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

An application of quaternion neural network to identification of crack positions in materials using the time reversal based nonlinear elastic wave spectroscopy (TR-NEWS) is proposed. Transducers which emit forward propagating solitonic waves and time-reversed backward propagating solitonic waves are produced by memristers, are placed on a line of the left wall and scattered by cracks in the material and received by receivers which are placed on the right wall on the line parallel to that of transducers. By minimizing the difference of the scattered forward propagating wave and the scattered backward propagating 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. When the soliton is expressed by conformal waves, symmetry protected topological inpurities and gravitational effects would manifest itself due to Atiyah-Patodi-Singer's theorem.