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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
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