## 3 Numerical Modelling and Analysis of Ultrasonic Inspection of Grounded Flat Steel
### Inverse Transmission Characteristics of SH0 Wave and DAC Curve  
After long-term service, grounded flat steel is prone to local corrosion. Its corrosion morphology varies depending on the local environmental conditions. Figure 7a shows that the corrosion pit morphology is more common [1]. According to the detection principle of ultrasonic guided waves, when confronting a defect during propagation, a certain proportion of the reflected waves are returned at the location of the defect. The amplitude of the reflected signal is related to the depth and length of the defect. However, in reality, the morphology of corrosion defects varies, making it impractical to simulate every circumstance in research. Therefore, for the convenience of modeling and calculation, we chose the most representative form of groove defects for the study. As shown in Figure 7, we set a groove defect on the centerline of the grounded flat steel using a 30 \(\times\) 5 \(\times\) 1 mm groove defect as an example; by varying the specification parameters of the groove defect model, we investigated the reflection and transmission of the guided wave acting on the defect and the effect of the defect location on the amplitude of the guided wave signal. Figure 6: (a) Guided wave at each receiving point and (b) SH wave attenuation curve. We set up a through-groove defect (20 \(\times\) 5 \(\times\) 5.8) at 350 mm from the excitation source and defined the signal receiving point at 100 mm at each end of the groove defect. We then changed the length of the groove defect. The trend of the reflected and transmitted wave amplitudes at the receiving point are shown in Figure 8 below. As the length of the defect increases, both the amplitude of the reflected guided wave and the amplitude of the transmitted wave progressively decrease. However, when the defect length is relatively short, the detected echo signal experiences a significant amplitude decline with increasing defect length. In contrast, when the defect length is sufficiently large, the growth rate of the detected echo signal amplitude slows down, eventually approaching a stable state as the defect length continues to increase. To investigate the impact of different defect variations on defect echoes, we modified the position and width of the defects in the model to simulate the guided wave displacement field in the flat steel for each scenario. The resulting DAC curves for each defect are shown in Figure 9.  
Figure 8: The relationship between reflection, transmission wave amplitude, and defect length. Figure 7: (**a**) Actual corrosion of grounded flat steel and (**b**) grounding flat steel corrosion defect model (30 \(\times\) 5 \(\times\) 1 mm). The amplitude of a defective echo is augmented proportionally with the size of the defect. As the length of the corrosion defect increases, the surface area of ultrasonic reflection increases as well, resulting in an increase in the energy of the reflected echo and the echo amplitude. Similarly, for identical corrosion defects, the amplitude of the echo diminishes with an increase in detection distance. Moreover, the rate of decline gradually decelerates. The Relationship between the Size of the Grounding Flat Steel Corrosion Defects and the Echo Amplitude  
Starting with the width of the corrosion defect at 5 mm, we changed the length and depth of the corrosion defect, examined the effect of different corrosion depths and lengths on the amplitude of the ultrasonic guided wave, and plotted the depth and width of the corrosion defect and the relationship curve of the echo amplitude, as shown in Figures 10a and 10b, respectively. By conducting simulation calculations on corrosion defect widths of 5, 10, and 15 mm for guided wave detection, we found a relationship between the corrosion defect width and the echo signal amplitude, as can be seen in Figure 10c.