(Meta)modelarea circuitelor electronice➢ Simularea la nivel de circuit este costisitoare din punct de vedere al

calculelor, în special dacă circuitul este complex şi necesită mai

multe tipuri de analize (în timp, în frecvenţă, etc.).

➢ Alternativa: nivele ierarhic superioare de abstractizare în descrierea

circuitului; utilizare modele compacte.

➢ Doi factori determină utilitatea modelului:

❖ eficient din punct de vedere al volumului şi complexităţii calculelor

❖ precizia (suficient de exact).

Modelarea

circuitelor

• modelarea

functiilor de

performanta

(statice)

• modelarea

functionala

(dinamice)

(Meta)modelarea circuitelor electroniceutilizand sisteme fuzzy

➢ Modelarea circuitelor electronice

❖ modelarea functiilor de performanta

▪ modelare SOTA

❖ modelarea functionala

▪ modelare FCOTA

▪ model Simulink

Modelarea functiilor de performanta ale unui circuit

analogic

SOTA – Simple Operational Transconductance amplifier

( )

( )

( ) ( ) 1cu;1;100

0,75μcu;1;10

0,5μcu;1;8

μA20;70

5656

3434

1212

=

=

=

LWW,L

LLW

LLW

IB

•Parametrii

• Functii de performanta:

21 ii

o

vv

vAvo

−=

BAvoGBW =

PM

cA

AvoCMRR =

Procedura de

modelareDesign of

experiment

! Metamodel (surrogate model);

a model of the model

❖ Generally speaking, a metamodel, or a surrogate model, is a

model of the model, i.e. a simplified model of an actual model

of a circuit, system, or software like entity.

❖ A metamodel can be a mathematical relation or algorithm

representing input and output relations.

❖ A model is an abstraction of phenomena in the real world; a

metamodel is yet another abstraction, highlighting properties

of the model itself.

❖Metamodeling typically involves studying the output and input

relationships and then fitting proper metamodels to represent

that behavior.

Metamodeling

➢ Once the metamodels are generated, the designer can conduct

more extensive analyses of the circuit and use the same

metamodel for different criteria to be optimized.

➢ The detailed simulation is significantly more time

consuming than using the metamodel.

➢ The key points of metamodeling:

▪ accuracy - capability of generating the system response over the

design space;

▪ efficiency - computational effort required for constructing the

metamodel;

▪ transparency - capability of providing the information concerning

contributions and variations of design variables and correlation

among the variables;

▪ simplicity - simple methods should require less user input and be

easily adapted to different problem.

Metamodeling

Determinarea setului de parametric (DoE)

➢ LHS – Latin Hypercube Sample (+ Full Factorial Design)

• Domeniul fiecarei variabile se imparte in K intervale (egale)

• În fiecare interval se alege aleator o valoare.

• Cele K valori ale fiecărui parametru sunt asociate în mod aleator cu cele

K valori ale altui parametru ş.a.m.d. rezultand K vectori ai parametrilor.

• LHS

• 2 level Full Factorial Design – toate combinatiile posibile ale

parametrilor, considerand numai valorile extreme (minim si maxim)

DoE

9 /29

❑ For the design of the experiment, it is necessary to generate those

parameter combinations that fill in the parameter space, in order to

encompass all the regions (in the parameter space).

❑ A good experimental design (ED) is essential to simultaneously reduce

the possible effect of noise and bias error.

❑ It is recommended to construct an experimental design by combining

multiple techniques for design experiment to reduce the risk of using a

poor ED.

LHS designs may leave out the boundary and the final model may lead to large

extrapolation errors. To avoid this, one should generate the experimental design by

mixing the LHS design with a 2 level (or n level) full factorial design:

1. Latin Hypercube sampling is used to generate a specified number of randomly

distributed values for each parameter, these values being randomly permuted to

obtain different parameter combinations.

