## 5 Results  
The stress PSD parameters of the test group are shown in Table 3. The spectral parameters and kurtosis values of the stress PSDs of the test group are input into the neural network to obtain its output bi-Gamma model parameters. By incorporating these parameters into the bi-Gamma model, the predicted stress rainflow range PDF of the stress range can be obtained. During the testing of the network, the predicted PDF results obtained from the neural network model proposed in this paper are compared with the rainflow range PDF results of the non-Gaussian stress time history under the same stress PSD, as shown in Figure 7. To analyze the consistency between the predicted and calculated PDFs and the corresponding \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Group No.** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \(f_{1}\) [Hz] & 33 & 15 & 13 & 44 & 10 & 33 & 13 & 33 & 21 & 15 \\ \(f_{2}\) [Hz] & 80 & 111 & 150 & 108 & 161 & 71 & 196 & 172 & 72 & 76 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The PSDs of the test group. Figure 6: Flowchart for the generation of the datasets used for training neural networks. rainflow statistical results, a correlation coefficient is introduced. The definition for the correlation coefficient is as follows  
\[R_{XY}=\frac{\text{E}[(X-\mu_{X})(Y-\mu_{Y})]}{\sigma_{x}\sigma_{y}} \tag{26}\]  
where \(X\) and \(Y\) represent two signal sequences where \(\mu\) denotes the signal's mean and \(\sigma\) denotes the signal's standard deviation. The range of the correlation coefficient \(R_{XY}\) is between 0 and 1, where 0 indicates a complete lack of correlation between the two signals, and 1 indicates a perfect correlation between them. The results of the correlation coefficient analysis are depicted in Figure 8.  
Figure 8: Correlation coefficients between predicted PDFs and rainflow PDFs. (**a**) \(K_{u}=5\); (**b**) \(K_{u}=6\); (**c**) \(K_{u}=7.5\). Figure 7: PDF results of rainflow and predictions for Group 5 (\(f_{1}=10\) Hz\({}_{r}f_{2}=161\) Hz). The lifetimes under Gaussian and non-Gaussian stresses with different kurtosis values for the stress PSD described for the test group are calculated separately. The material used for the calculation is aluminum alloy 6061-T6, with \(S\)-\(N\) curve parameters as shown in Table 4. Table 5 presents a comparison of the lifetime calculation results for a kurtosis of \(K_{u}=7.5\). Additionally, the lifetimes for kurtosis values of \(K_{u}=5\) and \(K_{u}=6\) are also calculated, as depicted in Figure 9.  
Figure 9: Comparison of predicted life with non-Gaussian corrected life. (**a**) \(K_{u}=5\); (**b**) \(K_{u}=6\); (**c**) \(K_{u}=7.5\). \(L_{\text{RF}}^{\text{ng}}\), the correction method with the Dirlik model \(L_{\text{DK}}^{\text{ng}}\), the correction method with the Tovo-Benasciutti model \(L_{\text{TB}}^{\text{ng}}\), and the neural network's prediction method \(L_{\text{NP}}\). The results are shown in Figure 9a, 9b and 9c, respectively, for the three different kurtosis values. It can be seen that the results of this article method are within the 2-scatter band in comparison to the rainflow life, while the correction method results fall outside the 3-scatter band. Furthermore, based on the calculation results for the lifetimes under different kurtosis values, it can be observed that when the kurtosis is 7.5, the correction method results based on the Dirlik and Tovo-Benasciutti models are consistently conservative, as shown in Figure 9c. However, as the kurtosis decreases, the predictive results become less conservative, as shown in Figure 9a,b. This also indicates that, for the correction of the non-Gaussian fatigue life, not only should the accuracy of the original Gaussian life calculation should be considered, but the selection of correction coefficients should also be considered. Different training set sizes were used to train the neural network.