A CoEvolutionary Strategy for Structural Damage Identification

1
A Co-Evolutionary Strategy for Structural Damage
Identification

• Wilkins Aquino
• Assistant Professor
• School of Civil and Environmental Engineering
• Cornell University

2
Acknowledgments

• This work was carried out in collaboration with
• Hod Lipson and Josh Bongard
• Computational Synthesis Lab, Mechanical and
  Aerospace Engineering
• Cornell University

3
Outline

• Motivation
• Background
• Coevolution and Damage Detection
• Numerical Examples and Results
• Conclusions

4
Motivation

• One of the main challenges in structural damage
  identification is how to obtain sufficient
  information to accurately quantify the state of a
  given structure.
• In many problems, a single test does not suffice
  to thoroughly characterize a system.
• Multiple tests can increase the level of
  information and observability of a system in many
  practical problems. However, how can we decide
  what tests to perform in order to maximize
  information?

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Co-evolution

• A strategy based on co-evolution will be
  presented that not only searches for damage, but
  also helps in the selection of structural test
  that elucidate new information.
• What is co-evolution? A biological process where
  populations of interacting individuals challenge
  each other in an ongoing cycle of adaptation
  (e.g. preys-predators Preys evolve to elude
  predators, while predators evolve to catch the
  preys)

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The Estimation-Exploration Algorithm (EEA)

• Uses the notion of co-evolution to find good
  solutions with minimum physical testing.
• Two phases Estimation and Exploration.
• Estimation phase A set of candidate solutions
  are evolved based on current tests.
• Exploration Phase Tests are evolved to maximize
  discrepancy among current candidate models.
• Some applications
• Damage identification in structures
• Gene network inference
• Automated robot function recovery
• Identification of dynamical systems

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Estimation-Exploration Algorithm (EEA)
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Co-Evolutionary Damage Detection The Concept
Estimation Phase Find candidate models that
predict current tests
Physical system
GA
F
U
Exploration Phase Find tests that create
discrepancy among solutions
GA
The answer
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Example Structural Damage Detection in Truss
Structures
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Problem Description
Equilibrium equations
Damage representation
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The Estimation Phase

• The estimation phase consists in finding
  candidate damage scenarios that minimize the
  error between the predicted response and the
  tests that have been carried on the structure.
• Multiple damage scenarios will be found as long
  as tests do not carry sufficient information to
  determine a unique solution.
• Candidate damage scenarios are transferred to the
  exploration phase.

Optimization problem
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Test Encoding in Exploration Phase
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The Exploration Phase

• The goal of the exploration phase is to find a
  test that maximizes discrepancy among candidate
  solutions (i.e. damage scenarios) selected from
  the estimation phase.
• The fitness of a test in the exploration phase is
  proportional to its ability to create
  disagreement among candidate solutions.

Optimization problem
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Stopping Criteria

• One individual can explain all tests in a
  predefined number of consecutive cycles. This
  indicates that a potentially good solution has
  been found.
• Diversity is not maintained. At least two
  different individuals need to be transferred from
  the estimation phase to the exploration phase.
  Loss of diversity may be due to various factors
  such as inadequate parameters in the niching
  method, size of the population, number of
  generations, etc.
• The exploration phase cannot find a test that
  causes disagreement among candidate solutions. In
  this case, the algorithm cannot single out a
  unique solution. This situation may indicate that
  the problem is not fully observable

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Numerical Examples

• Five damaged elements.
• Tests encoded three vertical loads and three
  sensors.
• Loads applied only on the bottom chord.

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Results

• Two different strategies
• EEA
• Control algorithm tests were generated randomly.
  That is, exploration phase was deactivated.

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Results (2)
EEA. No Noise. 10 Tests.
Control. No Noise. 10 tests.
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Results (3)
EEA. 1 Noise. 10 tests.
Control. 1 Noise. 10 Tests.
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Results(4)
Subjective Error
Objective Error
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Evolution of Tests in EEA
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Conclusions and General Remarks

• EEA has shown promise for its application in
  damage identification problems.
• It has been shown that EEA is a better
  alternative than blind testing of a structure and
  even engineered tests.
• Further studies will consider its extension to
  crack identification in continua.

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References

• B. Kouchmeshky, W. Aquino, J.C. Bongard, and H.
  Lipson (2007).Coevolutionary Strategy for
  Structural Damage Identification using Minimal
  Physical Testing. International Journal for
  Numerical Methods in Engineering Volume 69, Issue
  5, pp 1085-1107.
• B. Kouchmeshky, W. Aquino, and Adam E. Billek.
  (2007). Structural Damage Identification Using
  Frequency Response Functions and Coevolutionary
  Algorithms. Journal of Structural Control and
  Health Monitoring, Volume 15, Issue 2, pp 162-182.