Parameterized Ultrasonic Echo Model And Parameters Estimation

In nondestructive evaluation (NDE) testing, target can be detected by the transducertransmitting ultrasonic pulse and target backscattering echo. By inspecting the backscatteredechoes, the patterns of ultrasonic backscattered echoes represent valuable informationpertaining to the geometric shape, size, and orientation of the reflectors as well as themicrostructure of the propagation path. Accurate estimation of the ultrasonic echo pattern isessential. In practice, however, because of the complexity of the material structure and noiseon the influence of the echo signal, the received echo signal will be corrupted. Furthermore,the echo attenuation becomes more serious as the depth of the target increases. Multilayermaterials detection technology by ultrasonic echo aims at estimating the thickness of the layerby time delay. However, when the layer thickness is reduced, echoes of different layers willoverlap, and it will result in difficulties and errors for time measurement. Furthermore, theexisting methods still have performance gap compared with the CRLB when SNR is low.Especially for superimposed echoes, the error is larger. Thus, method for estimatingparameters of ultrasonic echoes which approach the CRLB when SNR is low are the keypoint in the study of parameter estimation.In this study, algorithm of research on parameter estimation aims to improve the anti noisecharacteristic and the estimation precision, especially for superimposed echoes. The followinginnovative results are obtained.1) A novel method for estimating parameters of ultrasonic echoes based on envelope isproposed. We also deduce the effects of White Gaussian Noise (WGN) on the performanceand CRLB of Gaussian signal. By considering only the envelope of the ultrasonic signalswhich contains Time-Of-Flight (TOF), the number of parameters can be reduced, thecomputational burden can be reduced and the estimation accuracy can be improved. Firstly,the Hilbert transform (HT) is used in ultrasonic signal processing in order to extract theenvelope of the echo and to reduce the computational burden. Then, the wavelet denoisingtechnique is applied to the extracted noisy envelope to improve the estimation accuracy.Finally, the echo parameters are estimated by using a Modified Gauss Newton (MGN) basednonlinear Least Squares (LS) estimation method. And, the Space Alternating GeneralizedExpectation-Maximization (SAGE) algorithm is adopted to estimate the parameters ofM-superimposed echoes. Compared with the other exsiting methods, the proposed method ismore efficient and is fit for the cases of low SNRs. The drawback of the proposed method isthat TOFs of two overlaping echoes can not be effectively estimated. 2) a novel method for parameter estimation based on the Gabor transform (GT) isproposed according to the characteristics of time-frequency analysis in Gabor transform. Thesimilarity (i.e. distance) for echo signal and the Gabor transform window function is modeled.Time of Flight (TOF) and Center Frequency (CF) of echo signal are estimated by translatingmodel for solving the minimum into solving the maximum of Gabor transform coefficientmodulus. Firstly, TOF and CF are estimated by grid search method. Then, Quasi-Newtonmethod is employed to improve the estimation accuracy and reduce computational complexity.Gabor transform function of the signal has an analytic expression which contributes to deriveother estimators relating to TOF and CF such as bandwidth factor, phase and amplitude. Theparameters of multi-component echo signal are estimated by estimating the parameters ofeach component successively. The Monte Carlo simulation and experimental results show thatthe proposed method outperforms the existing cross-correlation algorithm and MUSICalgorithm and approaches the CRLB.3) The fractional Fourier transform (FRFT) is an effective technique to display thetime-frequency information of signals. A method for estimating parameters of ultrasonicechoes based on FRFT is proposed. Fractional energy spectrum of each componentoverlapping ultrasonic Gaussian echo signals on parameter plane (α u)is projected ontothe fractional domain u. In order to separate overlapping ultrasonic echo signals, the optimaltransform order is obtained by minimizing the mean square error (MSE) between the outputand the reference signal. TOF of each component is estimated by cross-correlation algorithm.Furthermore, windowing in FRFT domain is discussed. Numerical simulation results showthat the proposed method in separating signals overlapping in time and estimating TOF ofeach component outperforms the cross-correlation algorithm.