A multiband approach for accurate numerical simulation of frequency dependent ultrasonic wave propagation in the time domain.

Finite element (FE) simulations are popular for studying propagation and scattering of ultrasonic waves in nondestructive evaluation. For a large number of degrees of freedom, time domain FE simulations are much more efficient than the equivalent frequency domain solution. However, unlike frequency domain simulations, time domain simulations are often poor at representing the speed and the attenuation of waves if the material is strongly damping or highly dispersive. Here, the authors demonstrate efficient and accurate representation of propagated and scattered waves, achieved by combining a set of time domain solutions that are obtained for a set of frequency ranges known as bands, such that, in combination, the authors' multiband solution accurately represents the whole wave spectrum. Consequently, high accuracy is achieved, at minor computational cost, using a modest number of bands. The multiband technique is implemented for ultrasonic wave propagation in highly attenuating polyethylene material, using three frequency bands, and can yield a reduction in empirical acoustic properties fractional error compared with respective time domain simulations, in propagation duration, of a factor of 1.4, and in full-width-half-maximum, of a factor of 10. Last, the accuracy of this approach is further exemplified in a wave scattering simulation.

Ultrasonic attenuation and phase velocity of high-density polyethylene pipe material.

Knowledge of acoustic properties is crucial for ultrasonic or sonic imaging and signal detection in nondestructive evaluation (NDE), medical imaging, and seismology. Accurately and reliably obtaining these is particularly challenging for the NDE of high-density polyethylene (HDPE), such as is used in many water or gas pipes, because the properties vary greatly with frequency, temperature, direction and spatial location. Therefore the work reported here was undertaken in order to establish a basis for such a multiparameter description. The approach is general but the study specifically addresses HDPE and includes measured data values. Applicable to any such multiparameter acoustic properties dataset is a devised regression method that uses a neural network algorithm. This algorithm includes constraints to respect the Kramers-Kronig causality relationship between speed and attenuation of waves in a viscoelastic medium. These constrained acoustic properties are fully described in a multidimensional parameter space to vary with frequency, depth, temperature, and direction. The resulting uncertainties in acoustic properties dependence on the above variables are better than 4% and 2%, respectively, for attenuation and phase velocity and therefore can prevent major defect imaging errors.