Physics-based modelling and simulation of reverberating reflections in ultrasonic guided wave inspections applied to welded rail tracks

The development of ultrasonic guided wave monitoring systems has become increasingly important as they have demonstrated the ability to detect damage in structures. An example of such a system is the Ultrasonic Broken Rail Detection system which uses pitch-catch piezoelectric transducers permanently attached to the rail to excite and receive ultrasonic guided wave signals. Changes in signals can provide a reliable indication of damage growth in the rail and ultimately reduce broken rails and derailments. However, the challenge during system development is obtaining monitoring data containing damage signatures as damaged sections of rail are immediately replaced when detected. Laboratory damage experiments are also not plausible due to end reflections from short rail sections dominating the response. Modelling and simulation thus become increasingly important to enable the simulation of unavailable damage scenarios for the upgradation of existing (or development of new reliable) guided wave-based monitoring systems. Two numerical procedures to model and simulate guided wave inspections encompassing the excitation, propagation and scattering from discontinuities in 1D waveguides are presented and applied to the inspection of the web of a welded rail. The major contribution highlighted by these procedures is the ability to simulate complex back and forth reverberating reflections. These reflections occur between various reflectors such as welds and other discontinuities such as damage. The two methods are different but complementary. The first one, which is based on a simple manual simulation of finite reverberating reflections, is useful for interpreting the results to understand how different reflections interact, especially where they overlap. The second method accounts for the scattering by all defects or discontinuities arbitrarily positioned in the waveguide. It offers a more accurate approximation of the simulated inspection since it accounts for infinite reflections. The simulation results obtained from the two modelling procedures are validated using a field experiment from a damage-free rail containing welds and holes as discontinuities. The results show that it would be possible to simulate inspections for unavailable damage scenarios. The paper is concluded with a thorough analysis of the inspection measurement using the first method.