Evolvable Fuzzy Systems - IEEE · PDF file1 Evolvable Fuzzy Systems Plamen Angelov Intelligent...
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Evolvable Fuzzy Systems
Plamen Angelov
Intelligent Systems Research LaboratoryDept of Communications SystemsInfoLab21, Lancaster University, UK
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Lancaster University
One of the top 10% of the UK Universities
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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
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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
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Intelligent Systems Lab
Collaborative mobile robots (5 Pioneer-3DX) with evolvable intelligence using embedded eTS systems for:prediction, classification and control
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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)
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Outline
Controllers with evolvable structure
Application to EEG signals classification
Classification of Carcinoma Kidney Tissue Status based on Protein Expression Data
Biotech process applications
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System Modeling
• predict object reactions;• control it;• detect faults;• study process performance
A. Conventional Models- First Principles Models- Black-box models
B. Fuzzy Models
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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
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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
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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
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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
)...()(...)(:
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11
ininii
nni
bxaxayTHENisXxANDANDisXxIFR
+++=
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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
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TSK in 2D Feature Space
• MIMO TSK in a 2D feature space
• eClustering
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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
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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)
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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
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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.)
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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=
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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 <
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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
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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
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⎟⎠⎞
⎜⎝⎛ <⎟
⎠⎞
⎜⎝⎛ >
==
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
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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
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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
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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
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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
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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
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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
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Fuzzy sets, Heavy naphtha
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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.
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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
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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)
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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.
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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)
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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)
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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
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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
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Agent 2
Agent 3
Agent 1
Agent 4
Unrecognized agent
Environment
Cooperative Rule-base
Co-operation in autonomous detection
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Underwater target recognition, J&S Marine
Object1
A
B
D
C
Area I Area II
Agents exchange new rule info
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Underwater target classification- scenario 2
Object1
Object2
Object3
Object4
A B
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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
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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)
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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
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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
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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
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Our experiment (B-69, InfoLab21)
bb.mpg
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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)
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Results
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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
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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
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eTS on FPGA - XtremeDSP
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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
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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
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eController - example
Tamb
k
Tset-point uk Toutk+1
Toutk
Toutk+1
Plant Evolvable Fuzzy Controller
∫
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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
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eController - results
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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
94
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
95
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)
96
EEG, Experimental set-up
• Hope Hospital, Liverpool, UK
• Female volunteer
• 64 electrode cap
97
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
98
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
100
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