Three Dimensional Characterization of Defects by Ultrasonic Time-of-Flight Diffraction (ToFD) Technique

Ultrasonic time-of-flight diffraction (ToFD) technique has high accuracy in locating and sizing discontinuities. The primary reason for this accuracy is the use of time instead of amplitude for measurement of the depth and size of discontinuities. Despite the many advantages of ToFD, it suffers from a number of shortcomings, the most notable one being its two-dimensional character. The goal of this paper is to develop an algorithm, as a prerequisite, to extend ToFD measurements to a three-dimensional space. For this purpose, a combination of multiple transmitting and receiving probes is proposed instead of just one pair commonly used in ToFD measurements. The approach for locating and sizing defects in a 3D space follows the methods used in radar and acoustic positioning systems. Non-iterative techniques are used for positioning a single source (defect) based on signals collected by several transducers. The estimation formula, in the form of a closed-form solution, is derived by linear least-squares minimization. In addition to existing conventional passive algorithms, a new active algorithm is also proposed for the general arrangement of transducers. This algorithm is tested on a steel specimen having an artificially implanted discontinuity and the three-dimensional location of the defect is estimated.