Ultrasonic data generation via interpolation

Data scarcity is a known issue in many ultrasonic applications, including non-destructive evaluation (NDE), medicine, structural health monitoring, and seismology. This issue has become particularly prominent with the ever-increasing use of machine learning algorithms, which require large amounts of data to reliably train. Also, particularly in NDE, there is a need for ultrasonic data for developing in-silico methods for qualification purposes.
While it is known that high-quality ultrasonic data is attainable through finite element (FE) modelling, the computational cost becomes prohibitive when generating the amounts of data required for in-silico qualification or machine learning purposes. To mitigate this, in this project, we are developing a method able to correctly interpolate ultrasonic signals, to generate more data at a minimal computational cost. The interpolation takes place in the frequency domain – by doing so, we gain the ability to interpolate the amplitude and phase of the signals independently, as they vary with frequency. This ensures interpolation results which are physically meaningful.

We are considering both linear interpolation for simple scattering phenomena, and higher order interpolation for cases where the parameter of interest is known a priori to vary nonlinearly. FE modelling is still used to obtain results for a coarsely populated parameter space, and the gaps are filled using data generated through interpolation. By implementing this method, we are able to demonstrate gains in computational cost exceeding 90%, with a minimal (<1%) loss in accuracy, both in the amplitude, time of arrival, and overall shape of the signals.

Schematic showing a comparison between time and frequency interpolation between two complex numbers. This is a simpler but analogous example to signal interpolation, as complex numbers, similarly to signals, possess both an amplitude and a phase.