Optimal Command of the Nonlinear Elastic Wave Spectroscopy Method (NWMS)

In the present study, the Nonlinear Elastic Wave Modulation Spectroscopy (NWMS) technique is combined to the optimal command in order to enhance the nonlinear effects due to the presence of micro damages in materials such as cracks. This method consists in simultaneously applying two continuous waves with different frequencies; the high probe and the lower pump frequency noted respectively
$f_{s}$
and
$f_{p}$
. When the material is damaged, the frequency spectrum exhibits harmonics and sidebands. An open loop NWMS system is modified to a closed loop system by adding a feedback. A simulation study makes possible to find simultaneously the pump and probe frequencices that optimize the nonlinear modulation effects. The considered cost function noted LS (left sidenbad) quantifies the sideband amplitude. For a comparison purpose, an empirical optimisation is achieved by computing a cartography of LS as a function of
$f_{s}$
and
$f_{p}$
. Then a genetic algorithm is used to find the optimal pump and probe frequencies.