Accelerated discrete Gaussian beam model for simulating the water-immersion phased array ultrasonic field

Ultrasonic phased array technique has shown significant advantages in the non-destructive testing of complex-geometry components due to its ability to flexibly generate desired inspection beams. Given the complexity of component geometry and acoustic field control, accurate and efficient ultrasonic field simulation before actual inspection is beneficial for properly designing the inspection parameters. However, the existing acoustic field simulation methods cannot satisfy the balance between accuracy and efficiency while simulating steered and focused beams, such as the efficient but less accurate multi-Gaussian beam (MGB) model versus the accurate but less efficient Rayleigh-Sommerfeld integral (RSI) model. In this paper, an accelerated discrete Gaussian beam (ADGB) semi-analytical model is proposed to realize accurate and efficient acoustic field simulation. By superposing Gaussian beams generated from discrete transducer segments, the proposed model ensures all field points remain within the paraxial zones and thus overcomes the accuracy limitations in the MGB model. Moreover, adjacent field points in a properly-sized neighborhood can share a central propagation ray based on Gaussian beam theory, thereby reducing the calculation amount with negligible accuracy loss. Consequently, the proposed ADGB model achieves high accuracy and efficiency in simulating varied phased array ultrasonic fields. Simulations and experiments are conducted using immersion linear phased arrays on test pieces. The simulation results show that the ADGB model maintains accuracy comparable to the RSI model, while its efficiency is enhanced by more than 14 times. Besides, the ADGB results incorporated with attenuation agree well with the experimental results, thereby validating the effectiveness of the proposed model.