Automatic microstructural characterization and classification using probabilistic neural network on ultrasound signals

During the gas tungsten arc welding of nickel based superalloys, the secondary phases such as Laves and carbides are formed in final stage of solidification. But, other phases such as \(\gamma ^{{\prime \prime }}\) and \(\delta \) phases can precipitate in the microstructure, during aging at high temperatures. However, it is possible to minimize the formation of the Nb-rich Laves phases and therefore reduce the possibility of solidification cracking by adopting the appropriate welding conditions. This paper aims at the automatic microstructurally characterizing the kinetics of phase transformations on an Nb-base alloy, thermally aged at 650 and 950  \(^{\circ }\)C for 10, 100 and 200 h, through backscattered ultrasound signals at frequency of 4 MHz. The ultrasound signals are inherently non-linear and thus the conventional linear time and frequency domain methods can not reveal the complexity of these signals clearly. Consequently, an automated processing system is designed using the higher-order statistics techniques, such as 3rd-order cumulant and bispectrum. These techniques are non-linear methods which are highly robust to noise. For this, the coefficients of 3rd-order cumulant and bispectrum of ultrasound signals are subjected to the independent component analysis (ICA) technique to reduce the statistical redundancy and reveal discriminating features. These dimensionality reduced features are fed to the probabilistic neural network (PNN) to automatic microstructural classification. The training process of PNN depends only on the selection of the smoothing parameters of pattern neurons. In this article, we propose the application of the bees algorithm to the automatic adaptation of smoothing parameters. The ICA components of cumulant coefficients coupled with the optimized PNN yielded the highest average accuracy of 97.0 and 83.5 %, respectively for thermal aging at 650 and 950 \(^{\circ }\)C. Thus, the proposed processing system provides high reliability to be used for microstructure characterization through ultrasound signals.