A Nonlinear Hanning-Windowed Chirplet Model for Ultrasonic Guided Waves Signal Parameter Representation

Parametric signal representation techniques with Chirplet models have attracted much attention in ultrasonic guided waves-based research of material property identification and structural integrity evaluation. The known Chirplet models are established using either the Gaussian windows or the linear chirp function. This is inconsistent with practical situations where the excitation is a Hanning-windowed sinusoidal signal, and the received signals have a nonlinear phase and asymmetric envelope due to the dispersive nature of the waves. A nonlinear Hanning-windowed Chirplet (NHWC) model was proposed to eliminate the above inconsistencies in which a nonlinear phase modulation term was designed to modulate the classical Hanning-window and the sine function. The phase modulation term was established with the hyperbolic tangent function. The mathematical properties of the nonlinear phase modulation term and the NHWC model were analyzed mathematically, including the time variability, parity, concavity, and convexity of the phase. These were used to guide the parameter setting in parametric signal representation techniques. The NHWC model can characterize various characteristics of guided waves signals, including the symmetric or asymmetric Hanning envelopes and the phase nonlinearity. Finally, an adaptive genetic algorithm was adopted to verify the effectiveness of the NHWC model in the parameter representation of experimentally measured ultrasonic signals.