2. Two-level full-factorial design is used to generate all possible parameter

combinations, considering only the extreme values (minimum and maximum) for all

parameter

Esantion al setului de date de antrenare

Structura modelului fuzzy Avo

• Sistem fuzzy

TS de ordin 1

Multimi fuzzy la intrare

• 6 reguli

• 6 mf pe fiecare

variabila

Multimi fuzzy la iesire. Reguli

•out1mf1=[-0.27907622925482 4.7336423208163 -0.22929012109304 -0.0028363221851113 45.49729161833]

•out1mf2=[-0.11955049624726 10.308484211334 -0.23201470784719 0.00408876941051388 25.0003432748168]

•out1mf3=[-0.50949884619065 5.4106958973798 -0.70345988469712 0.0282962177749871 52.5057718830839]

•out1mf4=[-0.32603181267357 11.099093462894 -0.98934580658441 0.0138103461621346 37.5543179917034]

•out1mf5=[-0.18956099089732 8.6928124102796 -0.96510752831766 0.016395396082041 33.7788736156701]

•out1mf6=[-0.38682872084570 7.5633681369785 -1.3443012661576 -0.042937570643951 49.8212643120914]

• Multimile fuzzy la iesire

• Baza de reguli

Evolutia RMSE pe durata instruirii

Suprapotrivire

(overfitting)

Suprapotrivire

(overfitting)

RMSE pentru modelele fuzzyFuncţia

de

circuit

Setul

de date

RMSE

3 reguli 6 reguli 10 reguli

antrenare verificare antrenare verif. antrenare verif.

Avo

450a+50v1.85

1.5

1.15

0.55

1.6

1.45

0.7

0.55

700a+150v1.39

1.27

1.16

1.05

1.29

1.18

1.06

0.93

1.21

1.15

1.00

0.93

GBW

[KHz]

450a+50v178

132

176

115

130

88

124

84

106

83

79

64

700a+150v205

156

142

89

155

142

80

58

145

140

68

65

PM [o]

450a+50v0.142

0.115

0141

0.115

0.115

0.110

0.079

0.056

0.116

0.108

0.084

0.073

700a+150v0.116

0.096

0.063

0.040

0.102

0.090

0.054

0.033

0.98

0.090

0.050

0.036

CMRR

450a+50v101735

95640

61735

46408

72200

70100

61735

46408

700a+150v107279

80529

72116

35201

36800

33400

27823

43875

75311

75188

30750

30706

• RMSE este dependenta de ordinul de marime

al functiei modelate( )

=

−

K

k

kdk yy

K1

21

Comparație model fuzzy –simulare Spice

Funcţia de

circuit

EPM [%]

instruire verificare

Avo 1,375 1,278

GBW 2,645 1,921

PM 0,049 0,0398

CMRR 3,04 4,67

•EPM – eroarea procentuala

medie

Suprafetele generate de modelele fuzzy

Modelarea functională a unui circuit analogic

Procedura de metamodelare

FCOTA – Folded Cascode OTA

Modelul functional fuzzy

Colectarea datelor

necesare modelarii

Structura modelului fuzzy

Antrenare

Evoluţia erorilor la antrenarea sistemului fuzzy

amplificare(frecvenţă, temperatură) pentru circuitul FCOTA.

Reguli

Suprafetele generate de modelele fuzzy

• Sistemul fuzzy

dupa antrenare

• Sistemul fuzzy

initial

Comparatie model fuzzy –simulare Spice

Modelul functional fuzzy

Implementare Simulink

Rezultate -1

Rezultate - 2

Exercitiu

32 /29

Graficele cu evolutia erorilor pentru

instruirea cu ANFIS a unor sisteme fuzzy

sunt prezentate in figurile alaturate.

Caracterizati procesul de instruire si realizati

o recomnadare referitoare la obtinerea unui

sistem fuzzy final optim, pastrand aceeasi

configuratie a slf si a setului de date.