ABSTRACT
A modelling framework for ultrasonic inspection of waveguides with arbitrary discontinuities, excited using piezoelectric transducers, is developed. The framework accounts for multi-modal, dispersive and damped one dimensional propagation over long distances. The proposed model is applied to simulate a realistic guided wave-based inspection of a welded rail. The framework models the excitation, propagation and scattering of guided waves from welds by respectively employing a hybrid model that couples a 3D FEM model of a piezoelectric transducer with a 2D SAFE model of the rail; a 2D SAFE model of the rail; and another hybrid method which couples a 3D FEM model of the arbitrary discontinuity (weld) with two SAFE models of the rail to represent the semi-infinite incoming and outgoing waveguides. Optimal damping parameters for hysteretic and viscous damping, respectively, are determined using a model updating procedure to approximate attenuation in the rail. Good agreement between the experimental measurement and simulation is demonstrated, even for weld reflections originating over 640 m from the transducer location. The proposed physics-based framework can be used to efficiently perform multiple analyses considering different numbers and locations of welds, different excitation signals or to investigate the effects of changes in parameters such as transducer geometry, or material property variations caused by temperature fluctuations. The framework could therefore be used in future to set up a digital twin of a section of rail track, or in the development of a rail monitoring system by predicting reflections from defects which cannot readily be measured, but which can be simulated.
ABSTRACT
Guided wave based monitoring systems require accurate knowledge of mode propagation characteristics such as wavenumber and group velocity dispersion curves. These characteristics may be computed numerically for a rail provided that the material and geometric properties of the rail are known. Generally, the rail properties are not known with sufficient accuracy and these properties also change due to temperature, rail wear and rail grinding. An automated procedure is proposed to estimate material and geometric properties of a rail by finding the properties which, when input into a Semi-Analytical Finite Element (SAFE) model, accurately reproduce measured dispersion characteristics. Pulse-echo measurements were performed and spectrograms show the reflections from aluminothermic welds of three modes of propagation. The SAFE method was used to solve the forward problem of predicting the dispersion characteristics for specified rail properties. Dispersion curves are computed for different combinations of Poisson's ratio and three geometric parameters. These dispersion curves are scaled to cover a range of longitudinal speeds of sound of the rail material. A technique is developed to determine which SAFE model provided the best fit to the experimental measurements. The technique does not require knowledge of the distances to the reflectors; rather these distances are estimated as part of the proposed procedure. A SAFE model with the estimated rail parameters produced dispersion curves and distances in very good agreement with the measured spectrograms. In addition, the estimated mean geometric parameters agreed with the measured profile of the rail head.
ABSTRACT
Variation in masticatory induced stress, caused by shape changes in the human skull, is quantified in this article. A comparison on masticatory induced stress is presented subject to a variation in human skull shape. Non-rigid registration is employed to obtain appropriate computational domain representations. This procedure allows the isolation of shape from other variations that could affect the results. An added benefit, revealed through the use of non-rigid registration to acquire appropriate domain representation, is the possibility of direct and objective comparison and manipulation. The effect of mapping uncertainty on the direct comparison is also quantified. As shown in this study, exact difference values are not necessarily obtained, but a non-rigid map between subject shapes and numerical results gives an objective indication on the location of differences.
