모달 퍼지 이론을 이용한 지진하중을 받는 구조물의 능동제어

Structural Dynamics & Vibration Control Lab. 1

모달 퍼지 이론을 이용한 지진하중을 받는 구조물의 능동제어

최강민 , 한국과학기술원 건설 및 환경공학과조상원 , 한국과학기술원 건설 및 환경공학과오주원 , 한남대학교 토목공학과이인원 , 한국과학기술원 건설 및 환경공학과

2004 년도 한국전산구조공학회 춘계 학술발표회국민대학교 , 서울2004 년 4 월 10 일


Outline

• Introduction

• Proposed Method

• Numerical Example

• Conclusions


Introduction

Fuzzy theory has been recently proposed for the active structural control of civil engineering systems.

The uncertainties of input data from the external loads and structural responses are treated in a much easier way by the fuzzy controller than by classical control theory.

If offers a simple and robust structure for the specification of nonlinear control laws.


Modal control algorithm represents one control class in which the vibration is reshaped by merely controlling some selected vibration modes.

Because civil structures has hundred or even thousand DOFs and its vibration is usually dominated by first few modes, modal control algorithm is especially desirable for reducing vibration of civil engineering structure.


Conventional Fuzzy Controller

One should determine state variables which are used as inputs of the fuzzy controller.

- It is very complicated and difficult for the designer to select state variables used as inputs among a lot of state variables.

One should construct the proper fuzzy rule.

- Control performance can be varied according to many kinds of fuzzy rules.


Objectives

Development of active fuzzy controller on modal coordinates

- An active modal-fuzzy control algorithm can be magnified efficiency caused by belonging their’ own advantages together.


Proposed Method

Modal Approach• Equations of motion for MDOF system

• Using modal transformation

• Modal equations

gxMtftKxtxCtxM )()()()(

n

iiiqtqtx

1

)()(

(1)

(2)

(3)gT

iT

iiiiii xftqtqtq )()()( 22

),,1( ni


• Displacement

where

• State space equation

where

gCCCCC xEtFBtwAtw )()()(

T

CCT

CC

CC

CC EB

IA

0,

0,

02

)()()( txtxtx RC

.:)( dsipcontrolledtxC )(,1

nlxm

iiiC

.:)( dsipresidualtxR

(4)

(5)


•Control force

•Modal approach is desirable for civil engineering structure

)()( twKtF CC

- Involve hundred or thousand DOFs- Vibration is dominated by the first few modes

(6)


Structure Modal Structure

dfFuzzy controller

qq ,

Force output

Active Modal-fuzzy Control System


Modal-fuzzy control system design

Input variables

Output variables

Fuzzification

Defuzzification

Fuzzy inference

• Fuzzy inference : membership functions, fuzzy rule

• Input variables : mode coordinates• Output variable : desired control force

),( qq )( df


Six-Story Building (Jansen and Dyke 2000)

Numerical Example

2cm/sN227.0im

cmN297ik

005.0

11

10

00

00

00

00

1

1

1

1

1

1

gx


Frequency Response Analysis• Under the scaled El Centro earthquake

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2.0

2.5

3.0

PS

D

frequency, Hz

102

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

x 105

PS

D

frequency, Hz0 1 2 3 4 5 6 7 8 9 10

0

2

4

6

8

10

12

14

16

x 106

PS

D

frequency, Hz

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

PS

D

frequency, Hz0 1 2 3 4 5 6 7 8 9 10

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PS

D

frequency, Hz

104

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

x 106

PS

D

frequency, Hz

PSD of Displacement PSD of Velocity PSD of Acceleration

1st F

loor

6th F

loor


• In frequency analysis, the first mode is dominant.

-The responses can be reduced by modal-fuzzy control using the lowest one mode.


Active Modal-fuzzy Controller Design

• input variables : first mode coordinates• output variable : desired control force

),( 11 qq

• Fuzzy inference

)( df

• Membership function

- A type : triangular shapes (inputs: 5MFs, output: 5MFs)

- B type : triangular shapes (inputs: 5MFs, output: 7MFs)

A type : for displacement reduction B type : for acceleration reduction


• Fuzzy rule

- A type

NL NS ZE PS PL

NL PL PL PM PS ZE

NS PL PM PS ZE NS

ZE PM PS ZE NS NM

PS PS ZE NS NM NL

PL ZE NS NM NL NL

- B type

1q

1q

NL NS ZE PS PL

NL PL PL PS PS ZE

NS PL PS PS ZE NS

ZE PS PS ZE NS NS

PS PS ZE NS NS NL

PL ZE NS NL NL NL


- Fuzzy rule surface (A type)


Acc

el.

