A hybrid method for ultrasonic echo of defects using spatial impulse response and finite element method

The numerical simulation modelling is challenging due to the increased mesh requirements to resolve the large propagation distance. A hybrid modeling method for ultrasonic echo of defects using spatial impulse response and finite element method is proposed. The local area around defect is meshed and the interaction between the ultrasonic wave and the defect is calculated by the finite element method. The vibration velocities of the nodes on the boundary are calculated by spatial impulse response method, which is considered as excitation of the finite element model. The velocity potential of the reflected wave at the receive transducer is also obtained by spatial impulse response method. This method enables efficient prediction of the response of complex scatterers. A simulation example of flat bottom hole is established by the hybrid method and the finite element method respectively, and both the waveforms are consistent. The total time for running the hybrid method is 5.9% against the finite element method, and the runtime for the finite element simulation can be reduced significantly. The echoes of cracks with different depth at shoulder root of idler shaft are simulated by the hybrid method. Echoes reflected from the shoulder and crack are overlapped, meaning crack information is lost. The results show the echo amplitude increases with the crack depth, and the echo amplitude can be used to size the root crack. The hybrid method proposed in this paper lays a foundation for improving the computational efficiency of large-scale finite element models.