Asymmetric Gaussian Chirplet model for ultrasonic echo analysis

Parametric modeling and estimation of ultrasonic backscattered echoes become a frequently used approach in NDE signal processing. Compared to classical transform based signal processing methods, the parametric echo representation approach offers significant advantages such as high-resolution estimation of test parameters (e.g., time-of-arrival, center frequency, and amplitude), the ability to resolve closely spaced overlapping echoes, and robustness with noise. In this context, parametric models such as Gaussian echo (Gabor function) and Gaussian Chirplet have been used to represent discrete echoes. Furthermore, their composite models have been used to analyze complex ultrasonic measurements such as overlapping echoes from thin layers, backscattered echoes from microstructure of materials, etc. One of the main shortcomings of these models is that their symmetric envelope does not properly represent ultrasonic echo envelopes. A more generic model accounting for this asymmetry will improve ultrasonic echo parameter estimation, (e.g., time-of-arrival, center frequency, bandwidth, chirp rate, etc.), as well as improve sparse decomposition of complex ultrasonic signals. In this study, we introduce the asymmetric Gaussian Chirplet (AGC) model that generalizes the existing parametric echo models. We developed a fast supervised Gauss-Newton algorithm to estimate model parameters subject to constraints defined by a priori knowledge. Supervision ensures convergence to the optimal solution given a reasonable initial guess. This echo model nicely fits echoes acquired from planar surface and geometric reflectors. Finally, this model is used to estimate microstructure grain echoes from a steel block and reverberation echoes from a multi-layered material. Estimation results confirm the advantage of this model compared to the existing models.