## 3 CNN-LSTM-MHSA Model-Based Multiple Bolt Looseness Detection  
The beam-column joint used in this study is shown in Figure 5. It is composed of an I-shaped steel beam and a T-shaped steel beam. The T-shaped steel beam is attached to the column. Since this study works on detecting bolt looseness in the web of the I-shaped steel beam, the column is not simulated. Eight bolts are arranged in four rows. In this case, the limited space between the bolts and the edge of the T-shaped steel beam makes it impossible to install transducers on both sides of the bolt-connected region to receive the transmitted waves. Therefore, transducers are installed at the same side to generate and receive SH-typed guided waves. S\({}_{1}\) and S\({}_{2}\) work as the actuators, and S\({}_{3}\) and S\({}_{4}\) act  
Figure 4: Wave mode component analysis by applying external load in the y direction (simulation of SH-typed guided wave). (**a**) External load in the y direction. (**b**) Distribution of \(\alpha_{p}\). (**c**) Mode 37. (**d**) Mode 39. (**e**) Mode 40. (**f**) Mode 43. (**g**) Mode 44. Figure 3: Wave mode component analysis by applying external load in the x direction (simulation of Lamb wave). (**a**) External load in the x direction. (**b**) Distribution of \(\alpha_{p}\). (**c**) Mode 1. (**d**) Mode 2. (**e**) Mode 7. (**f**) Mode 9. (**g**) Mode 10.  
as receivers. Four wave propagation paths are formed by the four transducers (S\({}_{1}\)-S\({}_{3}\), S\({}_{1}\)-S\({}_{4}\), S\({}_{2}\)-S\({}_{3}\), and S\({}_{2}\)-S\({}_{4}\)). The received signal at the transducer Sn from the actuator Sm is represented as ymn(t). The generated guided wave first reaches the receiver, then passes through the bolt joint and is reflected by the end of the I-shaped steel beam. A directly incoming wave and an end-reflected wave will be captured by the receiver. The amplitude of the end-reflected wave is influenced by the contact area between the two beams, which in turn is associated with the applied bolt torque. Thus, the state of bolt connection can be judged according to the characteristic change in the received signals. The CNN-LSTM-MHSA model is employed to locate the loosed bolt and evaluate the degree of looseness by the following steps, as illustrated in Figure 6.  
_Step I_: A FE model of the beam-column joint is established. Numerous bolt looseness scenarios are designed to simulate different damage cases. The bolt looseness severity is adjusted by modifying the bolt tension. Subsequently, SH-typed guided wave signals are applied to the actuators to simulate the wave propagation process. For each damage case, four received signals are obtained, and the training and testing datasets are constructed under various damage cases. _Step II_: Wavelet transform is applied to y\({}_{\text{mn}}\)(t) to analyze the information in the time-frequency domain. Effective regions are extracted from the time-frequency spectra of y\({}_{13}\)(t), y\({}_{14}\)(t), y\({}_{23}\)(t), and y\({}_{24}\)(t) to combine a new training pattern. The effective region should cover the directly incoming and end-reflected wave packets in the time domain and the frequency components around the central frequency of the excitation signal in the frequency domain. The new training pattern is converted to grayscale as the input to the neural network. Data augmentation techniques, including time masking and frequency masking, are then applied to the training pattern to expand the training dataset and enhance the robustness of the detection accuracy. _Step III_: The CNN-LSTM-MHSA model is constructed with the combined time-frequency spectrum as the input. The CNN model consists of two conventional layers and a pooling layer, and the extracted two-dimensional features are flattened before being input to the LSTM layer. The MHSA is used to consider the inner relations between the extracted features, and fully connected layers are then conducted to map the features to the label space.