Nonlinear ultrasonic early damage detection in thin specimens based on the variable-frequency standing wave and matrix pencil methods

Thin specimens exhibit limited signal cycles excitation during nonlinear ultrasonic longitudinal wave testing, resulting in insufficient spectral resolution and low excitation energy. The standing wave method is proposed for testing thin specimens. Among the same batch of specimens, minor length differences during the processing may make it difficult for the same frequency signals to stably form standing waves, thus affecting the detection effectiveness. To address this issue, variable-frequency standing wave method is further proposed. Simulation and experimental validations using 6061-T6 thin specimens with different tensile stresses demonstrate that this method can more effectively excite second harmonics. The ultrasonic nonlinearity coefficient shows more pronounced variation trends with the evolution of early-stage damage, enabling effective detection of early damage in thin specimens. In addition, to address spectral leakage and the fence effect caused by non-integer period truncation of standing wave signals, matrix pencil method based on time-domain feature extraction is proposed and compared with the FFT method. Simulation results demonstrate that this method can control the error of the ultrasonic nonlinearity coefficient within 5%. Experimental results further validate its superiority in signal amplitude extraction accuracy.