An advanced Wigner-Ville time-frequency analysis of lamb waves signals based upon AR model for efficient damage inspection

The generation and acquisition of the ultrasonic guided wave in metallic or composite structures to investigate the structural defects are quite straightforward; however, the interpretation and evaluation of the reflected/transmitted signal to extract the useful information is a challenging task. It is primarily due to the dispersion, and multi-modal behavior of the Lamb waves which is dependent on the exciting wave frequency and thickness of the material under investigation. These multi-modes and dispersion behavior lead to a complex waveform structure, and therefore, require an advanced signal processing technique to decipher the useful information in time and frequency domain. For this purpose, Wigner-Ville Distribution, due to its desirable mathematical properties, is considered as a powerful tool for estimating temporal and spectral features of this type of complex signals. However, because of its quadratic nature, the undesirable cross-terms and spurious energies are also generated, which limit the readability of the spectrum. To suppress this effect, the autoregressive model based upon Burg's Maximum Entropy method was employed that modified the kernels of the discrete Wigner-Ville Distribution. This technique was applied to ultrasonic Lamb wave signals, obtained numerically and experimentally, to extract useful discriminating spectral and temporal information that was required for mode identification, damage localization, and its quantification. For damage localization, based upon excellent time-frequency energy distribution, the proposed method precisely estimated the distance between two closely spaced notches in a plate from different simulated noisy signals with a maximum uncertainty of 5%. Moreover, time-frequency energy concentration in a combination with variation of its instantaneous frequency was also effective in identifying the overlapping modes of the Lamb wave signal. Lastly, for damage quantification, three time-frequency based damage indices namely, energy concentration, time-frequency flux, and instantaneous frequency were extracted from the five sets of specimens using the proposed time-frequency scheme and trained them for the regression model. The model testing proved that the damage indices has the potential to predict the crack sizes precisely and reliably.