Modeling the ultrasonic testing echoes by a combination of particle swarm optimization and Levenberg–Marquardt algorithms

Abstract

This paper presents an accurate and easy-to-implement algorithm for estimating the parameters of the asymmetric Gaussian chirplet model (AGCM) used for modeling echoes measured in ultrasonic nondestructive testing (NDT) of materials. The proposed algorithm is a combination of particle swarm optimization (PSO) and Levenberg–Marquardt (LM) algorithms. PSO does not need an accurate initial guess and quickly converges to a reasonable output while LM needs a good initial guess in order to provide an accurate output. In the combined algorithm, PSO is run first to provide a rough estimate of the output and this result is consequently inputted to the LM algorithm for more accurate estimation of parameters. To apply the algorithm to signals with multiple echoes, the space alternating generalized expectation maximization (SAGE) is used. The proposed combined algorithm is robust and accurate. To examine the performance of the proposed algorithm, it is applied to a number of simulated echoes having various signal to noise ratios. The combined algorithm is also applied to a number of experimental ultrasonic signals. The results corroborate the accuracy and reliability of the proposed combined algorithm.