Automatic Microstructural Characterization and Classification Using Higher-Order Spectra 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 γ′′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma {''}$$\end{document} and δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document} phases can precipitate in the microstructure, during aging at high temperatures. Nevertheless, choosing the appropriate conditions of welding can minimize the formation of the Nb-rich Laves phases and thus reduce the susceptibility to solidification cracking. This study aims at the automatic microstructurally characterizing the kinetics of phase transformations on an Nb-base alloy, thermally aged at 650 and 950 ∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}C for 10, 100 and 200 h, through backscattered ultrasound signals at frequency of 4 MHz. For this, an automated processing system was designed using the spectrum representation of higher order statistics. 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. Bispectrum (the spectral representation of third order correlation) is a non-linear method which is highly robust to noise. In the proposed system, the bispectrum coefficients are subjected to linear discriminant analysis (LDA) technique to reduce the statistical redundancy and reveal discriminating features. These dimensionality reduced features are fed to the classification and regression tree, random forest and k-nearest neighbor (k-NN) classifiers to automatic microstructural characterization. Bispectrum coupled with LDA and k-NN yielded the highest average accuracy of 95.0 and 78.0 %, respectively for thermal aging at 650 and 950 ∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}C. Thus, the proposed processing system provides high reliability to be used for microstructure characterization through ultrasound signals.