Using chaotic forcing to detect damage in a structure

Detecting variation in chaotic attractors

If the output of an experiment is a chaotic signal, it may be useful to detect small changes in the signal, but there are a limited number of ways to compare signals from chaotic systems, and most known methods are not robust in the presence of noise. One may calculate dimension or Lyapunov exponents from the signal, or construct a synchronizing model, but all of these are only useful in low noise situations. I introduce a method for detecting small variations in a chaotic attractor based on directly calculating the difference between vector fields in phase space. The differences are found by comparing close strands in phase space, rather than close neighbors. The use of strands makes the method more robust to noise and more sensitive to small attractor differences.

Refined fiber laser model

With modification, a recently proposed laser array model is found to agree quantitatively with fiber laser experiments. Comparisons of transient behavior, stable dynamical states, and transitions are made using both previously published and new experiments. While the original model agrees well for fibers with relatively low losses, achieving quantitative agreement over a wide range of operating conditions requires more physically appropriate descriptions of gain dynamics. The refined model is derived, and its predictions are found to be in excellent agreement with experiments.