## 8 Conclusions  
Based on the BS 7910 FAD method, this paper analyzed the important factors affecting the ultimate axial load of the X65 pipeline with cracked girth welds, and developed a prediction model for the ultimate axial load of the X65 pipeline, which provides a reference for the applicability evaluation and safe operation of X65 pipeline with girth weld cracks. The final conclusions are as follows:  
1. The larger the crack size, the higher the risk to the safe operation of the pipeline. For pipeline girth welds without misalignment, the safety requirements are met if the axial load does not exceed 0.9 times the yield strength, even when there is a large-size crack. Moreover, according to the results regarding the effect of crack size parameters on the evaluation results, the effect of crack depth on pipeline safety is far greater than that of crack length. 2. The smaller the pipeline wall thickness, the higher the load and fracture ratios, and the greater the possibility of damage. The presence of misalignment significantly increases the stress concentration, and the greater the misalignment, the more severe the stress concentration. Increasing the pipeline wall thickness or reducing misalignment can effectively improve the safety of the pipeline. 3. Under the same tensile strength, the higher the yield strength, the narrower the envelope range of the failure evaluation curve, and the higher the fracture ratio of the evaluation point. This indicates that a high yield ratio of steel is not conducive to pipeline safety. On the other hand, whether the improvement of the tensile strength of steel under the same yield ratio has a positive effect on the evaluation results requires further investigation. 4. When there is no pipeline misalignment, the ultimate axial load decreases slightly with increasing wall thickness. When there is pipeline misalignment, the ultimate axial load increases slightly with increasing wall thickness, which is because the stress concentration of the weld toe weakens with the occurrence of misalignment. In general, the larger the wall thickness, the higher the safety of the pipeline, and the ultimate axial load increases as well. 5. Under the same tensile strength, the higher the yield ratio of steel, the lower the ultimate axial load that the girth weld can withstand, which is more apparent when the crack size is small. Therefore, when the crack size increases, the effect of the yield ratio on the ultimate axial load weakens. Under the same yield ratio, the higher the tensile strength, the lower the ultimate axial load that the circumferential weld can bear. This this is more obvious when the crack size is large, and less significant when the crack size is small. 6. In this paper, a prediction model for the ultimate axial load of the X65 pipeline based on stress failure assessment criteria was developed. The correlation coefficients of the Option 1 and Option 2 evaluation models were above 99%, indicating that the prediction results of the PSO-SVR model are accurate and reliable. Conceptualization, H.Z. ; data curation, writing and editing, S.W. ; Methodology and formal analysis, J.L. and D.Z. ; Supervision, X.L. ; Validation, X.Z. All authors have read and agreed to the published version of the manuscript. This research has been co-financed by Beijing Municipal Natural Science Foundation (Grant No. 8214053), National Science Foundation of China (Grant No. 52004314), Tianshan Youth Program (Grant No. 2019Q088), the Open Project Program of Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development (Grant No. BIPT2020005), \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Option 1 Prediction Error** & **Option 2 Prediction Error** \\ \hline MSE (mean square error) & \(1.55\times 10^{-4}\) & \(1.39\times 10^{-4}\) \\ R (correlation coefficient) & 99.75\% & 99.77\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Prediction errors.