Methodology for Diagnosis of Defect or Damage in Reflection-Symmetric Multilayer Structures Using Analysis of Late-Time Natural-Mode Amplitudes

Temporal late-time reflection and transmission natural mode amplitudes (
$A_{n}$
,
$B_{n}$
,
$R_{n}$
, and
$Q_{n}$
) of an
${N}$
-layer multilayer structure are examined by separating the whole structure into left and right regions and middle layer. Due to this separation, some relations among these amplitudes are analytically disclosed. It is shown that if the structure has reflection symmetry, then the relation between
$A_{n}$
and
$B_{n}$
(and
$R_{n}$
and
$Q_{n}$
) is in the form
$A_{n} = (-1)^{n-1} B_{n}$
(and
$R_{n} = (-1)^{n-1} Q_{n}$
), where
$n$
is the mode number. These relationships are independent of material properties. A practical example related to damage or defect detection is considered to show the usefulness of these simple relations. The effect of noise on this detection was examined by introducing a Gaussian white noise (with a signal-to-noise ratio (SNR) ranging from 40, 30, and 20 dB to 10 dB) to the scattering parameters. It is observed that our proposed formalism is resistant to noise when detecting material defects or damages in reflection-symmetric multilayer structures. The effectiveness and feasibility of the derived objective function for a reflection-symmetric multiliayer structure were validated by coaxial line spectral (up to 26.5 GHz) and time-domain (via transformation) measurements of a three-layer structure.