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

Abstract

Identification of crack positions or anomalous scattering centers in materials using the time reversal (TR) 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 memristors 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 measuring the convolution of the scattered forward propagating wave and the scattered TR wave, we get information of the position of the scattering center by using the neural network technique. Routes of the solitonic wave are expressed by quaternions projected on 2 dimensional planes, and the optimal route from signals are searched. 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.