Analysis of $(3+1)D$ and $(2+1)D$ nonlinear ultrasonic waves using conformal invariance

TL;DR

This paper extends nonlinear ultrasonic wave analysis to 3D and 2D media using conformal invariance, quaternion and biquaternion bases, and machine learning techniques to improve localization and classification of damage signatures.

Contribution

It introduces a novel approach combining conformal invariance, quaternion analysis, and machine learning for ultrasonic wave analysis in complex media.

Findings

Successful extension of nonlinear ultrasonic analysis to 3D media.

Use of Echo State Network for optimal wave path weighting.

Application to Wire Arc Additive Manufacturing samples.

Abstract

Localization and classification of scattered nonlinear ultrasonic signatures in 2 dimensional complex damaged media using Time Reversal based Nonlinear Elastic Wave Spectroscopy (TR-NEWS) approach is extended to 3 dimensional complex damaged media. In (2+1)D, i.e. space 2 dimensional time 1 dimensional spacetime, we used quaternion bases for analyses, while in (3+1)D, we use biquaternion bases. The optimal weight function of the path of ultrasonic wave in (3+1)D lattice is obtained by using the Echo State Network (ESN) which is a Machine Learning technique. The hysteresis effect is incorporated by using the Preisach-Mayergoyz model. We analyze the spectrum data of Wire Arc Additive Manufacturing (WAAM) sample obtained by Quaternion Excitation Symmetry Analysis Method (QESAM) using the conformally invariant quantum mechanical variables of de Alfaro-Fubini-Furlan and their supersymmetrically extended variables of Fubini-Rabinovici.