## 5 Test Results and Analysis  
In order to verify the effectiveness of the proposed improved model, based on the fatigue test data of the material 18 CrNiMo7-6 listed in Table 3, the life prediction results of this model, the linear damage accumulation model, and the ductile dissipation model, are compared. The results are shown in Table 4. In addition, for 45# steel and Al-2024 aluminum alloy, commonly used in mechanical engineering, calculations and comparisons are also made based on the experimental data of the literature [23; 24]. The results are listed in Tables 5 and 6. For each material in the corresponding loading mode, the relative error between the experimental value and the theoretical calculation is shown in Figures 9-14. Figure 11: (331.5–284.4 MPa) The relative error of each model under different \(n_{1}\)/\(N_{/1}\) (45# steel). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Test Value**} & \multicolumn{3}{c}{**Miner’s Rule**} & \multicolumn{2}{c}{**Ductile Dissipation**} & \multicolumn{2}{c}{**The Proposed Model**} \\
**Two-Stage** & & & & & **(Formula (1))** & **Model (Formula (11))** & \multicolumn{2}{c}{**(Formula (19))**} \\ \cline{2-11}
**Loading Stress** & & & & & & & & & & & \\
**Level/MPa** & \(n_{1}\) & \(n_{1}\)/\(N_{/1}\) & \(n_{2}\) & \(n_{2}\)/\(N_{/2}\) & \(n_{2}\)/\(N_{/2}\) & **Relative Error/\%** & \(n_{2}\)/\(N_{/2}\) & **Relative Error/\%** & \(n_{2}\)/\(N_{/2}\) & **Relative Error/\%** \\ \hline  & 30,000 & 0.2000 & 228,700 & 0.5319 & 0.8000 & 50.40\% & 0.7844 & 47.47\% & 0.5623 & 5.71\% \\
200–150 & 60,000 & 0.4000 & 101,050 & 0.2350 & 0.6000 & 155.32\% & 0.5735 & 144.05\% & 0.2677 & 13.91\% \\  & 90,000 & 0.6000 & 76,050 & 0.1769 & 0.4000 & 126.12\% & 0.3689 & 108.53\% & 0.0941 & 46.80\% \\ \hline  & 86,000 & 0.2000 & 144,500 & 0.9633 & 0.8000 & 16.95\% & 0.8146 & 15.43\% & 0.9153 & 4.98\% \\
150–200 & 172,000 & 0.4000 & 133,500 & 0.8900 & 0.6000 & 32.58\% & 0.6254 & 29.73\% & 0.8186 & 8.02\% \\  & 258,000 & 0.6000 & 81,700 & 0.5447 & 0.4000 & 26.57\% & 0.4309 & 20.89\% & 0.6992 & 28.36\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Al-2024 aluminum alloy two-stage loading test data and remaining life prediction results of each model. Figure 10: (420–520 MPa) The relative error of each model under different \(n_{1}\)/\(N_{/1}\) (18 CrNiMo7-6). Figure 9: (520–420 MPa) The relative error of each model under different \(n_{1}\)/\(N_{/1}\) (18 CrNiMo7-6). It can be seen from Figures 9 and 10, for 18 CrNiMo7-6 material, under high-low load loading, as the proportion of high load continues to expand, the relative error of [PERSON]'s rule increases significantly. The relative error of the tough dissipation model is also gradually increasing, but the overall value is smaller than [PERSON]'s rule. The relative error between the result obtained by the improved model and the actual value is the smallest among these three models. In the case of low-high loading, the error between the results obtained by the three models and the actual value is smaller than the error obtained in the case of high-low loading. This also shows that, from the side, different loading sequences have different effects on the fatigue life. It can be seen from Figures 11 and 12, for 45# steel, under high-low load loading, as the proportion of high load continues to increases, the relative error of [PERSON]'s rule increases significantly. The relative error fluctuation of the toughness dissipation model  
Figure 14: (150–200 MPa) The relative error of each model under different \(n_{1}\)/\(N_{j1}\) (Al-2024). Figure 12: (284.4-331.5 MPa) The relative error of each model under different \(n_{1}\)/\(N_{j1}\) (45# steel). Figure 13: (200–150 MPa) The relative error of each model under different \(n_{1}\)/\(N_{j1}\) (Al-2024). is relatively stable, and the overall value is smaller than Miner's rule. The relative error between the result obtained by the improved model and the actual value is the smallest among these three models.