## 1 Introduction  
Ensuring the resilience of modern society demands structural systems to attain a requisite level of reliability throughout the phases of design and maintenance decision making. The implementation of robust procedures is crucial to pre-empt unexpected failures, averting potential catastrophic damage or losses. Consequently, the design processes of structures and engineering systems necessitate adept strategies for reliability assessment and optimization. However, the inherent need for repeated evaluations of system performance in reliability assessment often leads to substantial computational expenses. This challenge is particularly pronounced in cases where complex, high-dimensional models are indispensable for an accurate depiction of system performance. In response to these challenges, this dissertation proposes the incorporation of active learning frameworks. These frameworks leverage adaptive surrogate models, trained on computational simulation data, to facilitate reliability assessment in the design and evaluation of intricate structural systems under diverse uncertainties. The ensuing sections delve into the conceptualization and application of these frameworks, elucidating their efficacy in managing the intricacies of complex systems. Structural reliability methods [1, 2] are a set of techniques used to assess the probability of failure of complex systems, particularly those related to civil engineering, mechanical engineering, aerospace, and other fields where structural integrity is crucial. These methods are employed to account for uncertainties that arise from various sources, such as design, manufacturing [3], environmental factors, and operating conditions [4]. Addressing uncertainties is crucial in the design process to ensure the reliability of engineering systems and mitigate the risk of unexpected failures that could lead to catastrophic damage or losses. Effective strategies are needed for quantifying and optimizing uncertainties in the design of structures and other engineering systems. Reliability-baseddesign optimization (RBDO) [5; 6] and reliablity-based topology optimization (RBTO) [7; 8] have emerged as comprehensive approaches to achieving optimal designs with a low failure probability, ensuring that the likelihood of violating specified constraints remains below a predefined target level. The integration of diverse reliability analysis methods has been a subject of study in this context, and readers interested in a comprehensive overview can refer to [9] for a state-of-the-art review on RBD/TO and its applications. To estimate reliability, defined as the probability of failure for considered performance or constraint functions, various methods have been developed. Monte Carlo simulation (MCS), a simulation method, involves sampling the joint distribution of state variables to calculate failure probability [10; 11]. Despite their versatile applicability to complex problems, simulation methods like MCS can be computationally expensive due to the need for a large number of samples. The trade-off between precision and computational cost is a key consideration. Strategies such as stratified sampling and Latin hypercube sampling have been employed to enhance efficiency [12]. [PERSON] and [PERSON] [13] introduced an explicit time-domain method-based MCS for assessing the first-passage system dynamic reliability of jacket platforms under specific sea conditions, aiming for computational efficiency. Reliability analysis often employs approximation methods to estimate failure probability by locally approximating the limit-state function around a reference point. While these methods like FORM (first-order reliability method) and SORM (second-order reliability method) offer efficiency with a low number of model evaluations, they may face challenges with complex and nonlinear limit-state functions. [PERSON] et al. [14] introduced an uncertain-polar coordinates SORM capable of handling hybrid variables, demonstrating reduced computational complexity while maintaining precision.