

10

Ypred

linkerror

10

67

QoS for VoIP, NOKIA

• Real speech, female speaker• MOS 2.6 insignificant drop

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QoS for VoIP, NOKIA

• Real speech, female speaker• MOS 2.6 insignificant drop

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Distributed co-eClass

Agent n Local Classification/ Prediction/ Decision

…

Agent 1

Co-eClass Global Classification/ Prediction/ Decision

Local Classification/ Prediction/ Decision …

Agent i Local Classification/ Prediction/ Decision

Features

70

Agent 2

Agent 3

Agent 1

Agent 4

Unrecognized agent

Environment

Cooperative Rule-base

Co-operation in autonomous detection

71

Underwater target recognition, J&S Marine

Object1

A

B

D

C

Area I Area II

Agents exchange new rule info

72

Underwater target classification- scenario 2

Object1

Object2

Object3

Object4

A B

73

Our Pioneer3-DX Robots

• Onboard Computer (PIII CPU,256M RAM)

• Camera, Digital Compass, Sonar, bumpers, Laser

• Controller (embedded microprocessor ARCOS)

• A team of 5 robots with

WIFI connection

for collaborative tasks

74

Novelty detection and land mark recognition by eClustering

• Explore unknown environment

• No communication link (no GPS, maps…)

• Simple landmark (corner) recognition

• Fully unsupervised

(no pre-training

no model structure

assumed)

75

Novelty detection and landmark recognition by eClustering

Novelty Detection

• The ability to differentiate between common sensory stimuli and perceptions never experienced before

Landmark Recognition

• With Novelty Detection, robot can select aspects of the environment that are unusual and therefore can be used as landmarks for self-localization

76

Novelty detection and landmark recognition by eClustering

• Reference Nehmzow, 1991• SOM (50 neurons, supervised, off-line

pre-training, fixed structure)• Off-line Pre-training• Evolving SOM (Kasabov, 2000)– too

relaxed – based on a threshold, not robust enough to avoid noisebecoming cluster centres

77

Novelty detection and landmark recognition by eClass

A B

CNM

LK

H G

J I F

D

E

A B

CNM

LK

H G

J I F

D

E

A B

CNM

LK

H G

J I F

D

E

A B

CNM

LK

H G

J I F

D

E

78

Our experiment (B-69, InfoLab21)

bb.mpg

79

Novelty detection and landmark recognition by eClass

demo corner detectiondemo corner detection

Recursive calculation → less computing power required → real-time

Extend to image-based (CASPIA)R1: IF (φ is close to ¾) AND (d is close to 0.3000) THEN (Corner is 1)R2: IF (φ is close to ¾) AND (d is close to 0.1268) THEN (Corner is 2 )R3: IF (φ is close to ¼) AND (d is close to 0.0648) THEN (Corner is 3 )R4: IF (φ is close to ¾) AND (d is close to 0.2357) THEN (Corner is 4 )R5: IF (φ is close to ¾) AND (d is close to 0.0792) THEN (Corner is 5)R6: IF (φ is close to ¼) AND (d is close to 0.1744) THEN (Corner is 6)R7: IF (φ is close to ¾) AND (d is close to 0.0371) THEN (Corner is 8)

80

Results

81

Results analysis

Unsupervised → fully automatic

Learning from scratch → no pre-training

Cluster (fuzzy rules/neurons) number is not predetermined, defined by data only → structure is flexible and evolving

Recursive calculation → less computing power required for real-time execution

82

eTS on FPGA - XtremeDSP

Pk

flag

clusAddr

R

replaceFlag

newFlag

clusAddr

incR

we

<zValid>

upd

distSq

<Pmax>

delta

<index>

calcPmax&MinDist

PkUpdate

To Workspace8

d_synch

To Workspace5

idxMax

To Workspace4

delta

To Workspace3

Pmax

To Workspace2

Pk

To Workspace1

xlmcoderule_set_update

d_synch

R

Pk

Pmax

delta

index

clusAddr

Pk_out

replace_rule

new_rule

MCode

xl logical or

Logical1

xl logical and

Logical

xl inv not

Inverter

fpt dbl

Gateway Out9

fpt dbl

Gateway Out8

fpt dbl

Gateway Out7

fpt dbl

Gateway Out6

fptdbl

Gateway Out5

fptdbl

Gateway Out4

fptdbl

Gateway Out3

fpt dbl

Gateway Out2

fpt dbl

Gateway Out1

fpt dbl

Gateway Out

z -71

Delay3z -70

Delay1

z -1

Delay

xlconvertcast

Convert2

xlconvertcast

Convert1

xlconvertcast

Convert

<we>

upd

distSq

R

zValid

Z

<Pk>

Dsy nch

incRincR

replace

new

Z

clusAddr

Pk

upd

distSq

R

zValid

Z

f lag

RnewFlag

replaceFlag

clusAddr

83

eTS on FPGA - XtremeDSP

84

Applications: Classification and Control

Controllers with evolvable structure

Application to EEG signals classification

Classification of Carcinoma Kidney Tissue Status based on Protein Expression Data

Biotech process applications

85

Indirect learning (Psaltis et.al, 1988)Adaptive control (incl. controller structure)

