Biquaternion Signal Processing for Nonlinear Ultrasonics

TL;DR

This paper extends nonlinear ultrasonic localization and classification techniques from 2D to 3D damaged media using biquaternion analysis and machine learning, enhancing the understanding of complex ultrasonic signals.

Contribution

It introduces a biquaternion-based analysis framework for 3D nonlinear ultrasonics and integrates Echo State Networks for optimal wave path weighting.

Findings

Successful extension of TR-NEWS to 3D media

Effective use of biquaternion bases for analysis

Incorporation of hysteresis modeling with Preisach-Mayergoyz

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.