## 4 Numerical Example  
### Modeling of the Beam-Column Joint  
The FE model of the beam-column joint was constructed using the commercial software ABAQUS 6.14. The geometrical and material properties of the I-shaped and T-shaped steel beam are consistent with those detailed in Table 1 and Figure 5. The bolts were simulated using two bolt nuts and a bolt thread with diameter of 17 mm and 10 mm, respectively. The maximum mesh size for the beam and the bolts was set at 5 mm and 1.5 mm, with mesh refinement near the bolt of the web. The model comprises 92,160 nodes and 60,926 linear solid eight-node hexahedral elements. The contact condition between bolts and plates, as well as the contact between two plates, were modeled with hard and frictional contact in the normal and tangential directions, respectively. The friction coefficient was set to 0.3 to consider the roughness of the plates [15]. A static analysis process was initially performed to gradually add the bolt torque. The bolt torque (\(T\)) was transferred to bolt tension (\(F\)) by Equation (7). In this case, the bolt tension under the intact case was 23,000 kN, equivalent to 70% of the permissible limit. \[T=K\times F\times d \tag{7}\]  
where \(K\) is the torque quotient; \(d\) denotes the diameter of the bolt thread. Various bolt looseness conditions were simulated by changing the bolt tension. Then, an explicit dynamic analysis was conducted to model the propagation of SH-typed guided waves. The excitation signal is a three-cycle sinusoidal tone burst, with a central frequency of 80 kHz, as shown in Figure 8. SH-typed guided waves can be generated using piezoelectric transducers or magnetic effect-based transducers [41; 42; 43]. However, the multi-physics coupling simulations will decrease the computation efficiency. Thus, the SH-typed guided wave was generated by inducing nodal displacements at the y axis in Figure 5. A sampling frequency of 1 MHz was employed. Figure 8: The three-cycle tone burst excitation signal. (**a**) times history; (**b**) FFT. Figure 7: Structure of the LSTM and SA mechanism. (**a**) LSTM cell; (**b**) SA mechanism. The distance between the actuator and the receiver in the x direction is denoted as \(l\). The position of the receiver remains unchanged, and three different conditions with \(l\) values of 150 mm, 200 mm, and 250 mm were simulated. Figure 9 shows the received signals at the wave paths S\({}_{1}\)-S\({}_{3}\) and S\({}_{1}\)-S\({}_{4}\). The wave velocities for these three conditions were calculated as 3125 m/s, 3174 m/s, and 3205 m/s, respectively, which are very close to the group velocity of the main propagation mode (3191 m/s) obtained by SAFE analysis. The amplitudes of the received signals from S\({}_{1}\)-S\({}_{4}\) were much smaller than those from S\({}_{1}\)-S\({}_{3}\). When \(l\) equals 150 mm, the directly incoming and end-reflected wave packets are not clearly distinguishable, and the amplitude of the end-reflected wave packet starts to decrease as \(l\) is increased from 200 mm to 250 mm. Therefore, \(l\) was taken as 200 mm. The energy distribution of the SH-typed guided wave during the wave propagation process is shown in Figure 10. The SH wave reaches the left end of the I-shaped steel beam near 0.15 ms and then propagates backwards. It can be observed that the SH wave does not transmit to the flange, aligning with the wave propagation analysis results by the SAFE method. Figure 11 illustrates the amplitude changes for four different bolt looseness scenarios, while the corresponding local bolt looseness severities are detailed in Table 2. It is assumed that the looseness severities of the two bolts are identical for each row. Cases involving different bolt looseness severities within a single row will be explored in further studies. For example, the bolt tensions for Bolt 3 to Bolt 6 were 16,100 kN in Case 1. The amplitude of the directly incoming wave remained constant across all bolt looseness cases, as it was unaffected by bolt looseness.