Application of Quaternion Neural Network to Time Reversal Based Nonlinear Elastic Wave Spectroscopy

TL;DR

This paper introduces a novel approach combining quaternion neural networks with time reversal nonlinear elastic wave spectroscopy to improve crack detection in materials, leveraging soliton wave modeling and topological insights.

Contribution

It proposes a quaternion neural network method for analyzing soliton-based wave signals in TR-NEWS, incorporating topological and gravitational considerations for enhanced crack localization.

Findings

Reduced parameters for wave route estimation.

Effective crack position identification using quaternion neural networks.

Integration of topological and gravitational effects in wave analysis.

Abstract

Identification of crack positions or anomalies in materials using the time reversal based nonlinear elastic wave spectroscopy (TR-NEWS) is an established method. We propose a system using transducers which emit forward propagating solitonic wave and time-reversed propagating solitonic wave produced by memristers placed on a side of a rectangle and scattered by cracks in the material and received by receivers which are placed on the opposite side of the rectangle. By minimizing the difference of the scattered forward propagating wave and the scattered TR wave, we get information of the position of the crack by using the neural network technique. Route of the solitons are expressed by 2 dimensional projective quaternion functions, and parameters for getting the optimal route from signals are expected to be reduced. We consider the wave is expressed by a soliton which is conformal, and discuss symmetry protected topological impurities and gravitational effects using the Atiyah-Patodi-Singer's index theorem.