A Nonlinear Hanning-Windowed Chirplet Model for Ultrasonic Guided Waves Signal Parameter Representation
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A Nonlinear Hanning‑Windowed Chirplet Model for Ultrasonic Guided Waves Signal Parameter Representation Honglei Chen1,2 · Zenghua Liu1,2 · Bin Wu1,2 · Cunfu He1,2 Received: 18 September 2019 / Accepted: 8 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Parametric signal representation techniques with Chirplet models have attracted much attention in ultrasonic guided wavesbased 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. Keywords Parametric signal representation technique · Nonlinear Hanning-windowed Chirplet · Ultrasonic guided waves · Nonlinear phase modulation · Adaptive genetic algorithm Abbreviations IF Instantaneous frequency NHMC Nonlinear Hanning-windowed Chirplet AHW Asymmetric Hanning window AGA Adaptive genetic algorithm
1 Introduction Ultrasonic guided waves are a kind of elastic waves that propagate in waveguide structures, such as plates, pipelines, and rails. They have been widely studied in the field of nondestructive testing (NDT) and structural health monitoring * Zenghua Liu [email protected] 1
Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China
Beijing Engineering Research Center of Precision Measurement Technology and Instruments, Beijing University of Technology, Beijing 100124, China
2
(SHM) because of their multi-modes and sensitivity to the material and geometric features of the structure [1]. The quantitative estimation of signal parameters plays an important role in the algorithms used for defect location, imaging, and material property evaluation, etc. However, the signals may have nonlinear features and waveform superposition due to the dispersion of waves and the interactions between waves and defects
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