Andy Richardson

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23 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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Multi
-
Faceted U.S.
-
Japan
Program in Natural Hazard
Mitigation

Experiencing

WIND HAZARD EARTHQUAKE
ENGINEERING LAB WHEEL


Established

in

1999

by

Dr
.

Makola

Abdullah



Research

interests

include


Passive,

semi
-
active

and

active

structural

control

designs
.


Sensor/actuator

placement

using

evolutionary

algorithms
.


Damage

mitigation

assessment

after

natural

disasters
.


Computational

fluid

dynamics

for

the

design

and

analysis

of

structures

exposed

to

high

winds
.


Mitigation

of

pounding
.


Analysis

of

earthquakes

in

the

southeastern

U
.
S
.



Computational

fluid

dynamic

applications

to

multi
-
phase

separation
.


Sensor/Actuators Placement on Civil
Structures Using A Real Coded
Genetic Algorithm

FAMU
-
FSU College of Engineering

Department of Civil Engineering

By

Andy Richardson


Makola Abdullah, Ph.D



RESEARCH OBJECTIVE


Determine the optimal placement of
k

feedback controllers
on an
n
-
story structure.



Place and design controllers simultaneously using a real
coded genetic algorithm.



Compare results to similar work that uses a hybrid method.

GENETIC ALGORITHM

What?



Probabilistic search method based on the mechanics of


Darwin’s natural selection


Why?



Simple yet powerful search method for optimization


problems not readily solved by conventional search techniques

How?



Replicating evolution by selection and survival of the fittest


using the following steps:


Coding


Breeding


Selection

REAL CODED GENETIC ALGORITHM


Discrete Recombination
-
is the process whereby new chromosomes are
generated from existing individuals




Variable 1

Variable 2

Individual 1 12 25 5

Individual 2 123 4 34


Selected Ind 1 2 2 1

Selected Ind 2 1 2 1


Off Spring 1 123 4 5

Off Spring 2 12 4 5

REAL CODED GENETIC ALGORITHM

Real Valued Mutation
-

randomly created values are added to the variables
with a low probability.

Variable 1

Variable 2

S=
-
1

r

S=1

STOCHASTIC SELECTION




0


0.2


0.5


0.6


0.8


1


Pointer 1


Pointer 2


Pointer 3


Random number


Individual


1



2



3



4



5





N number of individuals to be selected, (N=3)

Pointer 1

[0,1/N]

Fitness

Individuals 1,3,5 are selected for future breeding operations

Equations of Motion

M

mass matrix
C
damping matrix

K
stiffness matrix

b
participation matrix for the control force

h
participation matrix of floor masses
u
controlled input


floor displacement

x
f

C
d

modal damping matrix


modal stiffness matrix


modal matrix


F
matrix of

controller gains



SYSTEM MODEL

x
System states

u C
ontrol force

Q
Weighting matrix with respect to the building’s response

R
Weighting matrix with respect to the controlled input



Modal stiffness matrix


I

Identity

PERFORMANCE FUNCTION

PLACEMENT DESIGN METHOD

Start

Evaluate

Generic

Gains

End

Genetic

Algorithm

Gradient

Optimization

Start

Evaluate

Generic

Gains

End

Genetic

Algorithm

Gradient

Optimization

Start

Evaluate

Generic

Gains

End

Genetic

Algorithm

Gradient

Optimization

End

Genetic

Algorithm

Gradient

Optimization

End

Genetic

Algorithm

Gradient

Optimization

Start

Evaluate

Generic

Gains

End

Genetic

Gradient

Optimization

Hybrid Design

Start

End

Real Coded

Genetic Algorithm

Start

End

Real Coded Design



Place
k

controllers on an
n
-
story structure


Example of a genetic string for the structure


shown below is

CODING GENETIC STRING

HYBRID

REAL CODED GA

GENETIC ALGORITHM ITERATIONS

SENSOR/ACTUATOR PLACEMENT

TOP FLOOR RESPONSE TO EL CENTRO
EARTHQUAKE

TOP FLOOR RESPONSE TO THE NORTH
RIDGE AT SANTA MONICA
EARTHQUAKE

SUMMARY OF BUILDING RESPONSE

SUMMARY OF CONTROL FORCES

CONCLUSION



Both methods are effective in reducing the buildings
response.


Proposed method is more convenient and less
computationally intensive than the hybrid method.


Proposed Method has a high convergence rate.


The convergence rate improves with the number of
iterations of the algorithm.


Both methods are subjective to the weighting matrices
Q

and
R.


FUTURE WORK



Consider actuator dynamics, controller saturation


Apply concept to a multi
-
bay frame 2
-
D building model


Apply concept to a multi
-
bay frame 3
-
D building model


Develop a general scheme for determining the optimal
placement of sensor/actuators

Expressing in terms of closed loop plant

STATE SPACE REPRESENTATION

Lyapunov equation

Gradient of the gain matrix

Lyapunov equation

PERFORMANCE FUNCTION (Cont.)

Expand in terms of fundamental transition matrix

Eliminating dependence on

x
(0),
average or expected value of


PERFORMANCE FUNCTION (Cont.)

BINARY GENETIC ALGORITHM

Mutation
-

randomly switches 1 to 0 or vice versa


10
0
01111
1

10
1
01111
0

Coding
-
representing variable parameter information in binary

Crossover
-

cutting and replacing the tail of one string with that of the other


10001
1111

10001
1000


11110
1000

11110
1111


Point of Crossover

Selection
-

the process of choosing the fittest strings from the
current population for use in future reproductive operations

w(t)


Earthquake

F

Building
Dynamics

x(t)

Building
response

u(t)

Control


Force

y(t)

Sensed
output

DECENTRALIZED COLLOCATED DESIGN