evolving fuzzy model method for online fuzzy model identification

University of Ljubljana

Faculty of electrical engineering

Wien, 2012 eFuMo 1

Evolving Fuzzy Model

Method for Online Fuzzy

Model Identification

Dejan Dovžan, Vito Logar and Igor Škrjanc

E-mail:: [email protected], [email protected] and [email protected]

Web page: http://msc.fe.uni-lj.si/



Outline:

Wien, 2012 eFuMo 2

•Description of the problem (monitoring of the

oxygen in WWT process)

•Proposed solution

•Used method

•Results

•Conclusion


Faculty of electrical engineering Description of problem:

Wien, 2012 eFuMo 3

1.Tank 2.Tank

NH4 in

Air flow

Valve opening

O2

NH4


Faculty of electrical engineering Description of the problem:

Wien, 2012 eFuMo 4

•Monitoring Waste Water Treatment process

•Problem:

•Sensors are falling out frequently, causing

problems in control.

•The process is nonlinear and time varying

•Goal: Creating soft sensor for oxygen and ammonia:

if the real signal differ from the calculated model output,

raise the alarm and propose a different output.

•Design and solution test performed on a real data from

plant gathered for aprox. 11 days with low amount of

sensor fallouts.


Faculty of electrical engineering Proposed solution for O2

monitoring:

Wien, 2012 eFuMo 5

•For oxygen monitoring two models are used describing

relations between:

•Valve opening and air flow

•Air flow and oxygen concentration in the tank

•The TS fuzzy model is used for model the relations

•Using evolving Fuzzy Model method, to learn and

adapt the process model.

•The local model structure is in form of:

y(k+1)=a y(k)+b u(k) + r (ARX)


Faculty of electrical engineering Proposed solution for O2

monitoring:

Wien, 2012 eFuMo 6

•The idea of fuzzy model is to approximate a nonlinear

process with linear models that are valid in a certain

input-output area.

•For space partitioning we use clustering

•For model identification weighted least squares

u

y


Faculty of electrical engineering Used method:

Wien, 2012 eFuMo 7

•For learning the fuzzy model

eFuMo toolbox was used

• Based on:

•Recursive Gustafson-Kessel / fuzzy c-means

clustering method

•Fuzzy weighted least squares

•Includes evolving mechanisms:

•Adding mechanism

•Removing mechanism

•Merging mechanism (on distance and firing levels

correlation)

•Splitting mechanism



Wien, 2012 eFuMo 8

•Recursive Gustafson-Kessel / fuzzy c-means

clustering method:

•On-line calculation of cluster centers

•On-line calculation of Fuzzy covariance matrix:



Wien, 2012 eFuMo 9

•Fuzzy weighted least squares for on-line local

models’ parameter estimation:



Used method:

Wien, 2012 eFuMo 10



Wien, 2012 eFuMo 11

•Removing mechanism:

oMinimal existence condition: oIn certain time after creation support must rise above a certain user defined

threshold in order to keep cluster.

oSupport is the number of samples assigned to clusters. The sample is

assigned to cluster with the highest firing level.

oSupport/Age based condition:

k…current sample number,

ki…cluster creation sample number

Nsi…support



Wien, 2012 eFuMo 12

•Merging mechanism:

oUnsupervised: oBased on normalized distance

oCorrelation analysis: oBased on correlation between firing levels and local-

models’ parameters (angle between them).



Wien, 2012 eFuMo 13

•Splitting mechanism:

oBased on cluster error

oModel error is calculated and assigned to clusters

based on their firing levels

oWhen the highest error rises above threshold the

cluster is split.

oNew position calculated based on standard

deviation of data around the cluster



Used method (Monitoring

system):

Wien, 2012 eFuMo 14

INPUT

Valve/Air monitor

Evolving model

Adaptive model

Static model

Y_e

Y_a

Y_s

Compare

model outputs

and real

output

Y_real

Y_soft

Alarm

Learning


Faculty of electrical engineering Used method (Monitoring

system):

Wien, 2012 eFuMo 15

If Alarm(k-200) = 0 then:

•Calculate model outputs for k-200 sample and

calculate their absolute error

•Assign the error to the model

(e_model=0.99*e_model+0.01*e_current)

• learn evolving model and adaptive model

•If evolving model adds a cluster or removes a cluster

replace the adaptive and static model with the

evolving model structure before adding/removing of

the cluster (only if the evolving model error is lower

than the static and adaptive model error)

Learning module

•Delayed learning for 200 samples



system):

Wien, 2012 eFuMo 16

Data sample

Evolving

mechanisms

Add or

remove

clusters?

NO

Adaptation

mechanisms

YES Replace static

and adaptive

model if

necessary

Add or

remove

cluster

If e_evolving<e_static

than static_model=evolving_model

If e_evolving<e_adaptive

than adaptive_model=evolving_model

Evolving model learning



Used method (Monitoring

system):

Wien, 2012 eFuMo 17

INPUT

Valve/Air monitor

Evolving model

Adaptive model

Static model

Y_e

Y_a

Y_s

Compare

model outputs

and real

output

Y_real

Y_soft

Alarm

Learning



system):

Wien, 2012 eFuMo 18

Comparison module

Ok_e=|Y_e-Y_real|>1.5 y_std

Ok_a=|Y_a-Y_real|>1.5 y_std

Ok_s=|Y_s-Y_real|>1.5 y_std

Y_soft

Alarm If any(Ok_e,a,s==0) then Alarm = 0 else Alarm = 1

If Alarm = 0 then Y_soft = Y_real else Y_soft = Y_e,a,s

Calculated from fuzzy

covariance matrices



Results

Wien, 2012 eFuMo 19

•We took the least faulty data and simulated sensor

fallouts, which are most common errors in WWT

process

•The data were normalized


Faculty of electrical engineering Results(valve/air flow)

Wien, 2012 eFuMo 20

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 104

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

sample number

valve

open

ing/co

ntroll

er ou

tput

0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 104

-1

-0.5

0

0.5

1

sample number

air flo

w

sensor output

soft-sensor output



Wien, 2012 eFuMo 21

0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 104

-1

-0.5

0

0.5

1

sample number

air flo

w

sensor output

soft-sensor output

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

sample number

air flo

w ala

rm



Wien, 2012 eFuMo 22

2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5

x 104

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

sample number

air f

low

sensor output

real output

soft-sensor output


Faculty of electrical engineering Results (air flow/O2)

Wien, 2012 eFuMo 23

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 104

-1

-0.5

0

0.5

1

sample number

O 2 in se

cond

tank

sensor output

soft-sensor output

0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 104

-1

-0.5

0

0.5

1

sample number

air flo

w

sensor output

soft-sensor output



Wien, 2012 eFuMo 24

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 104

-1

-0.5

0

0.5

1

sample number

O 2 in se

cond

tank

sensor output

soft-sensor output

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

sample number

O 2 alarm



Wien, 2012 eFuMo 25

3 3.1 3.2 3.3 3.4 3.5 3.6 3.7

x 104

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

sample number

O2 in s

econd t

ank

sensor output

soft-sensor output

real output


Faculty of electrical engineering Conclusions

Wien, 2012 eFuMo 26

•The first results are encouraging

•Maybe better tuning of O2 model

•Need of testing for other kind of sensor errors

•Implement additional methods for checking the models

(if they are valid)

•Do a monitoring algorithm for ammonia

evolving fuzzy model method for online fuzzy model identification

Documents