Ramazan Demirli

Model-based estimation of ultrasonic echoes. Part I: Analysis and algorithms

The patterns of ultrasonic backscattered echoes represent valuable information pertaining to the geometric shape, size, and orientation of the reflectors as well as the microstructure of the propagation path. Accurate estimation of the ultrasonic echo pattern is essential in determining the object/propagation path properties. In this study, we model ultrasonic backscattered echoes in terms of superimposed Gaussian echoes corrupted by noise. Each Gaussian echo in the model is a nonlinear function of a set of parameters: echo bandwidth, arrival time, center frequency, amplitude, and phase. These parameters are sensitive to the echo shape and can be linked to the physical properties of reflectors and frequency characteristics of the propagation path. We address the estimation of these parameters using the maximum likelihood estimation (MLE) principle, assuming that all of the parameters describing the shape of the echo are unknown but deterministic. In cases for which noise is characterized as white Gaussian, the MLE problem simplifies to a least squares (LS) estimation problem. The iterative LS optimization algorithms when applied to superimposed echoes suffer from the problem of convergence and exponential growth in computation as the number of echoes increases. In this investigation, we have developed expectation maximization (EM)-based algorithms to estimate ultrasonic signals in terms of Gaussian echoes. The EM algorithms translate the complicated superimposed echoes estimation into isolated echo estimations, providing computational versatility. The algorithm outperforms the LS methods in terms of independence to the initial guess and convergence to the optimal solution, and it resolves closely spaced overlapping echoes.

Model-based estimation of ultrasonic echoes. Part II: Nondestructive evaluation applications

For Part I see ibid., vol.48, no.3, pp.787-802 (2001). Accurate estimation of the ultrasonic echo pattern leading to the physical property of the object is desirable for ultrasonic NDE (nondestructive evaluation) applications. In Part I of this study, we have presented a generalized parametric ultrasonic echo model, composed of a number of Gaussian echoes corrupted by noise, and algorithms for accurately estimating the parameters. In Part II of this study, we explore the merits of this model-based estimation method in ultrasonic applications. This method produces high resolution and accurate estimates for ultrasonic echo parameters, i.e., time of flight (TOF) amplitude, center frequency, bandwidth, and phase. Furthermore, it offers a solution to the deconvolution problem for restoration of the target response, i.e., ultrasonic reflection and transmission properties of materials, from the backscattered echoes. The model-based estimation method makes deconvolution possible in the presence of significant noise. It can also restore closely spaced overlapping echoes beyond the resolution of the measuring system. These properties of the estimation method are investigated in various ultrasonic applications such as transducer pulse-echo wavelet estimation, subsample time delay estimation, and thickness sizing of thin layers.

A successive parameter estimation algorithm for chirplet signal decomposition

In ultrasonic imaging systems, the patterns of detected echoes correspond to the shape, size, and orientation of the reflectors and the physical properties of the propagation path. However, these echoes often are overlapped due to closely spaced reflectors and/or microstructure scattering. The decomposition of these echoes is a major and challenging problem. Therefore, signal modeling and parameter estimation of the nonstationary ultrasonic echoes is critical for image analysis, target detection, arid object recognition. In this paper, a successive parameter estimation algorithm based on the chirplet transform is presented. The chirplet transform is used not only as a means for time-frequency representation, but also to estimate the echo parameters, including the amplitude, time-of-arrival, center frequency, bandwidth, phase, and chirp rate. Furthermore, noise performance analysis using the Cramer Rao lower bounds demonstrates that the parameter estimator based on the chirplet transform is a minimum variance and unbiased estimator for signal-to-noise ratio (SNR) as low as 2.5 dB. To demonstrate the superior time-frequency and parameter estimation performance of the chirplet decomposition, ultrasonic flaw echoes embedded in grain scattering, and multiple interfering chirplets emitted by a large, brown bat have been analyzed. It has been shown that the chirplet signal decomposition algorithm performs robustly, yields accurate echo estimation, and results in SNR enhancements. Numerical and analytical results show that the algorithm is efficient and successful in high-fidelity signal representation

Reflection of Lamb waves obliquely incident on the free edge of a plate

The reflection of obliquely incident symmetric and anti-symmetric Lamb wave modes at the edge of a plate is studied. Both in-plane and Shear-Horizontal (SH) reflected wave modes are spawned by an obliquely incident in-plane Lamb wave mode. Energy reflection coefficients are calculated for the reflected wave modes as a function of frequency and angle of incidence. This is done by using the method of orthogonal mode decomposition and by enforcing traction free conditions at the plate edge using the method of collocation. A PZT sensor network, affixed to an Aluminum plate, is used to experimentally verify the predictions of the analysis. Experimental results provide support for the analytically determined results.

