## 5 Result Analysis
### Analysis of Simulation and Test Results  
Figure 18 illustrates the von Mises stress distribution of the numerical results during pressurization. During the pressurization process, the elastoplastic behavior of the PVC pipe was considered. From Figure 18, it is clear that the pipeline failure process in the simulation experienced three stages like the burst test: initially, in the elastic phase, the pipe remained cylindrical and no swell feature was detected. The first step is shown in blue. Next, in the plastic phase, the shape of the tested pipe became an ellipse caused by large deformation. It can be seen from the cloud diagram that the von Mises stress on the pipe wall increased. Finally, in the rupture phase, the tested sample was broken into pieces or cracks. The pipe wall is displayed in red with extreme stress. In addition, an extremely obvious swelling appearance in the pipe can be noticed by the high stress concentration.  
Figure 16: Pressure–displacement curve in burst process.  
Figure 17: The process of the pipe under pressure (P1200-1).  
The burst pressure results obtained by the experiment, theoretical analysis, and numerical simulation are recorded in Table 3. Figure 19 illustrates the load-strain curves obtained in the FE model and experiment. When analyzing the load-strain curve, the simulation curve and test data show good consistency during the loading process. For P1200-1, the maximum internal water pressure achieved a value of \(P\) = 3.66 MPa and \(P\) = 3.58 MPa for the test data and simulation curves, respectively. The experimental and numerical simulation values of P1200-2, P1200-3, and P1200-4 were 2.90 MPa, 2.32 MPa, and 1.85 MPa, and 2.82 MPa, 2.29 MPa, and 1.83 MPa, respectively. There are differences in the material properties because of the manufacturing process and the impact of aging [40, 41]. Figure 19 reveals that the increase in pipe wall thickness will increase the internal pressure bearing capacity.  
Figure 20 presents the correlation of the burst pressure calculated from Equation (15) with simulation and experimental results. As shown in Figure 20, the predicted values obtained from ASSY and FEM in this study are in good agreement with the ones that appeared in the burst tests.  
Root mean square error (_RMSE_), mean absolute error (_MAE_), maximum error (_ME_), and correlation coefficient (_R_\({}^{2}\)) were chosen as the model's predictive ability evaluation indicators to verify the performance of the ASSY burst pressure prediction model proposed in this paper.  
\[\begin{split} RMSE=\sqrt{\left[\frac{1}{N}\sum\limits_{i=1}^{N}{ \left(y_{i}-\widetilde{y}_{i}\right)^{2}}\right]},MAE=\frac{1}{N}\sum\limits_{ i=1}^{N}{\left|y_{i}-\widetilde{y}_{i}\right|},\\ ME=\underset{1\leq i\leq N}{\max}{\left|y_{i}-\widetilde{y}_{i} \right|},R^{2}=\frac{SSR}{SST}=\frac{\sum_{i=1}^{N}{\left(\widetilde{y}_{i}- \overline{y}\right)^{2}}}{\sum_{i=1}^{N}{\left(y_{i}-\overline{y}\right)^{2}} }\end{split} \tag{17}\]  
where \(y_{i}\) and \(\tilde{y}_{i}\) are the tested value and predictive value obtained by various yield criteria.  
Table 4 shows the statistical results of various models. As shown in Table 4, the _RMSE_, _MAE_, and _ME_ of the ASSY model and FEM approach were 0.05, 0.4, 0.11 and 0.04, 0.04, and 0.08 respectively. The evaluation index values were sorted from small to large as FEM < ASSY < von Mises < Tresca < TSSY, indicating the FEM model had the smallest prediction error, followed by the ASSY model. This confirms that the FEM approach and ASSY solution have a higher degree of coincidence, and the von Mises solution model is better than the TSSY and Tresca solutions.  
Figure 19: Numerical and experimental stress–strain curves.  
Figure 20: Correlation between predicted value and measured value.