## 6 Conclusions  
This study presented a CNN-LSTM-MHSA-based method for the quantitative assessment of bolt looseness in a beam-column joint connected by multiple bolts. A SAFE model was constructed to analyze the wave propagation properties of Lamb waves and SH-typed guided waves in an I-shaped steel beam. Two pairs of transducers were utilized for generating and receiving the SH waves across four distinct wave paths, and the time-frequency information was collected and combined to obtain the input pattern required for the deep neural network. Numerical simulations were conducted to verify the SAFE analysis results  
Figure 18: The received signal at S1–S3 with white noise under the intact case. (**a**) 10%; (**b**) 20%. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Noise in the** & \multicolumn{2}{c}{**CNN-LSTM-MHSA Trained with 10\% Noise**} \\
**Testing Samples** & **Acc** & \(Error^{local}\) & \(Error^{overall}\) \\ \hline No & 99.48\% & 8.90\% & 5.60\% \\
10\% & 97.92\% & 12.42\% & 6.23\% \\
20\% & 93.48\% & 17.24\% & 7.57\% \\ \hline
**Noise in the** & \multicolumn{2}{c}{**CNN-LSTM-MHSA Trained with 20\% Noise**} \\
**Testing Samples** & Acc & \(Error^{local}\) & \(Error^{overall}\) \\ \hline No & 99.74\% & 7.43\% & 3.97\% \\
10\% & 97.40\% & 11.43\% & 6.03\% \\
20\% & 97.14\% & 16.09\% & 7.57\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Noise injection testing results of the CNN-LSTM-MHSA method. and collect samples with varying bolt looseness conditions. Data augmentation techniques were employed to expand the training dataset. Comparative studies and noise injection testing were carried out to evaluate the performance of the proposed method. The following conclusions have been drawn:  
1. The proposed mode weight coefficient aids in understanding how wave modes are distributed under different external loads for the I-shaped steel beam with complex dispersion properties. This coefficient can also assist in selecting the appropriate mode and position for the excitation signal. 2. The looseness conditions of multiple bolts in the beam-column joint were easily detected using the proposed CNN-LSTM-MHSA model. The bolt looseness localization accuracy was 100%, with local and overall severity estimation errors of 3.96% and 2.09%, respectively. 3. The CNN-LSTM-MHSA model, which integrates the time-frequency spectrum extracted from the guided wave signals, outperformed traditional deep neural networks with inputs of time series data and Fourier amplitude spectra, as well as the wave energy reflection ratio-based method. 4. White noise levels of 10% and 20% were added to the training and testing samples to simulate the effects of measurement noise. The proposed method maintained good bolt looseness localization accuracy, with values exceeding 93%. The maximum errors for \(Error^{local}\) and \(Error^{overall}\) were 17.24% and 7.57%, respectively. Experimental studies and real applications will be carried out for the beam-column joint later. For laboratory tests, the bolt looseness scenarios considered in the FE simulations will be conducted on a beam-column joint with the same dimensions. The received signals will be measured by the magnetostrictive transducer and used to train the CNN-LSTM-MHSA model in order to verify the proposed method. However, it is not easy to acquire enough training samples with desirable bolt looseness conditions in real applications. Testing the experimental data using the neural network trained by the FE simulations may solve this problem. Thus, the FE model should be well modified according to the experimental data. Additionally, the influence of uncertain factors, such as temperature changes and the surface roughness of plates, on the detection accuracy will be investigated experimentally. Conceptualization, R.Z., X.S., Y.D. and Y.L. ; methodology, X.S. ; investigation, Y.F. and R.M. ; data curation, X.S. ; writing--original draft preparation, X.S. ; writing--review and editing, R.Z., Y.D. and Y.L. ; visualization, Y.F. ; supervision, Y.D. and Y.L.