Optimal Parameter Estimation of Ultrasonic Signals by Using a Combination of Particle Swarm Optimization and Gauss-Newton Algorithms

The echoes obtained from ultrasonic testing of materials contain valuable information about the geometry and grain structure of the test specimen. These echoes can be modeled by Gaussian pulses in a model-based estimation process. For precise modeling of an echo, the parameters of the Gaussian pulse should be estimated as accurately as possible. There are a number of algorithms that can be used for this purpose. In this study, three different algorithms are used: Gauss-Newton (GN), particle swarm optimization (PSO), and genetic algorithm (GA). The pros and cons of each of these three algorithms are reviewed and by combining them, the benefits of each algorithm are used while its shortcomings are avoided. For signals containing multiple echoes, the minimum description length (MDL) principle is used to estimate the numbers of required Gaussian echoes followed by space alternating generalized expectation maximization (SAGE) technique to translate it to separate echoes and to estimate the parameters of each echo. The performance of the proposed algorithms for simulated and experimental signals with overlapping and non-overlapping echoes is evaluated and shows to be quite effective.