MultiFaceted U.S.Japan Program in Natural Hazard Mitigation

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\
Experiencing

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

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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.

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Sensor/Actuators Placement on Civil Structures
Using A Real Coded Genetic Algorithm
By Andy Richardson Makola Abdullah, Ph.D
FAMU-FSU College of Engineering Department of
Civil Engineering
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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.

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GENETIC ALGORITHM

• What?
• Probabilistic search method based on the
  mechanics of
• Darwins 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

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REAL CODED GENETIC ALGORITHM

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

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
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REAL CODED GENETIC ALGORITHM
Real Valued Mutation- randomly created values are
added to the variables with a low probability.
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STOCHASTIC SELECTION
Pointer 1
Pointer 2
Pointer 3
 
1
 
Individual
2
3
4
5
Fitness
0
0.2
0.5
0.6
0.8
1
Random number
N number of individuals to be selected,
(N3) Pointer 1?0,1/N
Individuals 1,3,5 are selected for future
breeding operations
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SYSTEM MODEL
Equations of Motion
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PERFORMANCE FUNCTION
x System states u Control force Q
Weighting matrix with respect to the buildings
response R Weighting matrix with respect to the
controlled input ? Modal stiffness matrix I
Identity
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PLACEMENT DESIGN METHOD
Start
Evaluate
Generic
Start
Start
Gains
Real Coded Genetic Algorithm
Genetic
Algorithm
End
End
Gradient
Optimization
End
Hybrid Design
Real Coded Design
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CODING GENETIC STRING

• Place k controllers on an n-story structure
• Example of a genetic string for the structure
• shown below is

HYBRID
REAL CODED GA
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GENETIC ALGORITHM ITERATIONS
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SENSOR/ACTUATOR PLACEMENT
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TOP FLOOR RESPONSE TO EL CENTRO EARTHQUAKE
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TOP FLOOR RESPONSE TO THE NORTH RIDGE AT SANTA
MONICA EARTHQUAKE
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SUMMARY OF BUILDING RESPONSE
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SUMMARY OF CONTROL FORCES
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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.

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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

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STATE SPACE REPRESENTATION
Expressing in terms of closed loop plant
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PERFORMANCE FUNCTION (Cont.)
Lyapunov equation
Gradient of the gain matrix
Lyapunov equation
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PERFORMANCE FUNCTION (Cont.)
Expand in terms of fundamental transition matrix
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BINARY GENETIC ALGORITHM
Coding-representing variable parameter
information in binary Crossover - cutting and
replacing the tail of one string with that of the
other 100011111
100011000
111101000 111101111
Point of Crossover
Mutation - randomly switches 1 to 0 or vice
versa 100011111
101011110
Selection - the process of choosing the fittest
strings from the current population for use in
future reproductive operations
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DECENTRALIZED COLLOCATED DESIGN
x(t) Building response
w(t) Earthquake
Building Dynamics
y(t) Sensed output
u(t) Control Force
F