## 7 Results and Discussion
The target reliability index for OWT support structures is typically 3.71, corresponding to a probability of failure of \(10^{-4}\) according to the DNV [91]. In this work, the time-variant fatigue reliability assessment was carried out using the fatigue analysis guidelines in the DNV standard [71,92], and this is presented in Figure 10. In this study, the thickness-corrected cathodic-protected D curve given by DNV-OS-J101 [71] is chosen for fatigue analysis. The intercept (A) and slope (m) of the S-N curve used for studying the fatigue life of steel structure in seawater for \(N>10^{6}\) are given as 15.606 and 5, respectively. From the time-variant fatigue reliability index curve, it can be observed that the structure maintains a reliability index of 3.92, exceeding the defined threshold of target reliability as specified by DNV for the nominal 20 years of operation. It can be observed that the fatigue limit state dominates the design of OWT support structures, as the reliability index for the fatigue limit state is lower than other reliability index values (see the time-variant fatigue reliability assessment at time = 20 years). \begin{table}
\begin{tabular}{c c c} \hline
**Design Constraint** & **Computed Probability of Failure** & **Computed Safety Index** \\ \hline Stress constraint (ULS) & \(0.127\times 10^{-5}\) & 4.706 \\ Deflection constraint (SLS) & \(0.869\times 10^{-19}\) & 9.030 \\ Buckling constraint (ULS) & \(0.113\times 10^{-16}\) & 8.481 \\ Vibration constraint (SLS) & \(0.570\times 10^{-5}\) & 4.389 \\ \hline \end{tabular}
\end{table} 
Table 10: Computed probability of failure and safety index values using first-order reliability method (FORM) for different limit states. Figure 9: Reliability index of different design constraints (non-intrusive formulation). As observed in Table 11, the values of safety index, \(\beta\), predicted by the non-intrusive reliability analysis formulation were marginally higher than those predicted by the ANSYS probabilistic analysis for the different design constraints. However, the difference in the predicted reliability index values from both methods remains consistently below 5%; hence, the agreement of the two methods can be considered sufficient. Furthermore, considering the observed time required, the FORM simulations run instantly compared to the LHS (as packaged in the ANSYS DesignXplorer(c)), which requires about 15 min to run on a high-performance computer (i.e., for the \(1\times 10^{7}\) samples). Additionally, a case study is performed to investigate the effects of COV of the stochastic variables on the fatigue reliability index. In this case, two additional values of COV are considered, i.e., a 5% increase and 5% decrease. The calculated fatigue reliability index over 20-year service life with different values of COV is depicted in Figure 11. As can be seen from Figure 11, the reliability index is sensitive to the value of COV. The higher value of COV means higher uncertainties in stochastic variables, resulting in lower reliability. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Design Constraint/Limit State** & **Reliability Index (ANSYS)** & **Reliability Index (Non-Intrusive Formulation)** & **Percentage Difference (\%)** \\ \hline Stress constraint (ULS) & 4.696 & 4.706 & \(-\)0.21\% \\ Fatigue constraint (FLS) & 4.870 & 5.077 & \(-\)4.25\% \\ (time-invariant analysis) & - & 9.030 & \\ Deformation constraint (SLS) & - & 8.727 & \\ Buckling constraint (ULS) & 4.211 & 4.389 & \(-\)4.23\% \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison between the reliability index values computed by the two methods. Figure 10: Fatigue reliability assessment (non-intrusive formulation). A global sensitivity analysis is also presented from the ANSYS probabilistic analysis for each of the design constraints through post-processing the results. These depict the most critical and important parameters that can radically change the response and reliability performance of the structure.