CASSEM Project WP 5

1
CASSEM Project WP - 5

• FP6 STREP Project Contract N 013517NMP3 - CT
  - 2005 - 013517
• Bruxelles, 27thOctober 2006
• IST Lisbon Technical University, Portugal
• Participant nr. 8

2
WP 5 Parameters Sensitivities and Optimization
Scheduled start month 19 Task 5.1 Parameters
sensitivities analysis for robust control (TL
ULB) Task 5.2 Passive treatments optimization
for damping maximization (TL IST) Task 5.3
Sensors actuators optimization for control
efficiency (TL IST) Task 5.4 Validation for
passive, active and hybrid vibraton control (TL
IST, ULB)
3
WP 5 Parameters Sensitivities and Optimization
Task 5.1 Parameters sensitivities analysis for
robust control ULB
4
Principle
Input parameters
Matlab script to generate .dat file
FEM of complete structure in Samcef (laminate
shell theory)
Parameters sensitivity study
Samcef
Optimizer
Reduced (Craig-Bampton) model written to file
Matlab Script 1 (SamTech)
Reduced matrices are imported in Matlab
Matlab Script 2 (ULB/ASL)
I/O state-space model in Matlab/Simulink
5
Example collocated controller on a composite
boom equipped with MFCs
6
Parameters sensitivities
(10 change)
7
WP 5 Parameters Sensitivities and Optimization
Task 5.2 Passive treatments optimization for
damping maximization IST
Task not active yet. Viscoelastic numerical
models developed input from WP2. Optimization
problems to be solved using GA and/or SA.
8
WP 5 Parameters Sensitivities and Optimization
Task 5.3 Sensors actuators optimization for
control efficiency IST
9
WP 5 Parameters Sensitivities and Optimization

• Equilibrium equation
• where - consistent mass matrix
• - damping matrix
• - stiffness matrix
• - geometric stiffness matrix
• - electrical mechanical coupled stiffness
  matrix
• - electrical stiffness matrix
• - force vector
• the superscripts S and A indicate sensor and
  actuator laminas.

10
WP 5 Parameters Sensitivities and Optimization

• Generic optimization problem
• design variables
• discrete locations of piezoelectric actuators
  and sensors
• voltage input to the piezoelectric actuators
• ply angles and ply thicknesses in the
  composite structural element

11
WP 5 Parameters Sensitivities and Optimization

• Solving the optimization problem

continuous design variables
discrete design variables
Mathematical Programming techniques with
sensitivities information (requiring the
analytical or semi-analytical sensitivities
evaluation of objective and constraint
equations) DOT/ADS or FAIPA
Heuristic techniques Simulated Annealing
and Genetic Algorithms
J.Herskovits, P. Mappa, E.Goulard, C.M. Mota
Soares,Mathematical Programming Models and
Algorithms for Engineering Design Optimization
Computer Methods in Applied Mechanics and
Engineering , Elsevier, UK, Vol.194, pp
3244-3268, 2005.
12

• Optimization by using Simulated Annealing
• The implemented Simulated Annealing algorithm is
  based on the analogy to the physical process of
  annealing a metal. The simulated annealing
  process lowers the temperature by slow stages
  until the system freezes and no further changes
  occur. At each temperature the simulation must
  proceed long enough for the system to reach a
  steady state or equilibrium.
• The process employs a random search accepting not
  only the changes that decrease the Objective
  function but accepting also the changes that
  increase the Objective function O with a
  probability p given by (Metropolis
  criteria)
• - variation of objective function
• T - system temperature
• The initial value of the temperature T0 and the
  rate at which this is lowered a has a profound
  influence on the performance of the algorithm.
• A constant cooling rate can
  be used, where typically

13

• Optimization by using a Genetic Algorithm
• Very briefly, a genetic algorithm - GA - is a
  search/optimization technique based on natural
  selection. Successive generations evolve more fit
  individuals based on Darwinian survival of the
  fittest. The Genetic Algorithm is a computer
  simulation of such evolution where the user
  provides the environment (function) in which the
  population must evolve.
• Ref.
• David L. Carroll GA Fortran (http//cuaerospace.
  com/carroll/ga.html)
• David Goldberg - "Genetic Algorithms in Search,
  Optimization and Machine Learning,"
  Addison-Wesley, 1989.
• For CASSEM project an enhanced version of GA
  Fortran has been developped and implemented.

14
WP 5 Parameters Sensitivities and Optimization
Objective Find the actuators location for
maximum actuation performance, using Genetic
Algorithms
p/45º/-45º/45º/-45º/p
Evolution of the actuators location during the
optimization process
15
(No Transcript)
16
(No Transcript)
17
WP 5 Parameters Sensitivities and Optimization
Objective Find the actuators location for
maximum actuation performance (in this case
maximize the buckling load of the plate) using
Simulated Annealing
18
WP 5 Parameters Sensitivities and Optimization
Active damping, with negative feedback control,
in simply supported composite square plates with
piezoelectric actuators
19
Workshop Variational Formulations in Mechanics
Theory and Applications September 2006, Brazil
Invited Lecture.
20
(No Transcript)