Bayesian approach to inclusion characterization and uncertainty quantification in immersion ultrasound

Machine components' inherent defects play a significant role in defining the component's fatigue properties, and consequently its service life. Therefore, the ability to estimate the defects' characteristics and quantify the uncertainties present in the estimates is of great value. In the context of ultrasonic nondestructive testing, the size of detected defects is traditionally estimated by means of comparative amplitude-based methods. This paper investigates an alternative probabilistic characterization method that combines an approximate model for immersion ultrasound with approximate Bayesian computation. The capabilities of the method are assessed through estimation of the location, size, orientation, and material composition of ellipsoid non-metallic inclusions in attenuation-free steel from simulated data. Additionally, the influence of the number of ultrasound measurements, the choice of computation parameters, and the amount of noise on the inference result is investigated. Finally, a distribution for the projected area of the inclusion is evaluated and compared to an area estimate obtained by means of traditional equivalent reflector size estimation. Whereas the equivalent reflector size estimate is critically unconservative, the investigated method proves to be capable of characterizing an inclusion from simulated data and quantifying the uncertainty in the result. Thus, this method provides a promising alternative to traditional comparative sizing methods.