The scattering matrix (S-matrix) encodes the elastodynamic scattering behaviour of a defect. For the case of guided waves in the low-frequency regime, we explore how to minimise the number of incident/scattered directions used to accurately simulate the S-matrix of an arbitrary defect. The general approach is to use three-dimensional finite element (FE) analysis, implemented in a commercial FE package, to simulate the wave-defect interactions. The scattered wave field is measured at monitoring nodes on a circle that surrounds the defect. These scattered waves are decomposed into the multi-modal far-field scattering amplitudes. The angular order of the scattering is found and used to minimise the number of incident and scattered directions that must be computed. The method is then used to simulate the S-matrices of surface-breaking semi-elliptical cracks and circular through-holes with arbitrary sizes. It is found that the required number of incident/scattered directions varies with the scattered mode, and this is due to the differing scattering orders of these scattered fields. These results demonstrate how to achieve more efficient modelling of guided wave scattering, and also contribute to an understanding of experimental defect characterisation.

Ultrasonic guided wave testing is an essential technique in non-destructive testing for structural integrity of oil and gas pipelines. This technique, based on the pulse-echo method, is often used for the long-range detection of pipelines at any location. However, guided waves suffer from high attenuation when they propagate in attenuative material structures and multiple wave modes due to the excitation, which reduces the power of echo signals and induces corruption caused by coherent noise. In this paper, a developed hybrid coded excitation method that uses the convolution of a Barker code and Golay code pair is proposed and applied for an ultrasonic guided wave testing system to excite the torsional guided wave mode T(0,1) in a steel pipe. The proposed method combines the advantages of these two coding methods and increases the flexibility of code lengths. The performance is evaluated by signal to noise ratio and peak sidelobe level of the processed signal. Both theoretical simulations and experiments have investigated using the proposed codes composed of Barker codes and Golay code pairs of different lengths and combinations. The experimental results show the significant improvement of the signal to noise ratio and the peak sidelobe level due to the proposed hybrid code usage for the excitation of guided waves. The values are further improved to around 32 dB and around −24 dB, respectively. Overall, the proposed hybrid coded method for improving the echo SNR can benefit from guided wave testing to reduce coherent and random noise levels and many other potential applications.