Using Chaotic Interrogation and Attractor Deformation to Determine Damage Location and Extent
Author:Luke Kong ’22
Faculty Mentor(s):Professor Andrew Sloboda
Funding Source:Program for Undergraduate Research
One promising approach for detecting damage in non-linear systems is to use chaotic interrogation: a system is excited by a chaotic signal and the resulting response is used to infer the damaged state. In this work, a new method based on boundary transformation vectors (BTVs) is explored as a way of simultaneously ascertaining both damage level and location.
The process works as follows: (1) The system is excited by a chaotic signal. (2) The system response is recorded at some location. (3) The peaks of the system response are sampled and combined to create a picture of the chaotic signal known as a Poincare section. (4) By comparing the boundaries of Poincare sections for different damage states using BTVs, the damage level and location can be inferred.
Three different systems were explored: a 5-body mass-spring-damper model, a simulated cantilever beam, and a physical cantilever beam. To excite these systems, a chaotic Brusselator signal was chosen. Displacements were used as output signals in the simulated systems; for the physical beam, acceleration was used.
Results from the simulated systems demonstrate that chaotic interrogation and BTV analysis can be used to ascertain system damage in stiffness or damping and, in some cases, location because Poincare boundary changes scale with the level of damage. For the physical beam, damage extent was discernible for particular combinations of damage and observer locations. However, indications of damage location were inconsistent.
Overall, these results demonstrate that the BTV method has promise and can be improved with further research.