Fk yset-point uk yk+1 yk yk yk+1

Controller

Plant

∫

Fk yk+1 uk yk

Controller

Evolving Controllers

86

eController - example

Tamb

k

Tset-point uk Toutk+1

Toutk

Toutk+1

Plant Evolvable Fuzzy Controller

∫

87

eController - example

Cooling coil

Air Inlet Temperature

Sensor

Air Flow Direction

Water Inlet Temperature

Sensor

Chilled Water Suppy

Control Valve

Set Point

ControllerControl Signal

Supply Air Temperature

Sensor

Volumetric Air Flow Rate

Sensor

Fan

88

eController - results

89

eController - results

90

• Controller structure

• new rule:

• modified rule:

R1: IF ( ambkT is Low) AND ( out

kT 1+ is High) AND ( outkT is High) THEN ( ku is Low)

R2: IF ( ambkT is High) AND ( out

kT 1+ is Medium) AND ( outkT is Medium) THEN ( ku is High)

R3 IF ( ambkT is Very Low) AND ( out

kT 1+ is High) AND ( outkT is High) THEN ( ku is Very Low)

R4: IF ( ambkT is Medium) AND ( out

kT 1+ is Low) AND ( outkT is Low) THEN ( ku is Medium)

R5: IF ( ambkT is Medium) AND ( out

kT 1+ is Relatively High) AND ( outkT is Medium) THEN ( ku is Medium)

eController - results

91

eController - results

92

Off-line vs on-line: real data (air-conditioning system)

93

EEG signal classification procedure eClass

1) Establish the first EEG signal as the first prototype. Its S=0

2) Starting from the next the Scatter of each new EEG signal is calculated recursively

3) The Scatter of the existing prototypes are recursively updated

4) Scatter of new EEG signal is compared to updated scatter of the existing prototypes

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eClass: Procedure

5) If Snew < S* then the new EEG signal isadded as a new prototype and a new rule is formed (R := R+1)

6) If in addition to 5) the new EEG signal is close to an old prototype then the new EEG signal replaces this prototype

The condition to have lower S is a very strong one, which restricts excessively large rule base to be formed

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eClass

Class1 Classm

EEG signal selected as a prototype for Class1

EEG signal selected as a prototype for Classm

Classification result

........

Overall Rule-base

EEG vectorx∈RnxL

*1j

*jnRulej: IF (EEG1 is EEG ) AND …AND (EEGn is EEG )

THEN (Class is Pain/NoPain)

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EEG, Experimental set-up

• Hope Hospital, Liverpool, UK

• Female volunteer

• 64 electrode cap

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Prototype EEG signals‘No Pain’ class

0 50 100 150 200 250 300 350 400 450 500-10

-8

-6

-4

-2

0

2

4

6

8

10Prototype of Class NoPain

Sampling Instances of the EEG signals

Am

plitu

de in

mic

rovo

lts

EEG11

EEG21

Sample l

EEG31

EEG41

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Prototype EEG signals‘Pain’ class

0 50 100 150 200 250 300 350 400 450 500-15

-10

-5

0

5

10

15Prototype of Class Pain

Sampling Instances of the EEG signals

Am

plitu

de in

mic

rovo

lts

EEG11

EEG41

EEG31

EEG21

Sample l

99

eClass: EEG - results• The subject was a healthy female

• EEG data were recorded on 8th and 15th June 2000, and 2nd August 2000

• On each of these days, three EEG recordings were taken during “painful” laser stimulation of the right arm

• In total, 9 continuous EEG data files

• 355 Pain epochs (Class 1) and 355 No-Pain ones (Class2)

• 168 fuzzy rules formed by eClass; 79.45% rate

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First-principles model:

eTS model:

),,(1 kkkXk DOSXX μ=+ k= 0 ,...,N -1

),,(1 kkkSk DOSXqS =+

),,(1 kkkDOk DOSXqDO =+

R1: IF (S is Very High) AND (DO is Very High) THEN DOaSaaX 12

11

10 ++=

R2: IF (S is Very Low) AND (DO is Very Low) THEN DOaSaaX 22

21

20 ++=

R3: IF (S is High) AND (DO is High) THEN DOaSaaX 32

31

30 ++=

R4: IF (S is Low) AND (DO is Low) THEN DOaSaaX 42

41

40 ++=

R5: IF (S is Very Medium) AND (DO is Medium) THEN DOaSaaX 52

51

50 ++=

R6: IF (S is Extremely High) AND (DO is Extremely High) THEN DOaSaaX 62

61

60 ++=

R7: IF (S is Extremely Low) AND (DO is Extremely Low) THEN DOaSaaX 72

71

70 ++= )

Fermentation Processes On-line Prediction

101

BioProcess Modeling

102

eTS model of a fermentation

103

Concluding remarks

• Usable in real-time, intelligent sensors• Non-iterative (one-pass, incremental)• Recursive (comp very efficient)• adapts the structure (plus parameters)• enrich/adds and replaces = evolves• simple (locally linear, no search)• gradual changes (inheritance, R+1)• starts from scratch (no a priori info)• Number of applications