Characterization of BVID in CFRP via adaptive modulation signal bispectrum sideband estimator

Carbon fiber reinforced polymer composites are susceptible to barely visible impact damage, which necessitates reliable detection and quantitative assessment of damage severity. Air-coupled ultrasonic testing (ACUT) provides a non-contact sensing modality that avoids secondary contamination or specimen damage. However, in ACUT-based nonlinear cross-modulation measurements, the extraction of nonlinear features is frequently compromised by carrier amplitude fluctuations resulting from transducer positioning offsets and by the obscuration of weak sidebands by background noise. This study developed a feature extraction framework termed the Adaptive Modulated Signal Bispectrum Sideband Estimator (MSB-SE). The bispectrum was utilized as the analytical foundation to suppress random noise and identify phase-locked nonlinear components. To address carrier-induced interference, an MSB-SE estimator was implemented by incorporating a carrier power spectrum normalization operator into the bispectrum calculation, which mathematically decoupled nonlinear features from variations in carrier energy. Furthermore, a Spectrum Amplitude Modulation mechanism was integrated to enhance sensitivity to micro-damage. Using the Nonlinear Frequency Index as an optimization criterion, the magnitude order was adaptively tuned to amplify faint characteristic sidebands. Multiple experimental validations were performed on CFRP laminates subjected to impact energies ranging from 4 J to 10 J. The results demonstrated that the AMSBSE framework identified characteristic nonlinear features even at the low impact energy of 4 J. Quantitative analysis indicated that the extracted bicoherence coefficients exhibited a strong monotonic correlation with the impact energy levels (linearity coefficient > 0.97) and superior measurement consistency (standard deviation reduced to 0.042). This approach provides a non-contact solution for the quantitative characterization of early-stage impact damage severity in composite structures.