## 1 Introduction
Similarly, analytical models considering stress concentration in welded joints with angular distortions have been developed to estimate fatigue life in hydropower pipelines, incorporating the effects of water hammer damping [15]. Current research also emphasizes the importance of structural integrity assessment in offshore jacket structures, recognizing the complexities beyond initial assumptions. Challenges such as nonlinear effects in structural monitoring methods, particularly those based on principal component analysis, have been identified. A stochastic autoregressive moving average with exogenous input (ARMAX) models has been employed to address these challenges [16]. Additionally, stress concentration factors (SCFs) in ring-stiffened tubular KT-joints have been studied, leading to new SCF parametric formulas for fatigue design [17; 18]. Indirect damage detection methods, such as wavelet packet transform analysis, have demonstrated high accuracy in predicting damage locations in offshore jacket platforms [19]. Furthermore, recent developments include time-domain fatigue analysis methods that require fewer sea state simulations while maintaining accuracy in offshore jacket platform assessments [20]. The Damage Submatrices Method, which focuses on stiffness degradation, has also been effectively applied for damage detection in offshore jacket structures with limited modal information [21]. Another area of research involves assessing the structural integrity of aging offshore platforms for life extension, incorporating structural degradation simulations, loading history, and fatigue strength considerations for corroded components [22]. Some studies have analyzed tubular K-joints under fire-induced elevated temperatures using nonlinear regression methods to determine their ultimate strength under axial loading [23]. Moreover, risk assessment methodologies have been applied to floating production platforms to evaluate structural integrity loss due to gross errors [24], as well as to offshore mooring systems using reliability- and integrity-based design principles [25]. Risk-based structural integrity management frameworks have been developed specifically for offshore jacket platforms [26]. Despite these advancements, a comprehensive comparative analysis of different methodologies--linear, nonlinear, and fatigue analysis--has not been conducted. The present study aims to address this gap by providing a comparative assessment of these methods. Additionally, probabilistic wave analysis frameworks have been proposed to improve structural integrity assessment in offshore platforms, accounting for uncertainties in nonlinear dynamic time-domain modeling [27]. Large-scale experimental investigations on wave slam phenomena have contributed to the development of global slamming force models for offshore wind jacket structures [28]. Furthermore, grouted connection repair systems for offshore structures have been experimentally validated [29]. Given the increasing emphasis on renewable energy sources, researchers have highlighted the necessity of designing offshore structures for oil and gas exploration, wind energy generation, and other industries while minimizing environmental impact [30]. Surveys conducted among industry experts identified three critical factors influencing offshore platform inspections: environmental conditions, structural design, and defects/anomalies, with varying significance depending on professional perspectives [31]. The findings of this research enable continuous monitoring of platform behavior under different loading scenarios, ensuring compliance with the current regulations and verifying the structural integrity. Ultimately, this assessment confirms that offshore platforms meet safety and reliability standards throughout their service life. In addition, research has been conducted to obtain meteorological data related to wave conditions by comparing satellite-derived information to data from specific locations in the Arabian Gulf [32].