(m/s

ec2

)A

ccel

. (m

/sec

2)

Time(sec)

Acc

el.

(m/s

ec2

)

Kobe(PGA: 0.834g)

California(PGA: 0.156g)

El Centro(PGA: 0.348g)

0 10 20 30 40

-8

-4

0

4

8

- 8

- 4

0

4

8

0 4 8 12 16 20

-8

-4

0

4

8

- 8

- 4

0

4

8

0 10 20 30 40

-8

-4

0

4

8

- 8

- 4

0

4

8

Input Earthquakes


max,1

)(max

x

txJ i

it

max,2

/)(max

n

ii

it d

htdJ

max,3

)(max

ai

ai

it x

txJ

W

tfJ i

it

)(max

,4

Normalized maximum floor displacement

Normalized maximum inter-story drift

Normalized peak floor acceleration

Maximum control force normalized by the weight of the structure

- This evaluation criteria is used in the second generation linear control problem for buildings (Spencer et al. 1997)

Evaluation Criteria


Control Results

0

1

2

3

4

5

6

0 0.1 0.2 0.3

Peak interstory drif t (cm)

Flo

or o

f str

uctu

re

Uncontrolled

Fuzzy

Modal-f uzzy A

Modal-f uzzy B

0

1

2

3

4

5

6

0 100 200Peak absolute acceleration

Flo

or o

f str

uctu

re

Uncontrolled

Fuzzy

Modal-f uzzy A

Modal-f uzzy B

Fig. 1 Peak responses of each floor of structure to scaled El Centro earthquake


0

0.2

0.4

0.6

0.8

1

1.2

1.4

Evaluation criteria

Red

uct

ion

fac

tor

Control strategy J1 J2 J3 J4

Active Modal-fuzzy control (A type)

Active Modal-fuzzy control (B type)

Active Fuzzy control

0.343

0.548

0.600

0.562

0.635

0.756

1.186

0.601

0.660

0.0178

0.0134

0.0178

• Normalized Controlled Maximum Response due to Scaled El Centro Earthquake• Normalized Controlled Maximum Response due to Scaled El Centro Earthquake

J1 J2 J3

A typeFuzzy

B type





Active fuzzy control

0.449

0.729

0.745

0.727

0.762

0.885

1.856

0.842

0.939

0.0178

0.0134

0.0178

• High amplitude (the 120% El Centro earthquake)• High amplitude (the 120% El Centro earthquake)

0

0.5

1

1.5

2

Evaluation criteria

Red

uct

ion

fac

tor A type

Fuzzy

B type






0.231

0.403

0.473

0.467

0.509

0.640

1.110

0.619

0.531

0.0178

0.0134

0.0178

• Low amplitude (the 80% El Centro earthquake)• Low amplitude (the 80% El Centro earthquake)

0

0.2

0.4

0.6

0.8

1

1.2

Evaluation criteria

Red

uct

ion

fac

tor A type

Fuzzy

B type






0.294

0.360

0.430

0.321

0.366

0.402

0.677

0.660

0.614

0.0178

0.0134

0.0178

• Scaled Kobe earthquake (1995)• Scaled Kobe earthquake (1995)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Evaluation criteria

Red

uct

ion

fac

tor A type

Fuzzy

B type






0.175

0.173

0.178

0.485

0.268

0.244

1.144

0.561

0.260

0.0100

0.0070

0.0076

• Scaled California earthquake (1994)• Scaled California earthquake (1994)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Evaluation criteria

Red

uct

ion

fac

tor A type

Fuzzy

B type


Conclusions

• A new active modal-fuzzy control strategy for seismic response reduction is proposed.

• Verification of the proposed method has been investigated according to various amplitudes and frequency components.

• The performance of the proposed method is comparable to that of conventional method.

• The proposed method is more convenient and easy to apply to real system

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모달 퍼지 이론을 이용한 지진하중을 받는 구조물의 능동제어