# Assessment of the Length and Depth of Delamination-Type Defects Using Ultrasonic Guided Waves
## 1 Introduction
Mode conversions between Lamb wave modes and between Rayleigh wave and Lamb modes were analyzed. It was found that the transmission coefficients of Lamb waves are both defect length- and depth-dependent, and they vary for different transmitted modes. [PERSON] et al. [18] studied the dependencies between the magnitude of the reflected S\({}_{0}\) mode and the width of delamination. As a result of such complex scattering and mode conversion, various linear acoustic tools for the detection and localization of delamination-type defects can be developed. For example, by measuring the time-of-flight (ToF) of the reflected and transmitted waves, the existence and location of delamination can be estimated [8; 19]. Additionally, by analyzing the ToF and velocities of the modes propagating at the layers divided by delamination, the length of the defect can be assessed [20; 21]. However, the success of the above-mentioned methods is strongly influenced by the dispersion and superposition of the modes of guided waves. The defects are mostly weak reflectors, while the monitoring system tends to detect and locate them in a large structure by using a small number of sensors. This leads to a low signal-to-noise ratio (SNR), which further complicates the signal analysis and the estimation of the time of flight (ToF). Most of the researches in the field of linear acoustics are currently targeting the detection, localization and sizing of delamination-type defects. However, the assessment of the depth of a defect is no less important for the evaluation of defect severity. There are only a few works available which discuss the depth estimation of a delamination-type defect. Recently, [PERSON] et al. [22] analyzed the relationship between the length and depth of delamination with the scattering resonance frequencies of delamination. [PERSON] et al. [23] analyzed the reflection of A\({}_{0}\) mode as a function of the depth-wise position of delamination. It was concluded that mid-plane delamination scatters less energy of the asymmetric mode, meanwhile, off mid-plane delaminations additionally introduce a reflection of converted S\({}_{0}\) mode. [PERSON] et al. [24] exploited S\({}_{0}\) mode to analyze its reflection from delamination situated at different depths and ply layups. Reflection coefficients as a function of the through-thickness location of delamination were estimated for various ply layups, which showed the importance of the defect position and the composition of the material to the detectability of delamination. Recently, [PERSON] et al. [25; 26] analyzed the scattering of A\({}_{0}\) mode from delaminations of different sizes which were situated at different depths. It was observed that the delamination length exerts strong influence on the scattering directivity, while its depth influences the magnitude of the scattered wave. Despite some promising results, the abovementioned works in general have discussed the fundamental influence of the defect depth on the scattering of guided wave modes. There is still a lack of methods to extract the depth of the defect without any initial knowledge about its through-thickness location when dispersion is involved. This paper proposes the SHM method to extract the absolute depth and size of asymmetrical delamination-type defects in plate-like structures with parallel surfaces. The technique proposed in this study extracts the depth of the damage by analyzing the amplitude variation patterns of direct A\({}_{0}\) mode at different excitation frequencies. These magnitude variations are caused by the difference of wave velocities in the upper and lower sub-laminates due to their uneven thicknesses. This leads to the varying phase differences of the wave-packets at the trailing edge of the defect and results in an altering forward scattered amplitude of the direct A\({}_{0}\) mode. Hence, in comparison with the predefined reference dependencies, the absolute values of the delamination depth can be extracted.