Abstract: This paper aims to develop a robust and efficient method for modeling the performance of steel jacket platforms under parameter uncertainties. For this purpose, a combined approach using Linear Simulation (LS) and the improved Grey Wolf Optimization algorithm was developed. First, the performance of the developed model was evaluated on benchmark functions, and then, the probability of failure of the steel jacket structure due to wave loads was calculated. The results showed that the highest probability of platform failure occurred under wave impact with an angle of 315 degrees, a height of 12.2 meters, and a period of 11 seconds, with a probability of 1E-5. This indicates a high level of safety for the designed platform. The results showed that the proposed model has suitable accuracy and can calculate the safety level of various offshore structures with acceptable precision.
 
 
Introduction: Fixed steel platforms that are used for extracting oil and gas from deep sea depths are among the most important offshore structures. Due to the high cost of their construction, these platforms are designed for long-term use. Oil and gas platforms are subjected to various loads during their operational period, including dynamic loads such as forces caused by waves, ocean currents, and wind loads; impact loads such as collisions with vessels during loading and unloading, and the impact of heavy objects falling onto the platform deck (Gjerde 1993). The aim of this study is to develop a probabilistic model for modeling the performance of jacket-type metal platforms, taking into account the uncertainty of influential parameters. For this purpose, the performance of a linear simulation method was improved using a new hybrid metaheuristic algorithm and then used to estimate the reliability level of oil and gas metal platforms.

Methodology: In this study, to determine the failure and safe states of steel jacket platforms, the limit state function was used in the form of Eq. ‎(3) in which  is the stress in the structural members caused by compressive forces;  and  are the stresses resulting from the bending moment around the x and y axes, respectively, all represented in Eq. (4), where P is the axial force applied to the members,  and  are the calculated bending moments around the x and y axes, respectively; D and A reveal the diameter and cross-sectional area of the pipe members, respectively; and I is the moment of inertia of the members, calculated by Eq. (6), here t is the thickness of the pipe member wall.
To solve this problem, the Line Sampling (LS) method was used. The LS method is a robust and accurate method for evaluating the reliability of structures, which was first introduced by Koutsourelakis et al. (2004) based on a combined approach of Monte Carlo and first-order reliability methods. Here, a combination of meta-heuristic approach was developed to improve the performance of the LS method. Particle Swarm Optimization (PSO) was incorporated into Grey Wolf Optimizer (GWO) to upgrade the efficiency and robustness of GWO.

Results and Discussion: First, two numerical benchmark functions were solved by the developed hybrid model to validate the robustness of the method, Eqs. (24-25) in which,  and  are the random numbers with normal distribution, N (4, 0). Also, the mean and standard deviation of  in Eq. (24) are 1 and 0, respectively.
‎Table 1 presents the results of implementing the proposed method on the benchmark problems. It shows, the classical LS method was unable to solve both examples due to the nonlinearity of the problem functions and the use of gradient-based methods to find the direction of the unit vector, which failed to find the optimal point. However, all three LS-GWO, LS-PSO, and LS-WGOPSO methods were able to estimate the reliability index with reasonable accuracy compared to the MCS method. It is also observed that the LS-GWOPSO hybrid method was able to converge with fewer limit state function calls compared to the other two methods.
After validating and evaluating the performance of the proposed model on two benchmark examples, the new model's reliability was applied to assess the reliability level of metal jacket platforms, one of the oil platforms in the South Pars oil field was selected as a case study. This platform has a 4-legged jacket weighing 1240 tons and a height of 72.7 meters. The weight of the platform deck is 1050 tons, and the depth of the water at the installation site is 66.8 meters. The statistical properties of the uncertain parameters, including the yield stress of steel, member diameter, wall thickness, effective length factor, and member length, are presented in ‎Table 2.
In this study, the failure mode is considered the failure of the weakest member. For this purpose, the internal forces in the members are first generated in different directions due to wave loads. Then, based on the limit state function presented in Eq. ‎(24), the probability of failure of the metal jacket structure is calculated.
‎Table 3 shows the values of the failure probability and reliability index of the metal jacket platform for the internal forces generated in the members due to wave loads. As shown in ‎Table 3, the designed platform is highly safe against uncertainties, with a reliability level of 99% in all 8 wave-impact scenarios with different angles. Among the investigated scenarios, the highest probability of failure occurred in the wave impact with an angle of 135 degrees. This may be due to the high wave height in the direction of 135 degrees compared to other directions. It should be noted that the limit state function was called 400 times in all of the above scenarios.

Conclusion: In the present study, a new reliability assessment method based on the Linear Simulation (LS) approach was developed for probabilistic modeling of the performance of steel jacket platforms. The results showed that the highest probability of platform failure occurred due to the impact of a floating object and wave impact with an angle of 135 degrees. Overall, the safety assessment of the studied platform indicated that the platform has a suitable level of safety.