Generation of Ultrasonic Data Through High-Order Interpolation

Data scarcity is a known limitation associated with many ultrasonic applications, particularly those that, by their nature, require large amounts of data to be set up and perform as intended. Examples include the in-silico qualification of nondestructive evaluation methods and training machine learning algorithms for engineering or medical applications. Experimental data is typically difficult to obtain in sufficient quantities, and, while synthetic data generation is possible, the data is often either not sufficiently realistic or the process is computationally expensive. The latter is a major limitation of finite element (FE) modeling, which otherwise generates highly accurate data. In our previous work, we presented a linear interpolation technique to significantly reduce the computational cost associated with FE modeling by using results from a small number of full FE models to populate an entire parameter space via interpolation with negligible additional computational cost. While linear interpolation was demonstrated to be a helpful tool, it is beneficial to develop stronger interpolation, capable of addressing wider and more complex needs. In this work, we extend our previous method to use quadratic polynomial interpolation. After demonstrating that this interpolation order is sufficient, our method is validated using test cases of increasing complexity; validation is achieved by comparing the interpolation-assisted data with their corresponding true FE-generated counterparts. A method for interpolating complicated signals containing multiple features is also presented, implemented, and its performance is assessed through the test cases. Our results clearly show an improved agreement between the estimated and true results compared with linear interpolation. We also demonstrate robust performance in complex cases, and a very substantial reduction in computational cost in all instances.