Application of biquaternionic signal processing to non-destructive testing of (3+1)D with hysteresis effects

In Nondestructive Testing (NDT) of (2+1)D including hysteresis effects, Time Reversal based Nonlinear Elastic Wave Spectroscopy (TR-NEWS) was successful. In this method, amplitudes of ultrasonic waves and their time reversed waves consisting up to 3^rd order polynomials are represented by quaternions, and analyzed by the Quaternion Excitation Symmetry Analysis Model (QESAM).

(2+1)D data of Wire and Arc Additive Manufacturing (WAAM) samples are analyzed.



Extension of (2+1)D to (3+1)D is possible by assigning transducers and receivers in a 3D space and each receiver emits the TR ultrasonic(US) wave and receivers which detects strong correlation between the normal US and the TR US wave will be searched. For analyzing the path of phonons, data represented by biquaternions expressed by 2x2 matrices containing quaternion H, or M2(H) matrices are used.

The optimal weight of independent paths that yields the minimal action is searched by using Machine Learning techniques.



As a medical application, detection of anomalous scattering position in brain or in tooth are in sight.