Ultrasonic Signal Modelling and Parameter Estimation: A Comparative Study Using Optimization Algorithms

The parameter estimation from ultrasonic reverberations is used in applications such as non-destructive evaluation, characterization and defect detection of materials. The parameters of back scattered Gaussian ultrasonic echo altered by noise: Received time, Amplitude, Phase, bandwidth and centrefrequency should be estimated. Due to the assumption of the nature of noise as additive white Gaussian, the estimation can be approximated to a least square method. Hence different least square cure-fitting optimization algorithms can be used for estimating the parameters. Optimization techniques: LevenbergMarquardt(LM), Trust-region-reflective, Quasi-Newton, Active Set and Sequential Quadratic Programming are used to estimate the parameters of noisy echo. Wavelet denoising with Principal Component Analysis is also applied to check if it can make some improvement in estimation. The goodness of fit for noisy and denoised estimated signals are compared in terms of Mean Square Error (MSE). The results of the study shows that LM algorithm gives the minimum MSE for estimating echo parameters from both noisy and denoised signal, with minimum number of iterations.