Fatigue damage is a major cause of failure in many industrial mechanical components. In a highly competitive environmental and economic context, structures must meet increasing performance and cost-efficiency requirements while addressing climate-related challenges. Regulatory pressure to reduce carbon emissions encourages lightweight design, but this approach can increase susceptibility to fatigue damage. Structural optimization aims to achieve lightweight and cost-effective designs while maintaining adequate performance. However, structural performance is affected by uncertainties in material properties, loads, and environmental conditions. Reliability-Based Design Optimization (RBDO) offers a suitable framework to address these uncertainties by enforcing target failure probability constraints. Incorporating fatigue constraints into RBDO remains challenging, particularly under random vibrations, due to nonlinear fatigue limit states, geometry-dependent damage zones, and the high computational cost of repeated finite element simulations to obtain stress power spectral densities. Small design changes can also alter natural frequencies and resonance behaviour, significantly affecting reliability. This work proposes an original RBDO framework based on a sequential decoupled strategy combining the SORA (Sequential Optimization and Reliability Assessment) approach with an adaptive Kriging surrogate model and active learning strategy, referred to as AK-SORA (Adaptive Kriging for Sequential Optimization and Reliability Assessment). The surrogate model is iteratively enriched using the U learning function and constraint-boundary sampling (CBS). Multiaxial fatigue damage, estimated using the Dirlik spectral method, is integrated into the RBDO process through a decoupled strategy combined to kriging surrogate model to reduce computational cost. The proposed approach AK-SORA is applied to several structures, including a cantilever beam and more complex example, considering uncertainties in materials, excitation, and design parameters. Results demonstrate the effectiveness and efficiency of the AK-SORA framework for integrating random vibration fatigue constraints into RBDO.