3E-3 A Comparative Study of Echo Estimation Techniques for Ultrasonic NDE Applications

In this study two different echo estimation techniques with a chirplet model are evaluated: chirplet signal decomposition based on the chirplet transform (CTSD), and the matching pursuit signal decomposition framework that employs Maximum Likelihood Estimation (MPSD). Both techniques are used to decompose backscattered signals into a linear expansion of chirplet echoes and estimate the chirplet parameters. The chirplet parameter estimation is unbiased with minimum variance, i.e., it attains analytically derived Cramer-Rao lower bounds. When applied to simulated and experimental ultrasonic signals, both algorithms perform robustly, yield accurate echo estimations and result in considerable SNR enhancements. Moreover, the MPSD algorithm outperforms the CTSD in moderate noise levels whereas the CTSD performs better than MPSD in severe noise levels. Numerical and analytical results indicate that the two presented signal decomposition algorithms are effective tools for ultrasonic signal analysis accounting for narrow-band, broadband, and symmetric, skewed, dispersive or nondispersive echoes. The present study provides guidelines which can be useful when dealing with signal analysis, pattern recognition, target sizing and material characterization

Chirplet transform for ultrasonic signal analysis and nde applications

In this investigation, the chirplet transform is introduced as a means to obtain not only time-frequency representation, but also to estimate the echo amplitude, time of arrival, center frequency, bandwidth, phase, and chirp rate of multiple interfering ultrasonic echoes. This transformation can be used for signal decomposition and successive parameter estimation of multiple interfering echoes. It has been shown that by using both simulated chirp signals and the ultrasonic experimental data, the chirplet signal decomposition algorithm performs robustly, yields accurate echo estimation and results in SNR enhancements. Numerical and analytical results show that the algorithm is efficient and successful in precise signal representation. This type of study addresses a broad range of applications including flaw detection, deconvolution, object classification, velocity measurement, and ranging systems.

A high-fidelity time-frequency representation for ultrasonic signal analysis

The time-frequency (TF) characteristics of ultrasonic echoes provide valuable information leading to the characterization of materials and localization of defects. The conventional TF analysis methods such as Wigner-Ville distribution (WVD) and short-time Fourier transform (STFT) perform inadequately when applied to ultrasonic signals because they introduce cross terms, offer poor resolution and are sensitive to noise level. In this study, we present a TF representation for ultrasonic echoes based on a matching pursuit (MP) method. MP decomposes a signal into a linear expansion of Gabor functions and maintains energy conservation. MP offers a TF distribution of the signal by enabling the addition of the TF distribution of each composing Gabor function. This TF representation is free of cross terms and adaptive to signal characteristics. The performance of this TF method has been tested using simulated and experimental ultrasonic data, and then compared to conventional techniques such as WVD and STFT. In particular, we present TF results for ultrasonic flaw detection where the microstructure scattering echoes dominate the flaw echoes (SNR is about 0 dB).

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.

Model based time-frequency estimation of ultrasonic echoes for NDE applications

Modeling the ultrasonic signals in terms of the Gaussian echoes assures a solution for signal parameters and a technique for time-frequency representation. In this study, the parameter estimation is addressed using iterative Maximum A Posteriori (MAP) estimation algorithms. To reduce the computational complexity, we have developed a divide-and-conquer estimation procedure. Upon estimation, we have explored the merits of this model-based technique for time-frequency analysis of ultrasonic echoes. In particular, we are presenting ultrasonic experimental data where the microstructure scattering echoes dominate the flaw echoes (SNR is about 0 dB). This type of data is used to demonstrate the effectiveness of model based time-frequency representation over conventional techniques such as Wigner-Ville distribution and short-time Fourier transform.

Reflection and transmission of fundamental Lamb wave modes obliquely incident on a crack in a plate

Lamb waves are increasingly being used for structural health monitoring of plate-like structures. In order to take advantage of Lamb waves, it is important to have a good understanding of how they interact with defects such as cracks. In this study, the scattering of the fundamental S0 Lamb mode by a part-through transverse symmetric crack in an isotropic plate is examined. The modal decomposition technique coupled with the method of collocation is used to determine the energy reflection coefficients of reflected and transmitted waves. These coefficients are shown to depend on the crack depth and the incident frequency. Experiments were conducted to verify the analytical results. Two different crack depths and frequencies were used. The experimental results follow the trends seen in the analytical results.